Datasets:

unigram
/

fol-02b

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Split (3)

train · 12.9k rows

premise string	hypothesis string	label string	proof string	premise_tptp string	hypothesis_tptp string	deberta_pred string	deberta_pred_r1_label string	deberta_pred_r2_label string
Brenda is the only person in the room. Someone in the room who is not Brenda does not play a musical instrument. Brenda is not brave or is liked by Judy or both. Judy is richer than Brenda. Brenda is a rich tourist and does not enjoy snowboarding. Someone outside the room does not enjoy snowboarding. Someone outside the room who does not enjoy snowboarding is not Brenda. Brenda neither is not a rich tourist nor is not liked by Miguel. Everyone outside the room who does not enjoy snowboarding does not like Judy. It is not the case that 'Brenda is a brave tourist or does not play a musical instrument or both'.	Brenda plays a musical instrument or is a creative person or both.	entailment	% SZS status Unsatisfiable % SZS output start Proof tff(tptp_fun__mary__type, type, ( tptp_fun__mary_: $i)). tff(tptp_fun_X_3_type, type, ( tptp_fun_X_3: $i)). tff(room_type, type, ( room: $i > $o)). tff(person_type, type, ( person: $i > $o)). tff(mary_type, type, ( mary: $i)). tff(creative_type, type, ( creative: $i > $o)). tff(predb_type, type, ( predb: $i > $o)). tff(tourist_type, type, ( tourist: $i > $o)). tff(brave_type, type, ( brave: $i > $o)). tff(like_type, type, ( like: ( $i * $i ) > $o)). tff(susan_type, type, ( susan: $i)). tff(preda_type, type, ( preda: $i > $o)). tff(fred_type, type, ( fred: $i)). tff(rich_type, type, ( rich: $i > $o)). tff(richer_type, type, ( richer: ( $i * $i ) > $o)). tff(1,plain, (predb(mary) <=> predb(mary)), inference(rewrite,[status(thm)],[])). tff(2,plain, ((~(((room(mary) & ![X: $i] : (room(X) => (X = \|'mary'\|))) & ((((((((?[X: $i] : (room(X) => ((~(X = mary)) => (~predb(X)))) & ((~brave(mary)) \| like(mary, susan))) & richer(mary, susan)) & ((rich(mary) & tourist(mary)) & (~preda(mary)))) & ?[X: $i] : ((~room(X)) => (~preda(X)))) & ?[X: $i] : ((~room(X)) => ((~preda(X)) => (~(X = mary))))) & (~((~(rich(mary) & tourist(mary))) \| (~like(mary, fred))))) & ![X: $i] : ((~room(X)) => ((~preda(X)) => (~like(susan, X))))) & (~((brave(mary) & tourist(mary)) \| (~predb(mary)))))) => ((room(mary) & ![X: $i] : (room(X) => (X = \|'mary'\|))) & (predb(mary) \| (creative(mary) & person(mary)))))) <=> (~((~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ?[X: $i] : ((~predb(X)) \| (X = mary) \| (~room(X))) & ((~brave(mary)) \| like(mary, susan)) & richer(mary, susan) & rich(mary) & tourist(mary) & (~preda(mary)) & ?[X: $i] : (room(X) \| (~preda(X))) & ?[X: $i] : (room(X) \| (~(X = mary)) \| preda(X)) & (~((~(rich(mary) & tourist(mary))) \| (~like(mary, fred)))) & ![X: $i] : (room(X) \| preda(X) \| (~like(susan, X))) & (~((brave(mary) & tourist(mary)) \| (~predb(mary)))))) \| (room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (predb(mary) \| (creative(mary) & person(mary))))))), inference(rewrite,[status(thm)],[])). tff(3,axiom,(~(((room(mary) & ![X: $i] : (room(X) => (X = \|'mary'\|))) & ((((((((?[X: $i] : (room(X) => ((~(X = mary)) => (~predb(X)))) & ((~brave(mary)) \| like(mary, susan))) & richer(mary, susan)) & ((rich(mary) & tourist(mary)) & (~preda(mary)))) & ?[X: $i] : ((~room(X)) => (~preda(X)))) & ?[X: $i] : ((~room(X)) => ((~preda(X)) => (~(X = mary))))) & (~((~(rich(mary) & tourist(mary))) \| (~like(mary, fred))))) & ![X: $i] : ((~room(X)) => ((~preda(X)) => (~like(susan, X))))) & (~((brave(mary) & tourist(mary)) \| (~predb(mary)))))) => ((room(mary) & ![X: $i] : (room(X) => (X = \|'mary'\|))) & (predb(mary) \| (creative(mary) & person(mary)))))), file('/mnt/tmpfs//8529789233806433478775429.p','negated')). tff(4,plain, (~((~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ?[X: $i] : ((~predb(X)) \| (X = mary) \| (~room(X))) & ((~brave(mary)) \| like(mary, susan)) & richer(mary, susan) & rich(mary) & tourist(mary) & (~preda(mary)) & ?[X: $i] : (room(X) \| (~preda(X))) & ?[X: $i] : (room(X) \| (~(X = mary)) \| preda(X)) & (~((~(rich(mary) & tourist(mary))) \| (~like(mary, fred)))) & ![X: $i] : (room(X) \| preda(X) \| (~like(susan, X))) & (~((brave(mary) & tourist(mary)) \| (~predb(mary)))))) \| (room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (predb(mary) \| (creative(mary) & person(mary)))))), inference(modus_ponens,[status(thm)],[3, 2])). tff(5,plain, (room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ?[X: $i] : ((~predb(X)) \| (X = mary) \| (~room(X))) & ((~brave(mary)) \| like(mary, susan)) & richer(mary, susan) & rich(mary) & tourist(mary) & (~preda(mary)) & ?[X: $i] : (room(X) \| (~preda(X))) & ?[X: $i] : (room(X) \| (~(X = mary)) \| preda(X)) & (~((~(rich(mary) & tourist(mary))) \| (~like(mary, fred)))) & ![X: $i] : (room(X) \| preda(X) \| (~like(susan, X))) & (~((brave(mary) & tourist(mary)) \| (~predb(mary))))), inference(or_elim,[status(thm)],[4])). tff(6,plain, (~((brave(mary) & tourist(mary)) \| (~predb(mary)))), inference(and_elim,[status(thm)],[5])). tff(7,plain, (predb(mary)), inference(or_elim,[status(thm)],[6])). tff(8,plain, (predb(mary)), inference(modus_ponens,[status(thm)],[7, 1])). tff(9,plain, ((predb(mary) \| (~((~creative(mary)) \| (~person(mary))))) \| (~predb(mary))), inference(tautology,[status(thm)],[])). tff(10,plain, (predb(mary) \| (~((~creative(mary)) \| (~person(mary))))), inference(unit_resolution,[status(thm)],[9, 8])). tff(11,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(12,plain, (room(mary)), inference(and_elim,[status(thm)],[5])). tff(13,plain, (room(mary)), inference(modus_ponens,[status(thm)],[12, 11])). tff(14,plain, (((~room(mary)) \| (~((~room(X!3)) \| (X!3 = \|'mary'\|))) \| (~(predb(mary) \| (creative(mary) & person(mary))))) <=> ((~room(mary)) \| (~((~room(X!3)) \| (X!3 = \|'mary'\|))) \| (~(predb(mary) \| (~((~creative(mary)) \| (~person(mary)))))))), inference(rewrite,[status(thm)],[])). tff(15,plain, (((~room(mary)) \| (~((~room(X!3)) \| (X!3 = \|'mary'\|))) \| (~(predb(mary) \| (creative(mary) & person(mary))))) <=> ((~room(mary)) \| (~((~room(X!3)) \| (X!3 = \|'mary'\|))) \| (~(predb(mary) \| (creative(mary) & person(mary)))))), inference(rewrite,[status(thm)],[])). tff(16,plain, ((room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (predb(mary) \| (creative(mary) & person(mary)))) <=> (room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (predb(mary) \| (creative(mary) & person(mary))))), inference(rewrite,[status(thm)],[])). tff(17,plain, ((~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (predb(mary) \| (creative(mary) & person(mary))))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (predb(mary) \| (creative(mary) & person(mary)))))), inference(monotonicity,[status(thm)],[16])). tff(18,plain, ((~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (predb(mary) \| (creative(mary) & person(mary))))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (predb(mary) \| (creative(mary) & person(mary)))))), inference(rewrite,[status(thm)],[])). tff(19,plain, (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (predb(mary) \| (creative(mary) & person(mary))))), inference(or_elim,[status(thm)],[4])). tff(20,plain, (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (predb(mary) \| (creative(mary) & person(mary))))), inference(modus_ponens,[status(thm)],[19, 17])). tff(21,plain, (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (predb(mary) \| (creative(mary) & person(mary))))), inference(modus_ponens,[status(thm)],[20, 18])). tff(22,plain, (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (predb(mary) \| (creative(mary) & person(mary))))), inference(modus_ponens,[status(thm)],[21, 17])). unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary))))) (a!2 (forall ((X $i)) (or (not (room X)) (= X \|'mary'\|)))) (a!3 (not (or (not (room X!3)) (= X!3 \|'mary'\|)))) (a!4 (not (or (predb mary) (and (creative mary) (person mary)))))) (let ((a!5 (and (room mary) a!2 (or (predb mary) (and (creative mary) (person mary)))))) (let ((a!6 (~ (not a!5) (or (not (room mary)) a!3 a!4)))) (nnf-neg a!1 (sk (~ (not a!2) a!3)) (refl (~ a!4 a!4)) a!6))))	room(brenda)&(![X]:(room(X)=>(X='brenda')))& ((?[X]:(room(X)=>(((X!=brenda)=>(does_not_play_a_musical_instrument(X))))))& (((~brave(brenda))\|(like(brenda,judy))))& (richer(brenda,judy))& ((rich(brenda)&tourist(brenda))&(does_not_enjoy_snowboarding(brenda)))& (?[X]:(~room(X)=>(does_not_enjoy_snowboarding(X))))& (?[X]:(~room(X)=>(((does_not_enjoy_snowboarding(X))=>(X!=brenda)))))& (~((~(rich(brenda)&tourist(brenda)))\|(~like(brenda,miguel))))& (![X]:(~room(X)=>(((does_not_enjoy_snowboarding(X))=>(~like(judy,X))))))& (~(((brave(brenda)&tourist(brenda))\|(does_not_play_a_musical_instrument(brenda))))))	room(brenda)&(![X]:(room(X)=>(X='brenda')))& (((plays_a_musical_instrument(brenda))\|(creative(brenda)&person(brenda))))	entailment	neutral	entailment
Sheila, Jason, Patrick, Misty are the only persons in the room. Kim is taller than Patrick. Someone outside the room who is a rich happy tourist is not quiet, not rich, not tall, not happy. Sheila who is a sibling of Kim, likes James. Sheila and Misty are respectively brave and rich. James is a sibling of Jason. Jason who is a brave rich person, is not liked by Kim. Everyone outside the room who is not a happy brave tourist is not a happy tall person. Only one person outside the room is not a happy tall brave quiet tourist. Someone who is not rich like someone who likes Kim.	Jason is a sibling of James and is a tall rich person.	entailment	% SZS status Unsatisfiable % SZS output start Proof tff(tptp_fun__fred__type, type, ( tptp_fun__fred_: $i)). tff(tptp_fun_X_4_type, type, ( tptp_fun_X_4: $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__alice__type, type, ( tptp_fun__alice_: $i)). tff(tall_type, type, ( tall: $i > $o)). tff(paul_type, type, ( paul: $i)). tff(tourist_type, type, ( tourist: $i > $o)). tff(tptp_fun_X_1_type, type, ( tptp_fun_X_1: $i)). tff(quiet_type, type, ( quiet: $i > $o)). tff(brave_type, type, ( brave: $i > $o)). tff(happy_type, type, ( happy: $i > $o)). tff(like_type, type, ( like: ( $i * $i ) > $o)). tff(john_type, type, ( john: $i)). tff(rich_type, type, ( rich: $i > $o)). tff(person_type, type, ( person: $i > $o)). tff(sibling_type, type, ( sibling: ( $i * $i ) > $o)). tff(susan_type, type, ( susan: $i)). tff(alice_type, type, ( alice: $i)). tff(mary_type, type, ( mary: $i)). tff(taller_type, type, ( taller: ( $i * $i ) > $o)). tff(fred_type, type, ( fred: $i)). tff(lucy_type, type, ( lucy: $i)). tff(1,assumption,(~tall(paul)), introduced(assumption)). tff(2,plain, (((~tall(paul)) \| (~brave(paul)) \| (~happy(paul)) \| (~tourist(paul)) \| (~quiet(paul))) \| tall(paul)), inference(tautology,[status(thm)],[])). tff(3,plain, ((~tall(paul)) \| (~brave(paul)) \| (~happy(paul)) \| (~tourist(paul)) \| (~quiet(paul))), inference(unit_resolution,[status(thm)],[2, 1])). tff(4,assumption,((~happy(X!1)) \| (~tall(X!1)) \| (~brave(X!1)) \| (~quiet(X!1)) \| (~tourist(X!1))), introduced(assumption)). tff(5,assumption,(paul = X!1), introduced(assumption)). tff(6,plain, (room(paul) <=> room(X!1)), inference(monotonicity,[status(thm)],[5])). tff(7,plain, (room(X!1) <=> room(paul)), inference(symmetry,[status(thm)],[6])). tff(8,plain, ((~room(X!1)) <=> (~room(paul))), inference(monotonicity,[status(thm)],[7])). tff(9,plain, (?[X: $i] : ((~room(X)) & (~(happy(X) & tall(X) & brave(X) & quiet(X) & tourist(X)))) <=> ?[X: $i] : ((~room(X)) & (~(happy(X) & tall(X) & brave(X) & quiet(X) & tourist(X))))), inference(rewrite,[status(thm)],[])). tff(10,plain, ((~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)) \| (X = \|'alice'\|)))) & ((((((((taller(fred, john) & ?[X: $i] : ((~room(X)) => (((rich(X) & happy(X)) & tourist(X)) => ((((~quiet(X)) & (~rich(X))) & (~tall(X))) & (~happy(X)))))) & (sibling(john, mary) & like(susan, mary))) & (brave(mary) & rich(alice))) & sibling(paul, susan)) & (((brave(paul) & rich(paul)) & person(paul)) & (~like(paul, john)))) & ![X: $i] : ((~room(X)) => ((~((happy(X) & brave(X)) & tourist(X))) => (~((happy(X) & tall(X)) & person(X)))))) & (?[X: $i] : ((~room(X)) & (~((((happy(X) & tall(X)) & brave(X)) & quiet(X)) & tourist(X)))) & ![X: $i, Y: $i] : (((~((((happy(X) & tall(X)) & brave(X)) & quiet(X)) & tourist(X))) & (~((((happy(Y) & tall(Y)) & brave(Y)) & quiet(Y)) & tourist(Y)))) => (X = Y)))) & ?[X: $i, Y: $i] : (((~rich(X)) & like(john, Y)) & like(X, Y)))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)) \| (X = \|'alice'\|)))) & (sibling(susan, paul) & ((tall(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))) & taller(fred, john) & ?[X: $i] : (room(X) \| ((~quiet(X)) & (~rich(X)) & (~tall(X)) & (~happy(X))) \| (~(rich(X) & happy(X) & tourist(X)))) & sibling(john, mary) & like(susan, mary) & brave(mary) & rich(alice) & sibling(paul, susan) & brave(paul) & rich(paul) & person(paul) & (~like(paul, john)) & ![X: $i] : (room(X) \| (happy(X) & brave(X) & tourist(X)) \| (~(happy(X) & tall(X) & person(X)))) & ?[X: $i] : ((~room(X)) & (~(happy(X) & tall(X) & brave(X) & quiet(X) & tourist(X)))) & ![X: $i, Y: $i] : ((~((~(happy(X) & tall(X) & brave(X) & quiet(X) & tourist(X))) & (~(happy(Y) & tall(Y) & brave(Y) & quiet(Y) & tourist(Y))))) \| (X = Y)) & ?[X: $i, Y: $i] : ((~rich(X)) & like(john, Y) & like(X, Y)))) \| (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & sibling(susan, paul) & tall(paul) & rich(paul) & person(paul))))), inference(rewrite,[status(thm)],[])). tff(11,axiom,(~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)) \| (X = \|'alice'\|)))) & ((((((((taller(fred, john) & ?[X: $i] : ((~room(X)) => (((rich(X) & happy(X)) & tourist(X)) => ((((~quiet(X)) & (~rich(X))) & (~tall(X))) & (~happy(X)))))) & (sibling(john, mary) & like(susan, mary))) & (brave(mary) & rich(alice))) & sibling(paul, susan)) & (((brave(paul) & rich(paul)) & person(paul)) & (~like(paul, john)))) & ![X: $i] : ((~room(X)) => ((~((happy(X) & brave(X)) & tourist(X))) => (~((happy(X) & tall(X)) & person(X)))))) & (?[X: $i] : ((~room(X)) & (~((((happy(X) & tall(X)) & brave(X)) & quiet(X)) & tourist(X)))) & ![X: $i, Y: $i] : (((~((((happy(X) & tall(X)) & brave(X)) & quiet(X)) & tourist(X))) & (~((((happy(Y) & tall(Y)) & brave(Y)) & quiet(Y)) & tourist(Y)))) => (X = Y)))) & ?[X: $i, Y: $i] : (((~rich(X)) & like(john, Y)) & like(X, Y)))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)) \| (X = \|'alice'\|)))) & (sibling(susan, paul) & ((tall(paul) & rich(paul)) & person(paul)))))), file('/mnt/tmpfs//5485706487440520928877307.p','negated')). tff(12,plain, (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & taller(fred, john) & ?[X: $i] : (room(X) \| ((~quiet(X)) & (~rich(X)) & (~tall(X)) & (~happy(X))) \| (~(rich(X) & happy(X) & tourist(X)))) & sibling(john, mary) & like(susan, mary) & brave(mary) & rich(alice) & sibling(paul, susan) & brave(paul) & rich(paul) & person(paul) & (~like(paul, john)) & ![X: $i] : (room(X) \| (happy(X) & brave(X) & tourist(X)) \| (~(happy(X) & tall(X) & person(X)))) & ?[X: $i] : ((~room(X)) & (~(happy(X) & tall(X) & brave(X) & quiet(X) & tourist(X)))) & ![X: $i, Y: $i] : ((~((~(happy(X) & tall(X) & brave(X) & quiet(X) & tourist(X))) & (~(happy(Y) & tall(Y) & brave(Y) & quiet(Y) & tourist(Y))))) \| (X = Y)) & ?[X: $i, Y: $i] : ((~rich(X)) & like(john, Y) & like(X, Y)))) \| (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & sibling(susan, paul) & tall(paul) & rich(paul) & person(paul)))), inference(modus_ponens,[status(thm)],[11, 10])). tff(13,plain, (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & taller(fred, john) & ?[X: $i] : (room(X) \| ((~quiet(X)) & (~rich(X)) & (~tall(X)) & (~happy(X))) \| (~(rich(X) & happy(X) & tourist(X)))) & sibling(john, mary) & like(susan, mary) & brave(mary) & rich(alice) & sibling(paul, susan) & brave(paul) & rich(paul) & person(paul) & (~like(paul, john)) & ![X: $i] : (room(X) \| (happy(X) & brave(X) & tourist(X)) \| (~(happy(X) & tall(X) & person(X)))) & ?[X: $i] : ((~room(X)) & (~(happy(X) & tall(X) & brave(X) & quiet(X) & tourist(X)))) & ![X: $i, Y: $i] : ((~((~(happy(X) & tall(X) & brave(X) & quiet(X) & tourist(X))) & (~(happy(Y) & tall(Y) & brave(Y) & quiet(Y) & tourist(Y))))) \| (X = Y)) & ?[X: $i, Y: $i] : ((~rich(X)) & like(john, Y) & like(X, Y))), inference(or_elim,[status(thm)],[12])). tff(14,plain, (?[X: $i] : ((~room(X)) & (~(happy(X) & tall(X) & brave(X) & quiet(X) & tourist(X))))), inference(and_elim,[status(thm)],[13])). tff(15,plain, (?[X: $i] : ((~room(X)) & (~(happy(X) & tall(X) & brave(X) & quiet(X) & tourist(X))))), inference(modus_ponens,[status(thm)],[14, 9])). tff(16,plain,( (~room(X!1)) & (~(happy(X!1) & tall(X!1) & brave(X!1) & quiet(X!1) & tourist(X!1)))), inference(skolemize,[status(sab)],[15])). tff(17,plain, (~room(X!1)), inference(and_elim,[status(thm)],[16])). tff(18,plain, (~room(paul)), inference(modus_ponens,[status(thm)],[17, 8])). tff(19,plain, (room(paul) <=> room(paul)), inference(rewrite,[status(thm)],[])). tff(20,plain, (room(paul)), inference(and_elim,[status(thm)],[13])). tff(21,plain, (room(paul)), inference(modus_ponens,[status(thm)],[20, 19])). tff(22,plain, ($false), inference(unit_resolution,[status(thm)],[21, 18])). tff(23,plain,(~(paul = X!1)), inference(lemma,lemma(discharge,[]))). tff(24,plain, (^[X: $i, Y: $i] : refl(((X = Y) \| (~((~tall(X)) \| (~quiet(X)) \| (~happy(X)) \| (~brave(X)) \| (~tourist(X)))) \| (~((~happy(Y)) \| (~tall(Y)) \| (~quiet(Y)) \| (~tourist(Y)) \| (~brave(Y))))) <=> ((X = Y) \| (~((~tall(X)) \| (~quiet(X)) \| (~happy(X)) \| (~brave(X)) \| (~tourist(X)))) \| (~((~happy(Y)) \| (~tall(Y)) \| (~quiet(Y)) \| (~tourist(Y)) \| (~brave(Y))))))), inference(bind,[status(th)],[])). tff(25,plain, (![X: $i, Y: $i] : ((X = Y) \| (~((~tall(X)) \| (~quiet(X)) \| (~happy(X)) \| (~brave(X)) \| (~tourist(X)))) \| (~((~happy(Y)) \| (~tall(Y)) \| (~quiet(Y)) \| (~tourist(Y)) \| (~brave(Y))))) <=> ![X: $i, Y: $i] : ((X = Y) \| (~((~tall(X)) \| (~quiet(X)) \| (~happy(X)) \| (~brave(X)) \| (~tourist(X)))) \| (~((~happy(Y)) \| (~tall(Y)) \| (~quiet(Y)) \| (~tourist(Y)) \| (~brave(Y)))))), inference(quant_intro,[status(thm)],[24])). tff(26,plain, (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((happy(X) & tall(X) & brave(X) & quiet(X) & tourist(X)) <=> (~((~tall(X)) \| (~quiet(X)) \| (~happy(X)) \| (~brave(X)) \| (~tourist(X))))), ((~(happy(X) & tall(X) & brave(X) & quiet(X) & tourist(X))) <=> (~(~((~tall(X)) \| (~quiet(X)) \| (~happy(X)) \| (~brave(X)) \| (~tourist(X))))))), rewrite((~(~((~tall(X)) \| (~quiet(X)) \| (~happy(X)) \| (~brave(X)) \| (~tourist(X))))) <=> ((~tall(X)) \| (~quiet(X)) \| (~happy(X)) \| (~brave(X)) \| (~tourist(X)))), ((~(happy(X) & tall(X) & brave(X) & quiet(X) & tourist(X))) <=> ((~tall(X)) \| (~quiet(X)) \| (~happy(X)) \| (~brave(X)) \| (~tourist(X))))), trans(monotonicity(rewrite((happy(Y) & tall(Y) & brave(Y) & quiet(Y) & tourist(Y)) <=> (~((~happy(Y)) \| (~tall(Y)) \| (~quiet(Y)) \| (~tourist(Y)) \| (~brave(Y))))), ((~(happy(Y) & tall(Y) & brave(Y) & quiet(Y) & tourist(Y))) <=> (~(~((~happy(Y)) \| (~tall(Y)) \| (~quiet(Y)) \| (~tourist(Y)) \| (~brave(Y))))))), rewrite((~(~((~happy(Y)) \| (~tall(Y)) \| (~quiet(Y)) \| (~tourist(Y)) \| (~brave(Y))))) <=> ((~happy(Y)) \| (~tall(Y)) \| (~quiet(Y)) \| (~tourist(Y)) \| (~brave(Y)))), ((~(happy(Y) & tall(Y) & brave(Y) & quiet(Y) & tourist(Y))) <=> ((~happy(Y)) \| (~tall(Y)) \| (~quiet(Y)) \| (~tourist(Y)) \| (~brave(Y))))), (((~(happy(X) & tall(X) & brave(X) & quiet(X) & tourist(X))) & (~(happy(Y) & tall(Y) & brave(Y) & quiet(Y) & tourist(Y)))) <=> (((~tall(X)) \| (~quiet(X)) \| (~happy(X)) \| (~brave(X)) \| (~tourist(X))) & ((~happy(Y)) \| (~tall(Y)) \| (~quiet(Y)) \| (~tourist(Y)) \| (~brave(Y)))))), rewrite((((~tall(X)) \| (~quiet(X)) \| (~happy(X)) \| (~brave(X)) \| (~tourist(X))) & ((~happy(Y)) \| (~tall(Y)) \| (~quiet(Y)) \| (~tourist(Y)) \| (~brave(Y)))) <=> (~((~((~tall(X)) \| (~quiet(X)) \| (~happy(X)) \| (~brave(X)) \| (~tourist(X)))) \| (~((~happy(Y)) \| (~tall(Y)) \| (~quiet(Y)) \| (~tourist(Y)) \| (~brave(Y))))))), (((~(happy(X) & tall(X) & brave(X) & quiet(X) & tourist(X))) & (~(happy(Y) & tall(Y) & brave(Y) & quiet(Y) & tourist(Y)))) <=> (~((~((~tall(X)) \| (~quiet(X)) \| (~happy(X)) \| (~brave(X)) \| (~tourist(X)))) \| (~((~happy(Y)) \| (~tall(Y)) \| (~quiet(Y)) \| (~tourist(Y)) \| (~brave(Y)))))))), ((~((~(happy(X) & tall(X) & brave(X) & quiet(X) & tourist(X))) & (~(happy(Y) & tall(Y) & brave(Y) & quiet(Y) & tourist(Y))))) <=> (~(~((~((~tall(X)) \| (~quiet(X)) \| (~happy(X)) \| (~brave(X)) \| (~tourist(X)))) \| (~((~happy(Y)) \| (~tall(Y)) \| (~quiet(Y)) \| (~tourist(Y)) \| (~brave(Y))))))))), rewrite((~(~((~((~tall(X)) \| (~quiet(X)) \| (~happy(X)) \| (~brave(X)) \| (~tourist(X)))) \| (~((~happy(Y)) \| (~tall(Y)) \| (~quiet(Y)) \| (~tourist(Y)) \| (~brave(Y))))))) <=> ((~((~tall(X)) \| (~quiet(X)) \| (~happy(X)) \| (~brave(X)) \| (~tourist(X)))) \| (~((~happy(Y)) \| (~tall(Y)) \| (~quiet(Y)) \| (~tourist(Y)) \| (~brave(Y)))))), ((~((~(happy(X) & tall(X) & brave(X) & quiet(X) & tourist(X))) & (~(happy(Y) & tall(Y) & brave(Y) & quiet(Y) & tourist(Y))))) <=> ((~((~tall(X)) \| (~quiet(X)) \| (~happy(X)) \| (~brave(X)) \| (~tourist(X)))) \| (~((~happy(Y)) \| (~tall(Y)) \| (~quiet(Y)) \| (~tourist(Y)) \| (~brave(Y))))))), (((~((~(happy(X) & tall(X) & brave(X) & quiet(X) & tourist(X))) & (~(happy(Y) & tall(Y) & brave(Y) & quiet(Y) & tourist(Y))))) \| (X = Y)) <=> (((~((~tall(X)) \| (~quiet(X)) \| (~happy(X)) \| (~brave(X)) \| (~tourist(X)))) \| (~((~happy(Y)) \| (~tall(Y)) \| (~quiet(Y)) \| (~tourist(Y)) \| (~brave(Y))))) \| (X = Y)))), rewrite((((~((~tall(X)) \| (~quiet(X)) \| (~happy(X)) \| (~brave(X)) \| (~tourist(X)))) \| (~((~happy(Y)) \| (~tall(Y)) \| (~quiet(Y)) \| (~tourist(Y)) \| (~brave(Y))))) \| (X = Y)) <=> ((X = Y) \| (~((~tall(X)) \| (~quiet(X)) \| (~happy(X)) \| (~brave(X)) \| (~tourist(X)))) \| (~((~happy(Y)) \| (~tall(Y)) \| (~quiet(Y)) \| (~tourist(Y)) \| (~brave(Y)))))), (((~((~(happy(X) & tall(X) & brave(X) & quiet(X) & tourist(X))) & (~(happy(Y) & tall(Y) & brave(Y) & quiet(Y) & tourist(Y))))) \| (X = Y)) <=> ((X = Y) \| (~((~tall(X)) \| (~quiet(X)) \| (~happy(X)) \| (~brave(X)) \| (~tourist(X)))) \| (~((~happy(Y)) \| (~tall(Y)) \| (~quiet(Y)) \| (~tourist(Y)) \| (~brave(Y)))))))), inference(bind,[status(th)],[])). tff(27,plain, (![X: $i, Y: $i] : ((~((~(happy(X) & tall(X) & brave(X) & quiet(X) & tourist(X))) & (~(happy(Y) & tall(Y) & brave(Y) & quiet(Y) & tourist(Y))))) \| (X = Y)) <=> ![X: $i, Y: $i] : ((X = Y) \| (~((~tall(X)) \| (~quiet(X)) \| (~happy(X)) \| (~brave(X)) \| (~tourist(X)))) \| (~((~happy(Y)) \| (~tall(Y)) \| (~quiet(Y)) \| (~tourist(Y)) \| (~brave(Y)))))), inference(quant_intro,[status(thm)],[26])). tff(28,plain, (![X: $i, Y: $i] : ((~((~(happy(X) & tall(X) & brave(X) & quiet(X) & tourist(X))) & (~(happy(Y) & tall(Y) & brave(Y) & quiet(Y) & tourist(Y))))) \| (X = Y)) <=> ![X: $i, Y: $i] : ((~((~(happy(X) & tall(X) & brave(X) & quiet(X) & tourist(X))) & (~(happy(Y) & tall(Y) & brave(Y) & quiet(Y) & tourist(Y))))) \| (X = Y))), inference(rewrite,[status(thm)],[])). tff(29,plain, (![X: $i, Y: $i] : ((~((~(happy(X) & tall(X) & brave(X) & quiet(X) & tourist(X))) & (~(happy(Y) & tall(Y) & brave(Y) & quiet(Y) & tourist(Y))))) \| (X = Y))), inference(and_elim,[status(thm)],[13])). tff(30,plain, (![X: $i, Y: $i] : ((~((~(happy(X) & tall(X) & brave(X) & quiet(X) & tourist(X))) & (~(happy(Y) & tall(Y) & brave(Y) & quiet(Y) & tourist(Y))))) \| (X = Y))), inference(modus_ponens,[status(thm)],[29, 28])). tff(31,plain,( ![X: $i, Y: $i] : ((~((~(happy(X) & tall(X) & brave(X) & quiet(X) & tourist(X))) & (~(happy(Y) & tall(Y) & brave(Y) & quiet(Y) & tourist(Y))))) \| (X = Y))), inference(skolemize,[status(sab)],[30])). tff(32,plain, (![X: $i, Y: $i] : ((X = Y) \| (~((~tall(X)) \| (~quiet(X)) \| (~happy(X)) \| (~brave(X)) \| (~tourist(X)))) \| (~((~happy(Y)) \| (~tall(Y)) \| (~quiet(Y)) \| (~tourist(Y)) \| (~brave(Y)))))), inference(modus_ponens,[status(thm)],[31, 27])). tff(33,plain, (![X: $i, Y: $i] : ((X = Y) \| (~((~tall(X)) \| (~quiet(X)) \| (~happy(X)) \| (~brave(X)) \| (~tourist(X)))) \| (~((~happy(Y)) \| (~tall(Y)) \| (~quiet(Y)) \| (~tourist(Y)) \| (~brave(Y)))))), inference(modus_ponens,[status(thm)],[32, 25])). tff(34,plain, (((~![X: $i, Y: $i] : ((X = Y) \| (~((~tall(X)) \| (~quiet(X)) \| (~happy(X)) \| (~brave(X)) \| (~tourist(X)))) \| (~((~happy(Y)) \| (~tall(Y)) \| (~quiet(Y)) \| (~tourist(Y)) \| (~brave(Y)))))) \| ((~((~happy(X!1)) \| (~tall(X!1)) \| (~brave(X!1)) \| (~quiet(X!1)) \| (~tourist(X!1)))) \| (paul = X!1) \| (~((~tall(paul)) \| (~brave(paul)) \| (~happy(paul)) \| (~tourist(paul)) \| (~quiet(paul)))))) <=> ((~![X: $i, Y: $i] : ((X = Y) \| (~((~tall(X)) \| (~quiet(X)) \| (~happy(X)) \| (~brave(X)) \| (~tourist(X)))) \| (~((~happy(Y)) \| (~tall(Y)) \| (~quiet(Y)) \| (~tourist(Y)) \| (~brave(Y)))))) \| (~((~happy(X!1)) \| (~tall(X!1)) \| (~brave(X!1)) \| (~quiet(X!1)) \| (~tourist(X!1)))) \| (paul = X!1) \| (~((~tall(paul)) \| (~brave(paul)) \| (~happy(paul)) \| (~tourist(paul)) \| (~quiet(paul)))))), inference(rewrite,[status(thm)],[])). tff(35,plain, (((paul = X!1) \| (~((~tall(paul)) \| (~brave(paul)) \| (~happy(paul)) \| (~tourist(paul)) \| (~quiet(paul)))) \| (~((~happy(X!1)) \| (~tall(X!1)) \| (~brave(X!1)) \| (~quiet(X!1)) \| (~tourist(X!1))))) <=> ((~((~happy(X!1)) \| (~tall(X!1)) \| (~brave(X!1)) \| (~quiet(X!1)) \| (~tourist(X!1)))) \| (paul = X!1) \| (~((~tall(paul)) \| (~brave(paul)) \| (~happy(paul)) \| (~tourist(paul)) \| (~quiet(paul)))))), inference(rewrite,[status(thm)],[])). tff(36,plain, ((~((~happy(X!1)) \| (~tall(X!1)) \| (~quiet(X!1)) \| (~tourist(X!1)) \| (~brave(X!1)))) <=> (~((~happy(X!1)) \| (~tall(X!1)) \| (~brave(X!1)) \| (~quiet(X!1)) \| (~tourist(X!1))))), inference(rewrite,[status(thm)],[])). tff(37,plain, ((~((~tall(paul)) \| (~quiet(paul)) \| (~happy(paul)) \| (~brave(paul)) \| (~tourist(paul)))) <=> (~((~tall(paul)) \| (~brave(paul)) \| (~happy(paul)) \| (~tourist(paul)) \| (~quiet(paul))))), inference(rewrite,[status(thm)],[])). tff(38,plain, (((paul = X!1) \| (~((~tall(paul)) \| (~quiet(paul)) \| (~happy(paul)) \| (~brave(paul)) \| (~tourist(paul)))) \| (~((~happy(X!1)) \| (~tall(X!1)) \| (~quiet(X!1)) \| (~tourist(X!1)) \| (~brave(X!1))))) <=> ((paul = X!1) \| (~((~tall(paul)) \| (~brave(paul)) \| (~happy(paul)) \| (~tourist(paul)) \| (~quiet(paul)))) \| (~((~happy(X!1)) \| (~tall(X!1)) \| (~brave(X!1)) \| (~quiet(X!1)) \| (~tourist(X!1)))))), inference(monotonicity,[status(thm)],[37, 36])). tff(39,plain, (((paul = X!1) \| (~((~tall(paul)) \| (~quiet(paul)) \| (~happy(paul)) \| (~brave(paul)) \| (~tourist(paul)))) \| (~((~happy(X!1)) \| (~tall(X!1)) \| (~quiet(X!1)) \| (~tourist(X!1)) \| (~brave(X!1))))) <=> ((~((~happy(X!1)) \| (~tall(X!1)) \| (~brave(X!1)) \| (~quiet(X!1)) \| (~tourist(X!1)))) \| (paul = X!1) \| (~((~tall(paul)) \| (~brave(paul)) \| (~happy(paul)) \| (~tourist(paul)) \| (~quiet(paul)))))), inference(transitivity,[status(thm)],[38, 35])). tff(40,plain, (((~![X: $i, Y: $i] : ((X = Y) \| (~((~tall(X)) \| (~quiet(X)) \| (~happy(X)) \| (~brave(X)) \| (~tourist(X)))) \| (~((~happy(Y)) \| (~tall(Y)) \| (~quiet(Y)) \| (~tourist(Y)) \| (~brave(Y)))))) \| ((paul = X!1) \| (~((~tall(paul)) \| (~quiet(paul)) \| (~happy(paul)) \| (~brave(paul)) \| (~tourist(paul)))) \| (~((~happy(X!1)) \| (~tall(X!1)) \| (~quiet(X!1)) \| (~tourist(X!1)) \| (~brave(X!1)))))) <=> ((~![X: $i, Y: $i] : ((X = Y) \| (~((~tall(X)) \| (~quiet(X)) \| (~happy(X)) \| (~brave(X)) \| (~tourist(X)))) \| (~((~happy(Y)) \| (~tall(Y)) \| (~quiet(Y)) \| (~tourist(Y)) \| (~brave(Y)))))) \| ((~((~happy(X!1)) \| (~tall(X!1)) \| (~brave(X!1)) \| (~quiet(X!1)) \| (~tourist(X!1)))) \| (paul = X!1) \| (~((~tall(paul)) \| (~brave(paul)) \| (~happy(paul)) \| (~tourist(paul)) \| (~quiet(paul))))))), inference(monotonicity,[status(thm)],[39])). tff(41,plain, (((~![X: $i, Y: $i] : ((X = Y) \| (~((~tall(X)) \| (~quiet(X)) \| (~happy(X)) \| (~brave(X)) \| (~tourist(X)))) \| (~((~happy(Y)) \| (~tall(Y)) \| (~quiet(Y)) \| (~tourist(Y)) \| (~brave(Y)))))) \| ((paul = X!1) \| (~((~tall(paul)) \| (~quiet(paul)) \| (~happy(paul)) \| (~brave(paul)) \| (~tourist(paul)))) \| (~((~happy(X!1)) \| (~tall(X!1)) \| (~quiet(X!1)) \| (~tourist(X!1)) \| (~brave(X!1)))))) <=> ((~![X: $i, Y: $i] : ((X = Y) \| (~((~tall(X)) \| (~quiet(X)) \| (~happy(X)) \| (~brave(X)) \| (~tourist(X)))) \| (~((~happy(Y)) \| (~tall(Y)) \| (~quiet(Y)) \| (~tourist(Y)) \| (~brave(Y)))))) \| (~((~happy(X!1)) \| (~tall(X!1)) \| (~brave(X!1)) \| (~quiet(X!1)) \| (~tourist(X!1)))) \| (paul = X!1) \| (~((~tall(paul)) \| (~brave(paul)) \| (~happy(paul)) \| (~tourist(paul)) \| (~quiet(paul)))))), inference(transitivity,[status(thm)],[40, 34])). tff(42,plain, ((~![X: $i, Y: $i] : ((X = Y) \| (~((~tall(X)) \| (~quiet(X)) \| (~happy(X)) \| (~brave(X)) \| (~tourist(X)))) \| (~((~happy(Y)) \| (~tall(Y)) \| (~quiet(Y)) \| (~tourist(Y)) \| (~brave(Y)))))) \| ((paul = X!1) \| (~((~tall(paul)) \| (~quiet(paul)) \| (~happy(paul)) \| (~brave(paul)) \| (~tourist(paul)))) \| (~((~happy(X!1)) \| (~tall(X!1)) \| (~quiet(X!1)) \| (~tourist(X!1)) \| (~brave(X!1)))))), inference(quant_inst,[status(thm)],[])). tff(43,plain, ((~![X: $i, Y: $i] : ((X = Y) \| (~((~tall(X)) \| (~quiet(X)) \| (~happy(X)) \| (~brave(X)) \| (~tourist(X)))) \| (~((~happy(Y)) \| (~tall(Y)) \| (~quiet(Y)) \| (~tourist(Y)) \| (~brave(Y)))))) \| (~((~happy(X!1)) \| (~tall(X!1)) \| (~brave(X!1)) \| (~quiet(X!1)) \| (~tourist(X!1)))) \| (paul = X!1) \| (~((~tall(paul)) \| (~brave(paul)) \| (~happy(paul)) \| (~tourist(paul)) \| (~quiet(paul))))), inference(modus_ponens,[status(thm)],[42, 41])). tff(44,plain, ($false), inference(unit_resolution,[status(thm)],[43, 33, 23, 4, 3])). tff(45,plain,((~((~happy(X!1)) \| (~tall(X!1)) \| (~brave(X!1)) \| (~quiet(X!1)) \| (~tourist(X!1)))) \| tall(paul)), inference(lemma,lemma(discharge,[]))). tff(46,plain, (~((~happy(X!1)) \| (~tall(X!1)) \| (~brave(X!1)) \| (~quiet(X!1)) \| (~tourist(X!1)))), inference(unit_resolution,[status(thm)],[45, 1])). tff(47,plain, (((~happy(X!1)) \| (~tall(X!1)) \| (~brave(X!1)) \| (~quiet(X!1)) \| (~tourist(X!1))) \| tourist(X!1)), inference(tautology,[status(thm)],[])). tff(48,plain, (tourist(X!1)), inference(unit_resolution,[status(thm)],[47, 46])). tff(49,plain, (((~happy(X!1)) \| (~tall(X!1)) \| (~brave(X!1)) \| (~quiet(X!1)) \| (~tourist(X!1))) \| quiet(X!1)), inference(tautology,[status(thm)],[])). tff(50,plain, (quiet(X!1)), inference(unit_resolution,[status(thm)],[49, 46])). tff(51,assumption,(~happy(X!1)), introduced(assumption)). tff(52,plain, (((~happy(X!1)) \| (~tall(X!1)) \| (~brave(X!1)) \| (~quiet(X!1)) \| (~tourist(X!1))) \| happy(X!1)), inference(tautology,[status(thm)],[])). tff(53,plain, ((~happy(X!1)) \| (~tall(X!1)) \| (~brave(X!1)) \| (~quiet(X!1)) \| (~tourist(X!1))), inference(unit_resolution,[status(thm)],[52, 51])). tff(54,plain, ($false), inference(unit_resolution,[status(thm)],[43, 33, 23, 53, 3])). tff(55,plain,(tall(paul) \| happy(X!1)), inference(lemma,lemma(discharge,[]))). tff(56,plain, (happy(X!1)), inference(unit_resolution,[status(thm)],[55, 1])). tff(57,plain, (((~happy(X!1)) \| (~tall(X!1)) \| (~brave(X!1)) \| (~quiet(X!1)) \| (~tourist(X!1))) \| tall(X!1)), inference(tautology,[status(thm)],[])). tff(58,plain, (tall(X!1)), inference(unit_resolution,[status(thm)],[57, 46])). tff(59,plain, (((~happy(X!1)) \| (~tall(X!1)) \| (~brave(X!1)) \| (~quiet(X!1)) \| (~tourist(X!1))) \| brave(X!1)), inference(tautology,[status(thm)],[])). tff(60,plain, (brave(X!1)), inference(unit_resolution,[status(thm)],[59, 46])). tff(61,plain, ((~(~((~happy(X!1)) \| (~tall(X!1)) \| (~brave(X!1)) \| (~quiet(X!1)) \| (~tourist(X!1))))) <=> ((~happy(X!1)) \| (~tall(X!1)) \| (~brave(X!1)) \| (~quiet(X!1)) \| (~tourist(X!1)))), inference(rewrite,[status(thm)],[])). tff(62,plain, ((happy(X!1) & tall(X!1) & brave(X!1) & quiet(X!1) & tourist(X!1)) <=> (~((~happy(X!1)) \| (~tall(X!1)) \| (~brave(X!1)) \| (~quiet(X!1)) \| (~tourist(X!1))))), inference(rewrite,[status(thm)],[])). tff(63,plain, ((~(happy(X!1) & tall(X!1) & brave(X!1) & quiet(X!1) & tourist(X!1))) <=> (~(~((~happy(X!1)) \| (~tall(X!1)) \| (~brave(X!1)) \| (~quiet(X!1)) \| (~tourist(X!1)))))), inference(monotonicity,[status(thm)],[62])). tff(64,plain, ((~(happy(X!1) & tall(X!1) & brave(X!1) & quiet(X!1) & tourist(X!1))) <=> ((~happy(X!1)) \| (~tall(X!1)) \| (~brave(X!1)) \| (~quiet(X!1)) \| (~tourist(X!1)))), inference(transitivity,[status(thm)],[63, 61])). tff(65,plain, (~(happy(X!1) & tall(X!1) & brave(X!1) & quiet(X!1) & tourist(X!1))), inference(and_elim,[status(thm)],[16])). tff(66,plain, ((~happy(X!1)) \| (~tall(X!1)) \| (~brave(X!1)) \| (~quiet(X!1)) \| (~tourist(X!1))), inference(modus_ponens,[status(thm)],[65, 64])). tff(67,plain, ($false), inference(unit_resolution,[status(thm)],[66, 60, 58, 56, 50, 48])). tff(68,plain,(tall(paul)), inference(lemma,lemma(discharge,[]))). tff(69,plain, ((~(paul = susan)) <=> (~(paul = susan))), inference(rewrite,[status(thm)],[])). tff(70,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//5485706487440520928877307.p','b14')). tff(71,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)],[70])). tff(72,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)],[71])). tff(73,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)],[72])). tff(74,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)],[73])). tff(75,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)],[74])). tff(76,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)],[75])). tff(77,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)],[76])). tff(78,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)],[77])). tff(79,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)],[78])). tff(80,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)],[79])). tff(81,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)],[80])). tff(82,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)],[81])). tff(83,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)],[82])). tff(84,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)],[83])). tff(85,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)],[84])). tff(86,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)],[85])). tff(87,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)],[86])). tff(88,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)],[87])). tff(89,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)],[88])). tff(90,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)],[89])). tff(91,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)],[90])). tff(92,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)],[91])). tff(93,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)],[92])). tff(94,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)],[93])). tff(95,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)],[94])). tff(96,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)],[95])). tff(97,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)],[96])). tff(98,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)],[97])). tff(99,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)],[98])). tff(100,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)],[99])). tff(101,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)],[100])). tff(102,plain, (~(paul = susan)), inference(and_elim,[status(thm)],[101])). tff(103,plain, (~(paul = susan)), inference(modus_ponens,[status(thm)],[102, 69])). tff(104,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(105,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)],[104])). tff(106,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(107,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(108,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)],[107])). tff(109,axiom,(![X: $i, Y: $i] : ((~(X = Y)) => (sibling(X, Y) <=> sibling(Y, X)))), file('/mnt/tmpfs//5485706487440520928877307.p','b4')). tff(110,plain, (![X: $i, Y: $i] : ((X = Y) \| (sibling(X, Y) <=> sibling(Y, X)))), inference(modus_ponens,[status(thm)],[109, 108])). tff(111,plain, (![X: $i, Y: $i] : ((X = Y) \| (sibling(X, Y) <=> sibling(Y, X)))), inference(modus_ponens,[status(thm)],[110, 106])). tff(112,plain,( ![X: $i, Y: $i] : ((X = Y) \| (sibling(X, Y) <=> sibling(Y, X)))), inference(skolemize,[status(sab)],[111])). tff(113,plain, (![X: $i, Y: $i] : ((X = Y) \| (sibling(X, Y) <=> sibling(Y, X)))), inference(modus_ponens,[status(thm)],[112, 105])). tff(114,plain, (((~![X: $i, Y: $i] : ((X = Y) \| (sibling(X, Y) <=> sibling(Y, X)))) \| ((paul = susan) \| (sibling(paul, susan) <=> sibling(susan, paul)))) <=> ((~![X: $i, Y: $i] : ((X = Y) \| (sibling(X, Y) <=> sibling(Y, X)))) \| (paul = susan) \| (sibling(paul, susan) <=> sibling(susan, paul)))), inference(rewrite,[status(thm)],[])). tff(115,plain, ((~![X: $i, Y: $i] : ((X = Y) \| (sibling(X, Y) <=> sibling(Y, X)))) \| ((paul = susan) \| (sibling(paul, susan) <=> sibling(susan, paul)))), inference(quant_inst,[status(thm)],[])). tff(116,plain, ((~![X: $i, Y: $i] : ((X = Y) \| (sibling(X, Y) <=> sibling(Y, X)))) \| (paul = susan) \| (sibling(paul, susan) <=> sibling(susan, paul))), inference(modus_ponens,[status(thm)],[115, 114])). tff(117,plain, (sibling(paul, susan) <=> sibling(susan, paul)), inference(unit_resolution,[status(thm)],[116, 113, 103])). tff(118,plain, (sibling(paul, susan) <=> sibling(paul, susan)), inference(rewrite,[status(thm)],[])). tff(119,plain, (sibling(paul, susan)), inference(and_elim,[status(thm)],[13])). tff(120,plain, (sibling(paul, susan)), inference(modus_ponens,[status(thm)],[119, 118])). tff(121,plain, ((~(sibling(paul, susan) <=> sibling(susan, paul))) \| (~sibling(paul, susan)) \| sibling(susan, paul)), inference(tautology,[status(thm)],[])). tff(122,plain, ((~(sibling(paul, susan) <=> sibling(susan, paul))) \| sibling(susan, paul)), inference(unit_resolution,[status(thm)],[121, 120])). tff(123,plain, (sibling(susan, paul)), inference(unit_resolution,[status(thm)],[122, 117])). tff(124,plain, (person(paul) <=> person(paul)), inference(rewrite,[status(thm)],[])). tff(125,plain, (person(paul)), inference(and_elim,[status(thm)],[13])). tff(126,plain, (person(paul)), inference(modus_ponens,[status(thm)],[125, 124])). tff(127,plain, (rich(paul) <=> rich(paul)), inference(rewrite,[status(thm)],[])). tff(128,plain, (rich(paul)), inference(and_elim,[status(thm)],[13])). tff(129,plain, (rich(paul)), inference(modus_ponens,[status(thm)],[128, 127])). tff(130,plain, (room(alice) <=> room(alice)), inference(rewrite,[status(thm)],[])). tff(131,plain, (room(alice)), inference(and_elim,[status(thm)],[13])). tff(132,plain, (room(alice)), inference(modus_ponens,[status(thm)],[131, 130])). tff(133,plain, (room(fred) <=> room(fred)), inference(rewrite,[status(thm)],[])). tff(134,plain, (room(fred)), inference(and_elim,[status(thm)],[13])). tff(135,plain, (room(fred)), inference(modus_ponens,[status(thm)],[134, 133])). tff(136,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(137,plain, (room(mary)), inference(and_elim,[status(thm)],[13])). tff(138,plain, (room(mary)), inference(modus_ponens,[status(thm)],[137, 136])). tff(139,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~room(alice)) \| (~((X!4 = \|'alice'\|) \| (X!4 = \|'fred'\|) \| (X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|) \| (~room(X!4)))) \| (~sibling(susan, paul)) \| (~tall(paul)) \| (~rich(paul)) \| (~person(paul))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~room(alice)) \| (~((X!4 = \|'alice'\|) \| (X!4 = \|'fred'\|) \| (X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|) \| (~room(X!4)))) \| (~sibling(susan, paul)) \| (~tall(paul)) \| (~rich(paul)) \| (~person(paul)))), inference(rewrite,[status(thm)],[])). tff(140,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(141,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~room(alice)) \| (~((X!4 = \|'alice'\|) \| (X!4 = \|'fred'\|) \| (X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|) \| (~room(X!4)))) \| (~sibling(susan, paul)) \| (~tall(paul)) \| (~rich(paul)) \| (~person(paul))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~room(alice)) \| (~((X!4 = \|'alice'\|) \| (X!4 = \|'fred'\|) \| (X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|) \| (~room(X!4)))) \| (~sibling(susan, paul)) \| (~tall(paul)) \| (~rich(paul)) \| (~person(paul)))), inference(monotonicity,[status(thm)],[140])). tff(142,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~room(alice)) \| (~((X!4 = \|'alice'\|) \| (X!4 = \|'fred'\|) \| (X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|) \| (~room(X!4)))) \| (~sibling(susan, paul)) \| (~tall(paul)) \| (~rich(paul)) \| (~person(paul))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~room(alice)) \| (~((X!4 = \|'alice'\|) \| (X!4 = \|'fred'\|) \| (X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|) \| (~room(X!4)))) \| (~sibling(susan, paul)) \| (~tall(paul)) \| (~rich(paul)) \| (~person(paul)))), inference(transitivity,[status(thm)],[141, 139])). tff(143,plain, ((room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & sibling(susan, paul) & tall(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))) & sibling(susan, paul) & tall(paul) & rich(paul) & person(paul))), inference(rewrite,[status(thm)],[])). tff(144,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & sibling(susan, paul) & tall(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))) & sibling(susan, paul) & tall(paul) & rich(paul) & person(paul)))), inference(monotonicity,[status(thm)],[143])). tff(145,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & sibling(susan, paul) & tall(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))) & sibling(susan, paul) & tall(paul) & rich(paul) & person(paul)))), inference(rewrite,[status(thm)],[])). tff(146,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & sibling(susan, paul) & tall(paul) & rich(paul) & person(paul))), inference(or_elim,[status(thm)],[12])). tff(147,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & sibling(susan, paul) & tall(paul) & rich(paul) & person(paul))), inference(modus_ponens,[status(thm)],[146, 144])). tff(148,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & sibling(susan, paul) & tall(paul) & rich(paul) & person(paul))), inference(modus_ponens,[status(thm)],[147, 145])). tff(149,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & sibling(susan, paul) & tall(paul) & rich(paul) & person(paul))), inference(modus_ponens,[status(thm)],[148, 144])). 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 (refl (~ (not (sibling susan paul)) (not (sibling susan paul))))) (a!8 (refl (~ (not (tall paul)) (not (tall 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 (sibling susan paul) (tall paul) (rich paul) (person paul))) (or (not (room mary)) (not (room paul)) (not (room fred)) (not (room alice)) a!6 (not (sibling susan paul)) (not (tall 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(sheila)&room(jason)&room(patrick)&room(misty)&(![X]:(room(X)=>(X='sheila'\|X='jason'\|X='patrick'\|X='misty')))& ((taller(patrick,kim))& (?[X]:(~room(X)=>(((rich(X)&happy(X)&tourist(X))=>(~quiet(X)&~rich(X)&~tall(X)&~happy(X))))))& ((sibling(kim,sheila))&(like(james,sheila)))& ((brave(sheila))&(rich(misty)))& (sibling(jason,james))& ((brave(jason)&rich(jason)&person(jason))&(~like(jason,kim)))& (![X]:(~room(X)=>(((~(happy(X)&brave(X)&tourist(X)))=>(~(happy(X)&tall(X)&person(X)))))))& (((?[X]:(~room(X)&~(happy(X)&tall(X)&brave(X)&quiet(X)&tourist(X))))&(![X,Y]:((~(happy(X)&tall(X)&brave(X)&quiet(X)&tourist(X))&~(happy(Y)&tall(Y)&brave(Y)&quiet(Y)&tourist(Y)))=>(X=Y)))))& (?[X,Y]:((~rich(X))&(like(kim,Y))&(like(X,Y)))))	room(sheila)&room(jason)&room(patrick)&room(misty)&(![X]:(room(X)=>(X='sheila'\|X='jason'\|X='patrick'\|X='misty')))& ((sibling(james,jason))&(tall(jason)&rich(jason)&person(jason)))	contradiction	contradiction	contradiction
Not all of the following are true:. -Wayne is not a creative person and does not hate Max. -Wayne who enjoys salsa dancing, is richer than Max. -Max is quieter than Josephine.	Wayne who is a rich person, is a rich creative quiet person.	neutral	% SZS status Satisfiable	room(josephine)&room(wayne)&(![X]:(room(X)=>(X='josephine'\|X='wayne')))& (~((~(creative(wayne)&person(wayne)))&(~hate(max,wayne))&(enjoys_salsa_dancing(wayne))&(richer(max,wayne))&quieter(josephine,max)))	room(josephine)&room(wayne)&(![X]:(room(X)=>(X='josephine'\|X='wayne')))& ((rich(wayne)&person(wayne))&(rich(wayne)&creative(wayne)&quiet(wayne)&person(wayne)))	contradiction	contradiction	contradiction
Sharon is the only person in the room. Someone outside the room who is not liked by Arnold is a client of Arnold. Only one person outside the room does not read mystery novels. More than one person outside the room does not hate Arnold. Someone who is not creative like someone who hates Tim. Sharon is the least tall in the room. Sharon is not creative and reads mystery novels. Someone who is not Sharon hate someone who is not liked by Tim. Sharon neither is not liked by Arnold nor does not read mystery novels.	Someone who is not a creative tall person is taller than someone who reads mystery novels.	entailment	% SZS status Unsatisfiable % SZS output start Proof tff(taller_type, type, ( taller: ( $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(predb_type, type, ( predb: $i > $o)). tff(like_type, type, ( like: ( $i * $i ) > $o)). tff(alice_type, type, ( alice: $i)). tff(hate_type, type, ( hate: ( $i * $i ) > $o)). tff(susan_type, type, ( susan: $i)). tff(creative_type, type, ( creative: $i > $o)). tff(client_type, type, ( client: ( $i * $i ) > $o)). tff(person_type, type, ( person: $i > $o)). tff(tall_type, type, ( tall: $i > $o)). tff(tptp_fun_X_8_type, type, ( tptp_fun_X_8: $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] : ((~room(X)) => ((~like(X, alice)) => client(alice, X))) & (?[X: $i] : ((~room(X)) & (~predb(X))) & ![X: $i, Y: $i] : (((~predb(X)) & (~predb(Y))) => (X = Y)))) & ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & ((~hate(alice, X)) & (~hate(alice, Y)))) & (~(X = Y)))) & ?[X: $i, Y: $i] : (((~creative(X)) & hate(susan, Y)) & like(X, Y))) & ![X: $i] : taller(mary, X)) & ((~creative(mary)) & predb(mary))) & ?[X: $i, Y: $i] : (((~(X = mary)) & (~like(Y, susan))) & hate(X, Y))) & (~((~like(mary, alice)) \| (~predb(mary)))))) => ((room(mary) & ![X: $i] : (room(X) => (X = \|'mary'\|))) & ?[X: $i, Y: $i] : (((~((creative(X) & tall(X)) & person(X))) & predb(Y)) & taller(X, Y))))) <=> (~((~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ?[X: $i] : (room(X) \| client(alice, X) \| like(X, alice)) & ?[X: $i] : ((~room(X)) & (~predb(X))) & ![X: $i, Y: $i] : ((~((~predb(X)) & (~predb(Y)))) \| (X = Y)) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~hate(alice, X)) & (~hate(alice, Y)) & (~(X = Y))) & ?[X: $i, Y: $i] : ((~creative(X)) & hate(susan, Y) & like(X, Y)) & ![X: $i] : taller(mary, X) & (~creative(mary)) & predb(mary) & ?[X: $i, Y: $i] : ((~(X = mary)) & (~like(Y, susan)) & hate(X, Y)) & (~((~like(mary, alice)) \| (~predb(mary)))))) \| (room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ?[X: $i, Y: $i] : ((~(creative(X) & tall(X) & person(X))) & predb(Y) & taller(X, Y)))))), inference(rewrite,[status(thm)],[])). tff(5,axiom,(~(((room(mary) & ![X: $i] : (room(X) => (X = \|'mary'\|))) & (((((((?[X: $i] : ((~room(X)) => ((~like(X, alice)) => client(alice, X))) & (?[X: $i] : ((~room(X)) & (~predb(X))) & ![X: $i, Y: $i] : (((~predb(X)) & (~predb(Y))) => (X = Y)))) & ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & ((~hate(alice, X)) & (~hate(alice, Y)))) & (~(X = Y)))) & ?[X: $i, Y: $i] : (((~creative(X)) & hate(susan, Y)) & like(X, Y))) & ![X: $i] : taller(mary, X)) & ((~creative(mary)) & predb(mary))) & ?[X: $i, Y: $i] : (((~(X = mary)) & (~like(Y, susan))) & hate(X, Y))) & (~((~like(mary, alice)) \| (~predb(mary)))))) => ((room(mary) & ![X: $i] : (room(X) => (X = \|'mary'\|))) & ?[X: $i, Y: $i] : (((~((creative(X) & tall(X)) & person(X))) & predb(Y)) & taller(X, Y))))), file('/mnt/tmpfs//4902125563612423596914779.p','negated')). tff(6,plain, (~((~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ?[X: $i] : (room(X) \| client(alice, X) \| like(X, alice)) & ?[X: $i] : ((~room(X)) & (~predb(X))) & ![X: $i, Y: $i] : ((~((~predb(X)) & (~predb(Y)))) \| (X = Y)) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~hate(alice, X)) & (~hate(alice, Y)) & (~(X = Y))) & ?[X: $i, Y: $i] : ((~creative(X)) & hate(susan, Y) & like(X, Y)) & ![X: $i] : taller(mary, X) & (~creative(mary)) & predb(mary) & ?[X: $i, Y: $i] : ((~(X = mary)) & (~like(Y, susan)) & hate(X, Y)) & (~((~like(mary, alice)) \| (~predb(mary)))))) \| (room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ?[X: $i, Y: $i] : ((~(creative(X) & tall(X) & person(X))) & predb(Y) & taller(X, Y))))), inference(modus_ponens,[status(thm)],[5, 4])). tff(7,plain, (room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ?[X: $i] : (room(X) \| client(alice, X) \| like(X, alice)) & ?[X: $i] : ((~room(X)) & (~predb(X))) & ![X: $i, Y: $i] : ((~((~predb(X)) & (~predb(Y)))) \| (X = Y)) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~hate(alice, X)) & (~hate(alice, Y)) & (~(X = Y))) & ?[X: $i, Y: $i] : ((~creative(X)) & hate(susan, Y) & like(X, Y)) & ![X: $i] : taller(mary, X) & (~creative(mary)) & predb(mary) & ?[X: $i, Y: $i] : ((~(X = mary)) & (~like(Y, susan)) & hate(X, Y)) & (~((~like(mary, alice)) \| (~predb(mary))))), 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, (taller(mary, \|'mary'\|) <=> taller(\|'mary'\|, \|'mary'\|)), inference(monotonicity,[status(thm)],[18])). tff(20,plain, (taller(\|'mary'\|, \|'mary'\|) <=> taller(mary, \|'mary'\|)), inference(symmetry,[status(thm)],[19])). tff(21,plain, ((~taller(\|'mary'\|, \|'mary'\|)) <=> (~taller(mary, \|'mary'\|))), inference(monotonicity,[status(thm)],[20])). tff(22,plain, (\|'mary'\| = mary), inference(symmetry,[status(thm)],[18])). tff(23,plain, (predb(\|'mary'\|) <=> predb(mary)), inference(monotonicity,[status(thm)],[22])). tff(24,plain, (predb(mary) <=> predb(\|'mary'\|)), inference(symmetry,[status(thm)],[23])). tff(25,plain, (predb(mary) <=> predb(mary)), inference(rewrite,[status(thm)],[])). tff(26,plain, (predb(mary)), inference(and_elim,[status(thm)],[7])). tff(27,plain, (predb(mary)), inference(modus_ponens,[status(thm)],[26, 25])). tff(28,plain, (predb(\|'mary'\|)), inference(modus_ponens,[status(thm)],[27, 24])). tff(29,plain, (creative(\|'mary'\|) <=> creative(mary)), inference(monotonicity,[status(thm)],[22])). tff(30,plain, (creative(mary) <=> creative(\|'mary'\|)), inference(symmetry,[status(thm)],[29])). tff(31,plain, ((~creative(mary)) <=> (~creative(\|'mary'\|))), inference(monotonicity,[status(thm)],[30])). tff(32,plain, ((~creative(mary)) <=> (~creative(mary))), inference(rewrite,[status(thm)],[])). tff(33,plain, (~creative(mary)), inference(and_elim,[status(thm)],[7])). tff(34,plain, (~creative(mary)), inference(modus_ponens,[status(thm)],[33, 32])). tff(35,plain, (~creative(\|'mary'\|)), inference(modus_ponens,[status(thm)],[34, 31])). tff(36,plain, (((~creative(\|'mary'\|)) \| (~person(\|'mary'\|)) \| (~tall(\|'mary'\|))) \| creative(\|'mary'\|)), inference(tautology,[status(thm)],[])). tff(37,plain, ((~creative(\|'mary'\|)) \| (~person(\|'mary'\|)) \| (~tall(\|'mary'\|))), inference(unit_resolution,[status(thm)],[36, 35])). tff(38,assumption,(~((~room(X!8)) \| (X!8 = \|'mary'\|))), introduced(assumption)). tff(39,plain, (((~room(X!8)) \| (X!8 = \|'mary'\|)) \| (~(X!8 = \|'mary'\|))), inference(tautology,[status(thm)],[])). tff(40,plain, (~(X!8 = \|'mary'\|)), inference(unit_resolution,[status(thm)],[39, 38])). tff(41,plain, (((~room(X!8)) \| (X!8 = \|'mary'\|)) \| room(X!8)), inference(tautology,[status(thm)],[])). tff(42,plain, (room(X!8)), inference(unit_resolution,[status(thm)],[41, 38])). tff(43,plain, (((~![X: $i] : ((~room(X)) \| (X = \|'mary'\|))) \| ((~room(X!8)) \| (X!8 = \|'mary'\|))) <=> ((~![X: $i] : ((~room(X)) \| (X = \|'mary'\|))) \| (~room(X!8)) \| (X!8 = \|'mary'\|))), inference(rewrite,[status(thm)],[])). tff(44,plain, ((~![X: $i] : ((~room(X)) \| (X = \|'mary'\|))) \| ((~room(X!8)) \| (X!8 = \|'mary'\|))), inference(quant_inst,[status(thm)],[])). tff(45,plain, ((~![X: $i] : ((~room(X)) \| (X = \|'mary'\|))) \| (~room(X!8)) \| (X!8 = \|'mary'\|)), inference(modus_ponens,[status(thm)],[44, 43])). tff(46,plain, ($false), inference(unit_resolution,[status(thm)],[45, 11, 42, 40])). tff(47,plain,((~room(X!8)) \| (X!8 = \|'mary'\|)), inference(lemma,lemma(discharge,[]))). tff(48,plain, (((~room(mary)) \| (~((~room(X!8)) \| (X!8 = \|'mary'\|))) \| ![X: $i, Y: $i] : ((~predb(Y)) \| (~taller(X, Y)) \| (~((~creative(X)) \| (~tall(X)) \| (~person(X)))))) <=> ((~room(mary)) \| (~((~room(X!8)) \| (X!8 = \|'mary'\|))) \| ![X: $i, Y: $i] : ((~predb(Y)) \| (~taller(X, Y)) \| (~((~creative(X)) \| (~tall(X)) \| (~person(X))))))), inference(rewrite,[status(thm)],[])). tff(49,plain, (((~room(mary)) \| (~((~room(X!8)) \| (X!8 = \|'mary'\|))) \| ![X: $i, Y: $i] : (~((~(creative(X) & tall(X) & person(X))) & predb(Y) & taller(X, Y)))) <=> ((~room(mary)) \| (~((~room(X!8)) \| (X!8 = \|'mary'\|))) \| ![X: $i, Y: $i] : ((~predb(Y)) \| (~taller(X, Y)) \| (~((~creative(X)) \| (~tall(X)) \| (~person(X))))))), inference(rewrite,[status(thm)],[])). tff(50,plain, (((~room(mary)) \| (~((~room(X!8)) \| (X!8 = \|'mary'\|))) \| ![X: $i, Y: $i] : (~((~(creative(X) & tall(X) & person(X))) & predb(Y) & taller(X, Y)))) <=> ((~room(mary)) \| (~((~room(X!8)) \| (X!8 = \|'mary'\|))) \| ![X: $i, Y: $i] : (~((~(creative(X) & tall(X) & person(X))) & predb(Y) & taller(X, Y))))), inference(rewrite,[status(thm)],[])). tff(51,plain, ((room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ?[X: $i, Y: $i] : ((~(creative(X) & tall(X) & person(X))) & predb(Y) & taller(X, Y))) <=> (room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ?[X: $i, Y: $i] : ((~(creative(X) & tall(X) & person(X))) & predb(Y) & taller(X, Y)))), inference(rewrite,[status(thm)],[])). tff(52,plain, ((~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ?[X: $i, Y: $i] : ((~(creative(X) & tall(X) & person(X))) & predb(Y) & taller(X, Y)))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ?[X: $i, Y: $i] : ((~(creative(X) & tall(X) & person(X))) & predb(Y) & taller(X, Y))))), inference(monotonicity,[status(thm)],[51])). tff(53,plain, ((~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ?[X: $i, Y: $i] : ((~(creative(X) & tall(X) & person(X))) & predb(Y) & taller(X, Y)))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ?[X: $i, Y: $i] : ((~(creative(X) & tall(X) & person(X))) & predb(Y) & taller(X, Y))))), inference(rewrite,[status(thm)],[])). tff(54,plain, (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ?[X: $i, Y: $i] : ((~(creative(X) & tall(X) & person(X))) & predb(Y) & taller(X, Y)))), inference(or_elim,[status(thm)],[6])). tff(55,plain, (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ?[X: $i, Y: $i] : ((~(creative(X) & tall(X) & person(X))) & predb(Y) & taller(X, Y)))), inference(modus_ponens,[status(thm)],[54, 52])). tff(56,plain, (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ?[X: $i, Y: $i] : ((~(creative(X) & tall(X) & person(X))) & predb(Y) & taller(X, Y)))), inference(modus_ponens,[status(thm)],[55, 53])). tff(57,plain, (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ?[X: $i, Y: $i] : ((~(creative(X) & tall(X) & person(X))) & predb(Y) & taller(X, Y)))), inference(modus_ponens,[status(thm)],[56, 52])). unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary))))) (a!2 (forall ((X $i)) (or (not (room X)) (= X \|'mary'\|)))) (a!3 (not (or (not (room X!8)) (= X!8 \|'mary'\|)))) (a!4 (lambda ((X $i) (Y $i)) (let ((a!1 (and (not (and (creative X) (tall X) (person X))) (predb Y) (taller X Y)))) (refl (~ (not a!1) (not a!1)))))) (a!5 (exists ((X $i) (Y $i)) (and (not (and (creative X) (tall X) (person X))) (predb Y) (taller X Y)))) (a!6 (forall ((X $i) (Y $i)) (let ((a!1 (and (not (and (creative X) (tall X) (person X))) (predb Y) (taller X Y)))) (not a!1))))) (let ((a!7 (~ (not (and (room mary) a!2 a!5)) (or (not (room mary)) a!3 a!6)))) (nnf-neg a!1 (sk (~ (not a!2) a!3)) (nnf-neg (proof-bind a!4) (~ (not a!5) a!6)) a!7)))	room(sharon)&(![X]:(room(X)=>(X='sharon')))& ((?[X]:(~room(X)=>(((~like(X,arnold))=>(client(arnold,X))))))& (((?[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)))))& ((?[X,Y]:(~room(X)&~room(Y)&(~hate(arnold,X)&~hate(arnold,Y))&(X!=Y))))& (?[X,Y]:((~creative(X))&(hate(tim,Y))&(like(X,Y))))& (![X]:(taller(sharon,X)))& ((~creative(sharon))&(reads_mystery_novels(sharon)))& (?[X,Y]:((X!=sharon)&(~like(Y,tim))&(hate(X,Y))))& (~((~like(sharon,arnold))\|(does_not_read_mystery_novels(sharon)))))	room(sharon)&(![X]:(room(X)=>(X='sharon')))& (?[X,Y]:((~(creative(X)&tall(X)&person(X)))&(reads_mystery_novels(Y))&(taller(X,Y))))	contradiction	contradiction	contradiction
Lester is the only person in the room. Someone who is taller than Lee is taller than someone who does not practice urban gardening if Margret and Lester like each other. Lester is liked by Carrie. Someone who is not Lester like someone who is taller than Lee.	Lester neither does not practice urban gardening nor is liked by Carrie.	contradiction	-	room(lester)&(![X]:(room(X)=>(X='lester')))& ((((like(margret,lester) & like(lester,margret)))=>(?[X,Y]:((taller(lee,X))&(does_not_practice_urban_gardening(Y))&(taller(X,Y)))))& (like(lester,carrie))& (?[X,Y]:((X!=lester)&(taller(lee,Y))&(like(X,Y)))))	room(lester)&(![X]:(room(X)=>(X='lester')))& (~((does_not_practice_urban_gardening(lester))\|(like(lester,carrie))))	contradiction	neutral	contradiction
Sandra is the only person in the room. Sandra neither likes Dale nor does not enjoy photography. Sandra is not liked by Dale or is a happy tall person or both. Sandra is liked by Thomas or is taller than Jo or both. Sandra is liked by Dale. Sandra is the tallest in the room. More than one person outside the room is taller than Dale. Jo and Sandra like each other.	Sandra is taller than Dale or does not play a string instrument or both.	entailment	% SZS status Unsatisfiable % SZS output start Proof tff(tptp_fun__mary__type, type, ( tptp_fun__mary_: $i)). tff(tptp_fun_X_2_type, type, ( tptp_fun_X_2: $i)). tff(room_type, type, ( room: $i > $o)). tff(predc_type, type, ( predc: $i > $o)). tff(mary_type, type, ( mary: $i)). tff(taller_type, type, ( taller: ( $i * $i ) > $o)). tff(paul_type, type, ( paul: $i)). tff(like_type, type, ( like: ( $i * $i ) > $o)). tff(alice_type, type, ( alice: $i)). tff(fred_type, type, ( fred: $i)). tff(person_type, type, ( person: $i > $o)). tff(tall_type, type, ( tall: $i > $o)). tff(happy_type, type, ( happy: $i > $o)). tff(predb_type, type, ( predb: $i > $o)). tff(1,assumption,(~taller(paul, mary)), introduced(assumption)). tff(2,plain, (^[X: $i] : refl(taller(X, mary) <=> taller(X, mary))), inference(bind,[status(th)],[])). tff(3,plain, (![X: $i] : taller(X, mary) <=> ![X: $i] : taller(X, mary)), inference(quant_intro,[status(thm)],[2])). tff(4,plain, (![X: $i] : taller(X, mary) <=> ![X: $i] : taller(X, mary)), inference(rewrite,[status(thm)],[])). tff(5,plain, ((~(((room(mary) & ![X: $i] : (room(X) => (X = \|'mary'\|))) & (((((((~(like(paul, mary) \| (~predb(mary)))) & ((~like(mary, paul)) \| ((happy(mary) & tall(mary)) & person(mary)))) & (like(mary, fred) \| taller(alice, mary))) & like(mary, paul)) & ![X: $i] : taller(X, mary)) & ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & (taller(paul, X) & taller(paul, Y))) & (~(X = Y)))) & (like(alice, mary) & like(mary, alice)))) => ((room(mary) & ![X: $i] : (room(X) => (X = \|'mary'\|))) & (taller(paul, mary) \| (~predc(mary)))))) <=> (~((~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~(like(paul, mary) \| (~predb(mary)))) & ((~like(mary, paul)) \| (happy(mary) & tall(mary) & person(mary))) & (like(mary, fred) \| taller(alice, mary)) & like(mary, paul) & ![X: $i] : taller(X, mary) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & taller(paul, X) & taller(paul, Y) & (~(X = Y))) & like(alice, mary) & like(mary, alice))) \| (room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (taller(paul, mary) \| (~predc(mary))))))), inference(rewrite,[status(thm)],[])). tff(6,axiom,(~(((room(mary) & ![X: $i] : (room(X) => (X = \|'mary'\|))) & (((((((~(like(paul, mary) \| (~predb(mary)))) & ((~like(mary, paul)) \| ((happy(mary) & tall(mary)) & person(mary)))) & (like(mary, fred) \| taller(alice, mary))) & like(mary, paul)) & ![X: $i] : taller(X, mary)) & ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & (taller(paul, X) & taller(paul, Y))) & (~(X = Y)))) & (like(alice, mary) & like(mary, alice)))) => ((room(mary) & ![X: $i] : (room(X) => (X = \|'mary'\|))) & (taller(paul, mary) \| (~predc(mary)))))), file('/mnt/tmpfs//4091414189681181313677084.p','negated')). tff(7,plain, (~((~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~(like(paul, mary) \| (~predb(mary)))) & ((~like(mary, paul)) \| (happy(mary) & tall(mary) & person(mary))) & (like(mary, fred) \| taller(alice, mary)) & like(mary, paul) & ![X: $i] : taller(X, mary) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & taller(paul, X) & taller(paul, Y) & (~(X = Y))) & like(alice, mary) & like(mary, alice))) \| (room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (taller(paul, mary) \| (~predc(mary)))))), inference(modus_ponens,[status(thm)],[6, 5])). tff(8,plain, (room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~(like(paul, mary) \| (~predb(mary)))) & ((~like(mary, paul)) \| (happy(mary) & tall(mary) & person(mary))) & (like(mary, fred) \| taller(alice, mary)) & like(mary, paul) & ![X: $i] : taller(X, mary) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & taller(paul, X) & taller(paul, Y) & (~(X = Y))) & like(alice, mary) & like(mary, alice)), inference(or_elim,[status(thm)],[7])). tff(9,plain, (![X: $i] : taller(X, mary)), inference(and_elim,[status(thm)],[8])). tff(10,plain, (![X: $i] : taller(X, mary)), inference(modus_ponens,[status(thm)],[9, 4])). tff(11,plain,( ![X: $i] : taller(X, mary)), inference(skolemize,[status(sab)],[10])). tff(12,plain, (![X: $i] : taller(X, mary)), inference(modus_ponens,[status(thm)],[11, 3])). tff(13,plain, ((~![X: $i] : taller(X, mary)) \| taller(paul, mary)), inference(quant_inst,[status(thm)],[])). tff(14,plain, ($false), inference(unit_resolution,[status(thm)],[13, 12, 1])). tff(15,plain,(taller(paul, mary)), inference(lemma,lemma(discharge,[]))). tff(16,plain, ((taller(paul, mary) \| (~predc(mary))) \| (~taller(paul, mary))), inference(tautology,[status(thm)],[])). tff(17,plain, (taller(paul, mary) \| (~predc(mary))), inference(unit_resolution,[status(thm)],[16, 15])). tff(18,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(19,plain, (room(mary)), inference(and_elim,[status(thm)],[8])). tff(20,plain, (room(mary)), inference(modus_ponens,[status(thm)],[19, 18])). tff(21,plain, ((taller(paul, mary) \| (~predc(mary))) <=> (taller(paul, mary) \| (~predc(mary)))), inference(rewrite,[status(thm)],[])). tff(22,plain, ((~(taller(paul, mary) \| (~predc(mary)))) <=> (~(taller(paul, mary) \| (~predc(mary))))), inference(monotonicity,[status(thm)],[21])). tff(23,plain, (((~room(mary)) \| (~((~room(X!2)) \| (X!2 = \|'mary'\|))) \| (~(taller(paul, mary) \| (~predc(mary))))) <=> ((~room(mary)) \| (~((~room(X!2)) \| (X!2 = \|'mary'\|))) \| (~(taller(paul, mary) \| (~predc(mary)))))), inference(monotonicity,[status(thm)],[22])). tff(24,plain, ((room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (taller(paul, mary) \| (~predc(mary)))) <=> (room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (taller(paul, mary) \| (~predc(mary))))), inference(rewrite,[status(thm)],[])). tff(25,plain, ((~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (taller(paul, mary) \| (~predc(mary))))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (taller(paul, mary) \| (~predc(mary)))))), inference(monotonicity,[status(thm)],[24])). tff(26,plain, ((~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (taller(paul, mary) \| (~predc(mary))))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (taller(paul, mary) \| (~predc(mary)))))), inference(rewrite,[status(thm)],[])). tff(27,plain, (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (taller(paul, mary) \| (~predc(mary))))), inference(or_elim,[status(thm)],[7])). tff(28,plain, (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (taller(paul, mary) \| (~predc(mary))))), inference(modus_ponens,[status(thm)],[27, 25])). tff(29,plain, (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (taller(paul, mary) \| (~predc(mary))))), inference(modus_ponens,[status(thm)],[28, 26])). tff(30,plain, (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (taller(paul, mary) \| (~predc(mary))))), inference(modus_ponens,[status(thm)],[29, 25])). unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary))))) (a!2 (forall ((X $i)) (or (not (room X)) (= X \|'mary'\|)))) (a!3 (not (or (not (room X!2)) (= X!2 \|'mary'\|)))) (a!4 (not (or (taller paul mary) (not (predc mary)))))) (let ((a!5 (and (room mary) a!2 (or (taller paul mary) (not (predc mary)))))) (let ((a!6 (~ (not a!5) (or (not (room mary)) a!3 a!4)))) (nnf-neg a!1 (sk (~ (not a!2) a!3)) (refl (~ a!4 a!4)) a!6))))	room(sandra)&(![X]:(room(X)=>(X='sandra')))& ((~((like(dale,sandra))\|(does_not_enjoy_photography(sandra))))& (((~like(sandra,dale))\|(happy(sandra)&tall(sandra)&person(sandra))))& (((like(sandra,thomas))\|(taller(jo,sandra))))& (like(sandra,dale))& (![X]:(taller(X,sandra)))& ((?[X,Y]:(~room(X)&~room(Y)&(taller(dale,X)&taller(dale,Y))&(X!=Y))))& ((like(jo,sandra) & like(sandra,jo))))	room(sandra)&(![X]:(room(X)=>(X='sandra')))& (((taller(dale,sandra))\|(does_not_play_a_string_instrument(sandra))))	contradiction	neutral	entailment
Wayne is quieter than Larry.	Wayne is quieter than Larry or enjoys ceramics 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(predc_type, type, ( predc: $i > $o)). tff(mary_type, type, ( mary: $i)). tff(quieter_type, type, ( quieter: ( $i * $i ) > $o)). tff(john_type, type, ( john: $i)). tff(1,plain, (quieter(john, mary) <=> quieter(john, mary)), inference(rewrite,[status(thm)],[])). tff(2,plain, ((~(((room(mary) & ![X: $i] : (room(X) => (X = \|'mary'\|))) & quieter(john, mary)) => ((room(mary) & ![X: $i] : (room(X) => (X = \|'mary'\|))) & (quieter(john, mary) \| predc(mary))))) <=> (~((~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & quieter(john, mary))) \| (room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (quieter(john, mary) \| predc(mary)))))), inference(rewrite,[status(thm)],[])). tff(3,axiom,(~(((room(mary) & ![X: $i] : (room(X) => (X = \|'mary'\|))) & quieter(john, mary)) => ((room(mary) & ![X: $i] : (room(X) => (X = \|'mary'\|))) & (quieter(john, mary) \| predc(mary))))), file('/mnt/tmpfs//7534015551737703702966724.p','negated')). tff(4,plain, (~((~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & quieter(john, mary))) \| (room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (quieter(john, mary) \| predc(mary))))), inference(modus_ponens,[status(thm)],[3, 2])). tff(5,plain, (room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & quieter(john, mary)), inference(or_elim,[status(thm)],[4])). tff(6,plain, (quieter(john, mary)), inference(and_elim,[status(thm)],[5])). tff(7,plain, (quieter(john, mary)), inference(modus_ponens,[status(thm)],[6, 1])). tff(8,plain, ((quieter(john, mary) \| predc(mary)) \| (~quieter(john, mary))), inference(tautology,[status(thm)],[])). tff(9,plain, (quieter(john, mary) \| predc(mary)), inference(unit_resolution,[status(thm)],[8, 7])). tff(10,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(11,plain, (room(mary)), inference(and_elim,[status(thm)],[5])). tff(12,plain, (room(mary)), inference(modus_ponens,[status(thm)],[11, 10])). tff(13,plain, (((~room(mary)) \| (~((~room(X!0)) \| (X!0 = \|'mary'\|))) \| (~(quieter(john, mary) \| predc(mary)))) <=> ((~room(mary)) \| (~((~room(X!0)) \| (X!0 = \|'mary'\|))) \| (~(quieter(john, mary) \| predc(mary))))), inference(rewrite,[status(thm)],[])). tff(14,plain, ((quieter(john, mary) \| predc(mary)) <=> (quieter(john, mary) \| predc(mary))), inference(rewrite,[status(thm)],[])). tff(15,plain, ((~(quieter(john, mary) \| predc(mary))) <=> (~(quieter(john, mary) \| predc(mary)))), inference(monotonicity,[status(thm)],[14])). tff(16,plain, (((~room(mary)) \| (~((~room(X!0)) \| (X!0 = \|'mary'\|))) \| (~(quieter(john, mary) \| predc(mary)))) <=> ((~room(mary)) \| (~((~room(X!0)) \| (X!0 = \|'mary'\|))) \| (~(quieter(john, mary) \| predc(mary))))), inference(monotonicity,[status(thm)],[15])). tff(17,plain, (((~room(mary)) \| (~((~room(X!0)) \| (X!0 = \|'mary'\|))) \| (~(quieter(john, mary) \| predc(mary)))) <=> ((~room(mary)) \| (~((~room(X!0)) \| (X!0 = \|'mary'\|))) \| (~(quieter(john, mary) \| predc(mary))))), inference(transitivity,[status(thm)],[16, 13])). tff(18,plain, ((room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (quieter(john, mary) \| predc(mary))) <=> (room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (quieter(john, mary) \| predc(mary)))), inference(rewrite,[status(thm)],[])). tff(19,plain, ((~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (quieter(john, mary) \| predc(mary)))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (quieter(john, mary) \| predc(mary))))), inference(monotonicity,[status(thm)],[18])). tff(20,plain, ((~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (quieter(john, mary) \| predc(mary)))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (quieter(john, mary) \| predc(mary))))), inference(rewrite,[status(thm)],[])). tff(21,plain, (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (quieter(john, mary) \| predc(mary)))), inference(or_elim,[status(thm)],[4])). tff(22,plain, (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (quieter(john, mary) \| predc(mary)))), inference(modus_ponens,[status(thm)],[21, 19])). tff(23,plain, (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (quieter(john, mary) \| predc(mary)))), inference(modus_ponens,[status(thm)],[22, 20])). tff(24,plain, (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (quieter(john, mary) \| predc(mary)))), inference(modus_ponens,[status(thm)],[23, 19])). 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 (~ (not (or (quieter john mary) (predc mary))) (not (or (quieter john mary) (predc mary)))))) (let ((a!5 (not (and (room mary) a!2 (or (quieter john mary) (predc mary))))) (a!6 (or (not (room mary)) a!3 (not (or (quieter john mary) (predc mary)))))) (nnf-neg a!1 (sk (~ (not a!2) a!3)) (refl a!4) (~ a!5 a!6))))	room(wayne)&(![X]:(room(X)=>(X='wayne')))& (quieter(larry,wayne))	room(wayne)&(![X]:(room(X)=>(X='wayne')))& (((quieter(larry,wayne))\|(enjoys_ceramics(wayne))))	neutral	neutral	entailment
Jessie neither is not a tall rich brave tourist nor does not like Karen. Michael who is not brave, not tall, not rich, is hated by Carrie.	Michael neither is a rich quiet brave happy tourist nor is hated by Carrie.	contradiction	-	room(michael)&room(carrie)&room(jessie)&(![X]:(room(X)=>(X='michael'\|X='carrie'\|X='jessie')))& ((~((~(tall(jessie)&rich(jessie)&brave(jessie)&tourist(jessie)))\|(~like(karen,jessie))))& ((~brave(michael)&~tall(michael)&~rich(michael))&(hate(michael,carrie))))	room(michael)&room(carrie)&room(jessie)&(![X]:(room(X)=>(X='michael'\|X='carrie'\|X='jessie')))& (~((rich(michael)&quiet(michael)&brave(michael)&happy(michael)&tourist(michael))\|(hate(michael,carrie))))	contradiction	entailment	contradiction
Daniel is the only person in the room. “Daniel is the quietest in the room” only if “it is not the case that 'Daniel is the least tall in the room'”. Someone who is a happy quiet tourist hate someone who is not a tall european. Timothy and Daniel hate each other. Only one person outside the room is a happy tourist. Daniel is a tall european and is a happy european.	Daniel neither is not a happy quiet tourist nor is a brave happy tall quiet tourist.	contradiction	-	room(daniel)&(![X]:(room(X)=>(X='daniel')))& (((![X]:(quieter(X,daniel)))=>(~(![X]:(taller(daniel,X)))))& (?[X,Y]:((happy(X)&quiet(X)&tourist(X))&(~(tall(Y)&european(Y)))&(hate(X,Y))))& ((hate(timothy,daniel) & hate(daniel,timothy)))& (((?[X]:(~room(X)&happy(X)&tourist(X)))&(![X,Y]:((happy(X)&tourist(X)&happy(Y)&tourist(Y))=>(X=Y)))))& ((tall(daniel)&european(daniel))&(happy(daniel)&european(daniel))))	room(daniel)&(![X]:(room(X)=>(X='daniel')))& (~((~(happy(daniel)&quiet(daniel)&tourist(daniel)))\|(brave(daniel)&happy(daniel)&tall(daniel)&quiet(daniel)&tourist(daniel))))	neutral	entailment	contradiction
Not all of the following are true:. -Toni and Mary like each other. -Zelma is richer than Mary. -It is not the case that 'Zelma who is richer than Mary, is not liked by Mary'.	It is not the case that 'Doreen who likes Mary, does not like Mary'.	entailment	% SZS status Unsatisfiable % SZS output start Proof tff(room_type, type, ( room: $i > $o)). tff(tptp_fun_X_0_type, type, ( tptp_fun_X_0: $i)). tff(tptp_fun__mary__type, type, ( tptp_fun__mary_: $i)). tff(tptp_fun__paul__type, type, ( tptp_fun__paul_: $i)). tff(tptp_fun__fred__type, type, ( tptp_fun__fred_: $i)). tff(fred_type, type, ( fred: $i)). tff(like_type, type, ( like: ( $i * $i ) > $o)). tff(john_type, type, ( john: $i)). tff(richer_type, type, ( richer: ( $i * $i ) > $o)). tff(paul_type, type, ( paul: $i)). tff(mary_type, type, ( mary: $i)). tff(1,plain, (room(fred) <=> room(fred)), inference(rewrite,[status(thm)],[])). tff(2,plain, ((~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)))) & (~(((like(paul, john) & like(john, paul)) & richer(john, fred)) & (~(richer(john, fred) & (~like(fred, john))))))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)))) & (~(like(john, mary) & (~like(john, mary))))))) <=> (~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~(like(paul, john) & like(john, paul) & richer(john, fred) & (~(richer(john, fred) & (~like(fred, john)))))))) \| (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))))))), inference(rewrite,[status(thm)],[])). tff(3,axiom,(~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)))) & (~(((like(paul, john) & like(john, paul)) & richer(john, fred)) & (~(richer(john, fred) & (~like(fred, john))))))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)))) & (~(like(john, mary) & (~like(john, mary))))))), file('/mnt/tmpfs//2553996457294349470240690.p','negated')). tff(4,plain, (~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~(like(paul, john) & like(john, paul) & richer(john, fred) & (~(richer(john, fred) & (~like(fred, john)))))))) \| (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))))), inference(modus_ponens,[status(thm)],[3, 2])). tff(5,plain, (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~(like(paul, john) & like(john, paul) & richer(john, fred) & (~(richer(john, fred) & (~like(fred, john))))))), inference(or_elim,[status(thm)],[4])). tff(6,plain, (room(fred)), inference(and_elim,[status(thm)],[5])). tff(7,plain, (room(fred)), inference(modus_ponens,[status(thm)],[6, 1])). tff(8,plain, (room(paul) <=> room(paul)), inference(rewrite,[status(thm)],[])). tff(9,plain, (room(paul)), inference(and_elim,[status(thm)],[5])). tff(10,plain, (room(paul)), inference(modus_ponens,[status(thm)],[9, 8])). tff(11,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(12,plain, (room(mary)), inference(and_elim,[status(thm)],[5])). tff(13,plain, (room(mary)), inference(modus_ponens,[status(thm)],[12, 11])). tff(14,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!0 = \|'fred'\|) \| (X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0))))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!0 = \|'fred'\|) \| (X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0)))))), inference(rewrite,[status(thm)],[])). tff(15,plain, ((~((X!0 = \|'fred'\|) \| (X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0)))) <=> (~((X!0 = \|'fred'\|) \| (X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0))))), inference(rewrite,[status(thm)],[])). tff(16,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!0 = \|'fred'\|) \| (X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0))))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!0 = \|'fred'\|) \| (X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0)))))), inference(monotonicity,[status(thm)],[15])). tff(17,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!0 = \|'fred'\|) \| (X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0))))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!0 = \|'fred'\|) \| (X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0)))))), inference(transitivity,[status(thm)],[16, 14])). tff(18,plain, ((room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) <=> (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))))), inference(rewrite,[status(thm)],[])). tff(19,plain, ((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))))), inference(monotonicity,[status(thm)],[18])). tff(20,plain, ((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))))), inference(rewrite,[status(thm)],[])). tff(21,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))))), inference(or_elim,[status(thm)],[4])). tff(22,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))))), inference(modus_ponens,[status(thm)],[21, 19])). tff(23,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))))), inference(modus_ponens,[status(thm)],[22, 20])). tff(24,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))))), inference(modus_ponens,[status(thm)],[23, 19])). unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary))))) (a!2 (refl (~ (not (room paul)) (not (room paul))))) (a!3 (refl (~ (not (room fred)) (not (room fred))))) (a!4 (forall ((X $i)) (or (= X \|'fred'\|) (= X \|'paul'\|) (= X \|'mary'\|) (not (room X))))) (a!5 (not (or (= X!0 \|'fred'\|) (= X!0 \|'paul'\|) (= X!0 \|'mary'\|) (not (room X!0)))))) (let ((a!6 (~ (not (and (room mary) (room paul) (room fred) a!4)) (or (not (room mary)) (not (room paul)) (not (room fred)) a!5)))) (nnf-neg a!1 a!2 a!3 (sk (~ (not a!4) a!5)) a!6)))	room(doreen)&room(toni)&room(zelma)&(![X]:(room(X)=>(X='doreen'\|X='toni'\|X='zelma')))& (~((like(toni,mary) & like(mary,toni))&richer(mary,zelma)&~((richer(mary,zelma))&(~like(zelma,mary)))))	room(doreen)&room(toni)&room(zelma)&(![X]:(room(X)=>(X='doreen'\|X='toni'\|X='zelma')))& (~((like(mary,doreen))&(~like(mary,doreen))))	neutral	neutral	neutral
Aline, Thomas, Penny, Ramona are the only persons in the room. Thomas who likes Bessie, does not have lived in exactly three countries. Bessie is taller than Aline. More than one person outside the room has lived in exactly three countries. Only one person outside the room is not liked by Bessie. Someone who does not like Bessie is taller than someone who does not have lived in exactly three countries. Thomas is the tallest in the room.	Penny is taller than Bessie and does not like Bessie.	neutral	% SZS status Satisfiable	room(aline)&room(thomas)&room(penny)&room(ramona)&(![X]:(room(X)=>(X='aline'\|X='thomas'\|X='penny'\|X='ramona')))& (((like(bessie,thomas))&(does_not_have_lived_in_exactly_three_countries(thomas)))& (taller(aline,bessie))& ((?[X,Y]:(~room(X)&~room(Y)&(has_lived_in_exactly_three_countries(X)&has_lived_in_exactly_three_countries(Y))&(X!=Y))))& (((?[X]:(~room(X)&~like(X,bessie)))&(![X,Y]:((~like(X,bessie)&~like(Y,bessie))=>(X=Y)))))& (?[X,Y]:((~like(bessie,X))&(does_not_have_lived_in_exactly_three_countries(Y))&(taller(X,Y))))& (![X]:(taller(X,thomas))))	room(aline)&room(thomas)&room(penny)&room(ramona)&(![X]:(room(X)=>(X='aline'\|X='thomas'\|X='penny'\|X='ramona')))& ((taller(bessie,penny))&(~like(bessie,penny)))	neutral	contradiction	contradiction
Michael, Brooks are the only persons in the room. Someone who is not Michael hate someone who hates Brittany. Brooks is the least rich in the room. Michael is the least quiet in the room.	It is not the case that 'Brittany is quieter than Michael'.	contradiction	-	room(michael)&room(brooks)&(![X]:(room(X)=>(X='michael'\|X='brooks')))& ((?[X,Y]:((X!=michael)&(hate(brittany,Y))&(hate(X,Y))))& (![X]:(richer(brooks,X)))& (![X]:(quieter(michael,X))))	room(michael)&room(brooks)&(![X]:(room(X)=>(X='michael'\|X='brooks')))& (~(quieter(michael,brittany)))	entailment	entailment	entailment
Donna is the only person in the room. Donna does not have a piercing or is not hated by Dora or both if Donna who is hated by Dora, is not rich and vice versa. Only one person in the room enjoys fishing. Dora is taller than Donna. Donna is the least quiet in the room. More than one person outside the room is quieter than Dora.	Donna neither enjoys fishing nor does not hate Dora.	contradiction	-	room(donna)&(![X]:(room(X)=>(X='donna')))& ((((hate(donna,dora))&(~rich(donna)))<=>(((does_not_have_a_piercing(donna))\|(~hate(donna,dora)))))& (((?[X]:(room(X)&enjoys_fishing(X)))&(![X,Y]:((enjoys_fishing(X)&enjoys_fishing(Y))=>(X=Y)))))& (taller(donna,dora))& (![X]:(quieter(donna,X)))& ((?[X,Y]:(~room(X)&~room(Y)&(quieter(dora,X)&quieter(dora,Y))&(X!=Y)))))	room(donna)&(![X]:(room(X)=>(X='donna')))& (~((enjoys_fishing(donna))\|(~hate(dora,donna))))	contradiction	neutral	neutral
Erick, Janeen are the only persons in the room. "Harry is richer than Erick" only if "only one person in the room is not liked by Harry". "Only one person outside the room is liked by Lois" unless "someone outside the room who enjoys jogging is a sibling of Harry". If "Janeen and Erick are respectively tall and rich" then "Erick is not tall". Janeen does not hate Harry and is not creative, not rich, not tall. More than one person in the room is hated by Harry. Someone outside the room who enjoys jogging is a sibling of Harry. Erick does not hate Harry and is not Janeen. Erick neither is not tall nor is not hated by Harry.	Janeen neither is not brave, not rich nor is liked by Harry.	neutral	% SZS status Satisfiable	room(erick)&room(janeen)&(![X]:(room(X)=>(X='erick'\|X='janeen')))& (((richer(erick,harry))=>(((?[X]:(room(X)&~like(X,harry)))&(![X,Y]:((~like(X,harry)&~like(Y,harry))=>(X=Y))))))& (~(?[X]:(~room(X)=>(((enjoys_jogging(X))=>(sibling(harry,X))))))=>(((?[X]:(~room(X)&like(X,lois)))&(![X,Y]:((like(X,lois)&like(Y,lois))=>(X=Y))))))& (((tall(janeen))&(rich(erick)))=>(~tall(erick)))& ((~hate(harry,janeen))&(~creative(janeen)&~rich(janeen)&~tall(janeen)))& ((?[X,Y]:(room(X)&room(Y)&(hate(X,harry)&hate(Y,harry))&(X!=Y))))& (?[X]:(~room(X)=>(((enjoys_jogging(X))=>(sibling(harry,X))))))& ((~hate(harry,erick))&(erick!=janeen))& (~((~tall(erick))\|(~hate(erick,harry)))))	room(erick)&room(janeen)&(![X]:(room(X)=>(X='erick'\|X='janeen')))& (~((~brave(janeen)&~rich(janeen))\|(like(janeen,harry))))	contradiction	contradiction	contradiction
Matthew, Robert are the only persons in the room. At least one of the following is true:. -Matthew and Robert are not a tall quiet creative european. -Robert neither is not hated by Shirley nor does not hate Ladonna. -No one outside the room who is not Robert hates Ladonna.	It is not the case that 'Robert is not hated by Shirley and is a client of Shirley'.	neutral	% SZS status Satisfiable	room(matthew)&room(robert)&(![X]:(room(X)=>(X='matthew'\|X='robert')))& (((~(tall(matthew)&quiet(matthew)&creative(matthew)&european(matthew))&~(tall(robert)&quiet(robert)&creative(robert)&european(robert)))\| (~((~hate(robert,shirley))\|(~hate(ladonna,robert))))\| (~?[X]:(~room(X)=>(((X!=robert)=>(hate(ladonna,X))))))))	room(matthew)&room(robert)&(![X]:(room(X)=>(X='matthew'\|X='robert')))& (~((~hate(robert,shirley))&(client(shirley,robert))))	entailment	entailment	entailment
Randall, William, Carlos are the only persons in the room. Randall is liked by Annamarie. More than one person in the room likes Gloria.	Someone who is liked by Annamarie like someone who is not Randall.	entailment	% SZS status Unsatisfiable % SZS output start Proof tff(like_type, type, ( like: ( $i * $i ) > $o)). tff(susan_type, type, ( susan: $i)). tff(mary_type, type, ( mary: $i)). 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(john_type, type, ( john: $i)). tff(fred_type, type, ( fred: $i)). tff(paul_type, type, ( paul: $i)). tff(lucy_type, type, ( lucy: $i)). tff(alice_type, type, ( alice: $i)). tff(1,assumption,(~((X!2 = \|'fred'\|) \| (X!2 = \|'paul'\|) \| (X!2 = \|'mary'\|) \| (~room(X!2)))), introduced(assumption)). tff(2,plain, (((X!2 = \|'fred'\|) \| (X!2 = \|'paul'\|) \| (X!2 = \|'mary'\|) \| (~room(X!2))) \| room(X!2)), inference(tautology,[status(thm)],[])). tff(3,plain, (room(X!2)), inference(unit_resolution,[status(thm)],[2, 1])). tff(4,plain, (((X!2 = \|'fred'\|) \| (X!2 = \|'paul'\|) \| (X!2 = \|'mary'\|) \| (~room(X!2))) \| (~(X!2 = \|'mary'\|))), inference(tautology,[status(thm)],[])). tff(5,plain, (~(X!2 = \|'mary'\|)), inference(unit_resolution,[status(thm)],[4, 1])). tff(6,plain, (((X!2 = \|'fred'\|) \| (X!2 = \|'paul'\|) \| (X!2 = \|'mary'\|) \| (~room(X!2))) \| (~(X!2 = \|'paul'\|))), inference(tautology,[status(thm)],[])). tff(7,plain, (~(X!2 = \|'paul'\|)), inference(unit_resolution,[status(thm)],[6, 1])). tff(8,plain, (((X!2 = \|'fred'\|) \| (X!2 = \|'paul'\|) \| (X!2 = \|'mary'\|) \| (~room(X!2))) \| (~(X!2 = \|'fred'\|))), inference(tautology,[status(thm)],[])). tff(9,plain, (~(X!2 = \|'fred'\|)), inference(unit_resolution,[status(thm)],[8, 1])). tff(10,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(11,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)],[10])). tff(12,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(13,plain, ((~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)))) & (like(mary, susan) & ?[X: $i, Y: $i] : (((room(X) & room(Y)) & (like(john, X) & like(john, Y))) & (~(X = Y))))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)))) & ?[X: $i, Y: $i] : ((like(X, susan) & (~(Y = mary))) & like(X, Y))))) <=> (~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & like(mary, susan) & ?[X: $i, Y: $i] : (room(X) & room(Y) & like(john, X) & like(john, Y) & (~(X = Y))))) \| (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ?[X: $i, Y: $i] : (like(X, susan) & (~(Y = mary)) & like(X, Y)))))), inference(rewrite,[status(thm)],[])). tff(14,axiom,(~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)))) & (like(mary, susan) & ?[X: $i, Y: $i] : (((room(X) & room(Y)) & (like(john, X) & like(john, Y))) & (~(X = Y))))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)))) & ?[X: $i, Y: $i] : ((like(X, susan) & (~(Y = mary))) & like(X, Y))))), file('/mnt/tmpfs//1999622931107826427788337.p','negated')). tff(15,plain, (~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & like(mary, susan) & ?[X: $i, Y: $i] : (room(X) & room(Y) & like(john, X) & like(john, Y) & (~(X = Y))))) \| (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ?[X: $i, Y: $i] : (like(X, susan) & (~(Y = mary)) & like(X, Y))))), inference(modus_ponens,[status(thm)],[14, 13])). tff(16,plain, (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & like(mary, susan) & ?[X: $i, Y: $i] : (room(X) & room(Y) & like(john, X) & like(john, Y) & (~(X = Y)))), inference(or_elim,[status(thm)],[15])). tff(17,plain, (![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))), inference(and_elim,[status(thm)],[16])). tff(18,plain, (![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))), inference(modus_ponens,[status(thm)],[17, 12])). tff(19,plain,( ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))), inference(skolemize,[status(sab)],[18])). tff(20,plain, (![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))), inference(modus_ponens,[status(thm)],[19, 11])). tff(21,plain, (((~![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| ((X!2 = \|'fred'\|) \| (X!2 = \|'paul'\|) \| (X!2 = \|'mary'\|) \| (~room(X!2)))) <=> ((~![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| (X!2 = \|'fred'\|) \| (X!2 = \|'paul'\|) \| (X!2 = \|'mary'\|) \| (~room(X!2)))), inference(rewrite,[status(thm)],[])). tff(22,plain, ((~![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| ((X!2 = \|'fred'\|) \| (X!2 = \|'paul'\|) \| (X!2 = \|'mary'\|) \| (~room(X!2)))), inference(quant_inst,[status(thm)],[])). tff(23,plain, ((~![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| (X!2 = \|'fred'\|) \| (X!2 = \|'paul'\|) \| (X!2 = \|'mary'\|) \| (~room(X!2))), inference(modus_ponens,[status(thm)],[22, 21])). tff(24,plain, ($false), inference(unit_resolution,[status(thm)],[23, 20, 9, 7, 5, 3])). tff(25,plain,((X!2 = \|'fred'\|) \| (X!2 = \|'paul'\|) \| (X!2 = \|'mary'\|) \| (~room(X!2))), inference(lemma,lemma(discharge,[]))). tff(26,plain, (room(fred) <=> room(fred)), inference(rewrite,[status(thm)],[])). tff(27,plain, (room(fred)), inference(and_elim,[status(thm)],[16])). tff(28,plain, (room(fred)), inference(modus_ponens,[status(thm)],[27, 26])). tff(29,plain, (room(paul) <=> room(paul)), inference(rewrite,[status(thm)],[])). tff(30,plain, (room(paul)), inference(and_elim,[status(thm)],[16])). tff(31,plain, (room(paul)), inference(modus_ponens,[status(thm)],[30, 29])). tff(32,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(33,plain, (room(mary)), inference(and_elim,[status(thm)],[16])). tff(34,plain, (room(mary)), inference(modus_ponens,[status(thm)],[33, 32])). tff(35,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!2 = \|'fred'\|) \| (X!2 = \|'paul'\|) \| (X!2 = \|'mary'\|) \| (~room(X!2)))) \| ![X: $i, Y: $i] : ((~like(X, Y)) \| (Y = mary) \| (~like(X, susan)))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!2 = \|'fred'\|) \| (X!2 = \|'paul'\|) \| (X!2 = \|'mary'\|) \| (~room(X!2)))) \| ![X: $i, Y: $i] : ((~like(X, Y)) \| (Y = mary) \| (~like(X, susan))))), inference(rewrite,[status(thm)],[])). tff(36,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!2 = \|'fred'\|) \| (X!2 = \|'paul'\|) \| (X!2 = \|'mary'\|) \| (~room(X!2)))) \| ![X: $i, Y: $i] : ((~like(X, Y)) \| (Y = mary) \| (~like(X, susan)))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!2 = \|'fred'\|) \| (X!2 = \|'paul'\|) \| (X!2 = \|'mary'\|) \| (~room(X!2)))) \| ![X: $i, Y: $i] : ((~like(X, Y)) \| (Y = mary) \| (~like(X, susan))))), inference(rewrite,[status(thm)],[])). tff(37,plain, (^[X: $i, Y: $i] : trans(monotonicity(rewrite((like(X, susan) & (~(Y = mary)) & like(X, Y)) <=> (~((~like(X, Y)) \| (Y = mary) \| (~like(X, susan))))), ((~(like(X, susan) & (~(Y = mary)) & like(X, Y))) <=> (~(~((~like(X, Y)) \| (Y = mary) \| (~like(X, susan))))))), rewrite((~(~((~like(X, Y)) \| (Y = mary) \| (~like(X, susan))))) <=> ((~like(X, Y)) \| (Y = mary) \| (~like(X, susan)))), ((~(like(X, susan) & (~(Y = mary)) & like(X, Y))) <=> ((~like(X, Y)) \| (Y = mary) \| (~like(X, susan)))))), inference(bind,[status(th)],[])). tff(38,plain, (![X: $i, Y: $i] : (~(like(X, susan) & (~(Y = mary)) & like(X, Y))) <=> ![X: $i, Y: $i] : ((~like(X, Y)) \| (Y = mary) \| (~like(X, susan)))), inference(quant_intro,[status(thm)],[37])). tff(39,plain, ((~((X!2 = \|'fred'\|) \| (X!2 = \|'paul'\|) \| (X!2 = \|'mary'\|) \| (~room(X!2)))) <=> (~((X!2 = \|'fred'\|) \| (X!2 = \|'paul'\|) \| (X!2 = \|'mary'\|) \| (~room(X!2))))), inference(rewrite,[status(thm)],[])). tff(40,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!2 = \|'fred'\|) \| (X!2 = \|'paul'\|) \| (X!2 = \|'mary'\|) \| (~room(X!2)))) \| ![X: $i, Y: $i] : (~(like(X, susan) & (~(Y = mary)) & like(X, Y)))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!2 = \|'fred'\|) \| (X!2 = \|'paul'\|) \| (X!2 = \|'mary'\|) \| (~room(X!2)))) \| ![X: $i, Y: $i] : ((~like(X, Y)) \| (Y = mary) \| (~like(X, susan))))), inference(monotonicity,[status(thm)],[39, 38])). tff(41,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!2 = \|'fred'\|) \| (X!2 = \|'paul'\|) \| (X!2 = \|'mary'\|) \| (~room(X!2)))) \| ![X: $i, Y: $i] : (~(like(X, susan) & (~(Y = mary)) & like(X, Y)))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!2 = \|'fred'\|) \| (X!2 = \|'paul'\|) \| (X!2 = \|'mary'\|) \| (~room(X!2)))) \| ![X: $i, Y: $i] : ((~like(X, Y)) \| (Y = mary) \| (~like(X, susan))))), inference(transitivity,[status(thm)],[40, 36])). tff(42,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!2 = \|'fred'\|) \| (X!2 = \|'paul'\|) \| (X!2 = \|'mary'\|) \| (~room(X!2)))) \| ![X: $i, Y: $i] : (~(like(X, susan) & (~(Y = mary)) & like(X, Y)))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!2 = \|'fred'\|) \| (X!2 = \|'paul'\|) \| (X!2 = \|'mary'\|) \| (~room(X!2)))) \| ![X: $i, Y: $i] : (~(like(X, susan) & (~(Y = mary)) & like(X, Y))))), inference(rewrite,[status(thm)],[])). tff(43,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!2 = \|'fred'\|) \| (X!2 = \|'paul'\|) \| (X!2 = \|'mary'\|) \| (~room(X!2)))) \| ![X: $i, Y: $i] : (~(like(X, susan) & (~(Y = mary)) & like(X, Y)))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!2 = \|'fred'\|) \| (X!2 = \|'paul'\|) \| (X!2 = \|'mary'\|) \| (~room(X!2)))) \| ![X: $i, Y: $i] : (~(like(X, susan) & (~(Y = mary)) & like(X, Y))))), inference(monotonicity,[status(thm)],[39])). tff(44,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!2 = \|'fred'\|) \| (X!2 = \|'paul'\|) \| (X!2 = \|'mary'\|) \| (~room(X!2)))) \| ![X: $i, Y: $i] : (~(like(X, susan) & (~(Y = mary)) & like(X, Y)))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!2 = \|'fred'\|) \| (X!2 = \|'paul'\|) \| (X!2 = \|'mary'\|) \| (~room(X!2)))) \| ![X: $i, Y: $i] : (~(like(X, susan) & (~(Y = mary)) & like(X, Y))))), inference(transitivity,[status(thm)],[43, 42])). tff(45,plain, ((room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ?[X: $i, Y: $i] : (like(X, susan) & (~(Y = mary)) & like(X, Y))) <=> (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ?[X: $i, Y: $i] : (like(X, susan) & (~(Y = mary)) & like(X, Y)))), inference(rewrite,[status(thm)],[])). tff(46,plain, ((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ?[X: $i, Y: $i] : (like(X, susan) & (~(Y = mary)) & like(X, Y)))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ?[X: $i, Y: $i] : (like(X, susan) & (~(Y = mary)) & like(X, Y))))), inference(monotonicity,[status(thm)],[45])). tff(47,plain, ((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ?[X: $i, Y: $i] : (like(X, susan) & (~(Y = mary)) & like(X, Y)))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ?[X: $i, Y: $i] : (like(X, susan) & (~(Y = mary)) & like(X, Y))))), inference(rewrite,[status(thm)],[])). tff(48,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ?[X: $i, Y: $i] : (like(X, susan) & (~(Y = mary)) & like(X, Y)))), inference(or_elim,[status(thm)],[15])). tff(49,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ?[X: $i, Y: $i] : (like(X, susan) & (~(Y = mary)) & like(X, Y)))), inference(modus_ponens,[status(thm)],[48, 46])). tff(50,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ?[X: $i, Y: $i] : (like(X, susan) & (~(Y = mary)) & like(X, Y)))), inference(modus_ponens,[status(thm)],[49, 47])). tff(51,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ?[X: $i, Y: $i] : (like(X, susan) & (~(Y = mary)) & like(X, Y)))), inference(modus_ponens,[status(thm)],[50, 46])). unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary))))) (a!2 (refl (~ (not (room paul)) (not (room paul))))) (a!3 (refl (~ (not (room fred)) (not (room fred))))) (a!4 (forall ((X $i)) (or (= X \|'fred'\|) (= X \|'paul'\|) (= X \|'mary'\|) (not (room X))))) (a!5 (not (or (= X!2 \|'fred'\|) (= X!2 \|'paul'\|) (= X!2 \|'mary'\|) (not (room X!2))))) (a!6 (lambda ((X $i) (Y $i)) (let ((a!1 (and (like X susan) (not (= Y mary)) (like X Y)))) (refl (~ (not a!1) (not a!1)))))) (a!7 (exists ((X $i) (Y $i)) (and (like X susan) (not (= Y mary)) (like X Y)))) (a!8 (forall ((X $i) (Y $i)) (let ((a!1 (and (like X susan) (not (= Y mary)) (like 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(randall)&room(william)&room(carlos)&(![X]:(room(X)=>(X='randall'\|X='william'\|X='carlos')))& ((like(randall,annamarie))& ((?[X,Y]:(room(X)&room(Y)&(like(gloria,X)&like(gloria,Y))&(X!=Y)))))	room(randall)&room(william)&room(carlos)&(![X]:(room(X)=>(X='randall'\|X='william'\|X='carlos')))& (?[X,Y]:((like(X,annamarie))&(Y!=randall)&(like(X,Y))))	neutral	entailment	contradiction
Agnes, Matthew, Robert, Raquel are the only persons in the room. 'Robert is the least tall in the room' unless 'Agnes is a sibling of John'. Agnes is not liked by John and is a sibling of John. Robert plays video games and is liked by Edward. Edward and Agnes like each other.	It is not the case that 'Robert is a client of John or is a sibling of Edward or both'.	neutral	% SZS status Satisfiable	room(agnes)&room(matthew)&room(robert)&room(raquel)&(![X]:(room(X)=>(X='agnes'\|X='matthew'\|X='robert'\|X='raquel')))& ((~(sibling(john,agnes))=>(![X]:(taller(robert,X))))& ((~like(agnes,john))&(sibling(john,agnes)))& ((plays_video_games(robert))&(like(robert,edward)))& ((like(edward,agnes) & like(agnes,edward))))	room(agnes)&room(matthew)&room(robert)&room(raquel)&(![X]:(room(X)=>(X='agnes'\|X='matthew'\|X='robert'\|X='raquel')))& (~(((client(john,robert))\|(sibling(edward,robert)))))	entailment	entailment	entailment
At least one of the following is true:. -Yolanda does not practice calligraphy and is not brave, not creative. -Yolanda either is a rich creative european or is not a brave rich european.	Yolanda who does not practice calligraphy, is not creative.	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(creative_type, type, ( creative: $i > $o)). tff(mary_type, type, ( mary: $i)). tff(brave_type, type, ( brave: $i > $o)). tff(predb_type, type, ( predb: $i > $o)). tff(european_type, type, ( european: $i > $o)). tff(rich_type, type, ( rich: $i > $o)). tff(1,plain, ((~creative(mary)) <=> (~creative(mary))), inference(rewrite,[status(thm)],[])). tff(2,plain, ((~(((room(mary) & ![X: $i] : (room(X) => (X = \|'mary'\|))) & (((~predb(mary)) & ((~brave(mary)) & (~creative(mary)))) \| ((((rich(mary) & creative(mary)) & european(mary)) \| (~((brave(mary) & rich(mary)) & european(mary)))) & (~(((rich(mary) & creative(mary)) & european(mary)) \| (~((brave(mary) & rich(mary)) & european(mary)))))))) => ((room(mary) & ![X: $i] : (room(X) => (X = \|'mary'\|))) & ((~predb(mary)) & (~creative(mary)))))) <=> (~((~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~predb(mary)) & (~brave(mary)) & (~creative(mary)))) \| (room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~predb(mary)) & (~creative(mary)))))), inference(rewrite,[status(thm)],[])). tff(3,axiom,(~(((room(mary) & ![X: $i] : (room(X) => (X = \|'mary'\|))) & (((~predb(mary)) & ((~brave(mary)) & (~creative(mary)))) \| ((((rich(mary) & creative(mary)) & european(mary)) \| (~((brave(mary) & rich(mary)) & european(mary)))) & (~(((rich(mary) & creative(mary)) & european(mary)) \| (~((brave(mary) & rich(mary)) & european(mary)))))))) => ((room(mary) & ![X: $i] : (room(X) => (X = \|'mary'\|))) & ((~predb(mary)) & (~creative(mary)))))), file('/mnt/tmpfs//4234247847678052282184060.p','negated')). tff(4,plain, (~((~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~predb(mary)) & (~brave(mary)) & (~creative(mary)))) \| (room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~predb(mary)) & (~creative(mary))))), inference(modus_ponens,[status(thm)],[3, 2])). tff(5,plain, (room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~predb(mary)) & (~brave(mary)) & (~creative(mary))), inference(or_elim,[status(thm)],[4])). tff(6,plain, (~creative(mary)), inference(and_elim,[status(thm)],[5])). tff(7,plain, (~creative(mary)), inference(modus_ponens,[status(thm)],[6, 1])). tff(8,plain, ((~predb(mary)) <=> (~predb(mary))), inference(rewrite,[status(thm)],[])). tff(9,plain, (~predb(mary)), inference(and_elim,[status(thm)],[5])). tff(10,plain, (~predb(mary)), inference(modus_ponens,[status(thm)],[9, 8])). tff(11,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(12,plain, (room(mary)), inference(and_elim,[status(thm)],[5])). tff(13,plain, (room(mary)), inference(modus_ponens,[status(thm)],[12, 11])). tff(14,plain, (((~room(mary)) \| (~((~room(X!0)) \| (X!0 = \|'mary'\|))) \| predb(mary) \| creative(mary)) <=> (predb(mary) \| creative(mary) \| (~room(mary)) \| (~((~room(X!0)) \| (X!0 = \|'mary'\|))))), inference(rewrite,[status(thm)],[])). tff(15,plain, ((room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~predb(mary)) & (~creative(mary))) <=> (room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~predb(mary)) & (~creative(mary)))), inference(rewrite,[status(thm)],[])). tff(16,plain, ((~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~predb(mary)) & (~creative(mary)))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~predb(mary)) & (~creative(mary))))), inference(monotonicity,[status(thm)],[15])). tff(17,plain, ((~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~predb(mary)) & (~creative(mary)))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~predb(mary)) & (~creative(mary))))), inference(rewrite,[status(thm)],[])). tff(18,plain, (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~predb(mary)) & (~creative(mary)))), inference(or_elim,[status(thm)],[4])). tff(19,plain, (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~predb(mary)) & (~creative(mary)))), inference(modus_ponens,[status(thm)],[18, 16])). tff(20,plain, (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~predb(mary)) & (~creative(mary)))), inference(modus_ponens,[status(thm)],[19, 17])). tff(21,plain, (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~predb(mary)) & (~creative(mary)))), inference(modus_ponens,[status(thm)],[20, 16])). 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 (not (predb mary)) (not (creative mary)))))) (let ((a!5 (~ a!4 (or (not (room mary)) a!3 (predb mary) (creative mary))))) (nnf-neg a!1 (sk (~ (not a!2) a!3)) (refl (~ (predb mary) (predb mary))) (refl (~ (creative mary) (creative mary))) a!5))))	room(yolanda)&(![X]:(room(X)=>(X='yolanda')))& ((((does_not_practice_calligraphy(yolanda))&(~brave(yolanda)&~creative(yolanda)))\| ((((rich(yolanda)&creative(yolanda)&european(yolanda))\|(~(brave(yolanda)&rich(yolanda)&european(yolanda))))&(~((rich(yolanda)&creative(yolanda)&european(yolanda))\|(~(brave(yolanda)&rich(yolanda)&european(yolanda)))))))))	room(yolanda)&(![X]:(room(X)=>(X='yolanda')))& ((does_not_practice_calligraphy(yolanda))&(~creative(yolanda)))	entailment	neutral	contradiction
Matthew is the only person in the room. Matthew hates Julia and is not a tall european. Matthew is the least tall in the room. Someone in the room who does not hate Julia is not a tall creative brave european. Only one person outside the room is hated by Christopher. Matthew is not creative, not happy or is not a brave happy tourist or both. Julia and Julia hate each other.	Matthew who is a happy tall tourist, is not a creative tall happy tourist.	neutral	% SZS status Satisfiable	room(matthew)&(![X]:(room(X)=>(X='matthew')))& (((hate(julia,matthew))&(~(tall(matthew)&european(matthew))))& (![X]:(taller(matthew,X)))& (?[X]:(room(X)=>(((~hate(julia,X))=>(~(tall(X)&creative(X)&brave(X)&european(X)))))))& (((?[X]:(~room(X)&hate(X,christopher)))&(![X,Y]:((hate(X,christopher)&hate(Y,christopher))=>(X=Y)))))& (((~creative(matthew)&~happy(matthew))\|(~(brave(matthew)&happy(matthew)&tourist(matthew)))))& ((hate(julia,julia) & hate(julia,julia))))	room(matthew)&(![X]:(room(X)=>(X='matthew')))& ((happy(matthew)&tall(matthew)&tourist(matthew))&(~(creative(matthew)&tall(matthew)&happy(matthew)&tourist(matthew))))	contradiction	contradiction	contradiction
Michael, June, Robert, Tiffany are the only persons in the room. If "Tiffany is not creative and is a brave european" then "someone outside the room hates Linda". "Someone outside the room is hated by Linda" if "Tiffany is a quiet european and is a happy rich european" and vice versa. Someone outside the room hates Linda. Tiffany is the least rich in the room. Thersa is quieter than Tiffany. Tiffany who is not hated by Thersa, does not enjoy hiking. Someone outside the room hates Linda.	Robert and Michael are not rich, not quiet, not creative, not brave, not happy.	contradiction	-	room(michael)&room(june)&room(robert)&room(tiffany)&(![X]:(room(X)=>(X='michael'\|X='june'\|X='robert'\|X='tiffany')))& ((((~creative(tiffany))&(brave(tiffany)&european(tiffany)))=>(?[X]:(~room(X)=>(hate(linda,X)))))& (((quiet(tiffany)&european(tiffany))&(happy(tiffany)&rich(tiffany)&european(tiffany)))<=>(?[X]:(~room(X)=>(hate(X,linda)))))& (?[X]:(~room(X)=>(hate(linda,X))))& (![X]:(richer(tiffany,X)))& (quieter(tiffany,thersa))& ((~hate(tiffany,thersa))&(does_not_enjoy_hiking(tiffany)))& (?[X]:(~room(X)=>(hate(linda,X)))))	room(michael)&room(june)&room(robert)&room(tiffany)&(![X]:(room(X)=>(X='michael'\|X='june'\|X='robert'\|X='tiffany')))& (~rich(robert)&~quiet(robert)&~creative(robert)&~brave(robert)&~happy(robert)&~rich(michael)&~quiet(michael)&~creative(michael)&~brave(michael)&~happy(michael))	contradiction	neutral	neutral
Brenda, Esteban, Beth are the only persons in the room. “Brenda and Heather hate each other” if “Esteban is not tall or is not hated by Heather or both” and vice versa. “Esteban who hates Joseph, is hated by Anna” only if “Joseph and Esteban hate each other”. “Esteban who is hated by Heather, is hated by Laura” unless “Joseph and Brenda hate each other”. “Esteban and Beth are respectively tall and brave” only if “someone who does not hate Heather is taller than someone who is a client of Google”. Esteban is hated by Heather or is not hated by Joseph or both. More than one person outside the room is not Beth. Beth is not brave. Beth hates Laura. Brenda is hated by Anna or is not a tall european or both. Esteban neither hates Heather nor is not brave.	Brenda who is not a rich tall person, is hated by Joseph.	neutral	% SZS status Satisfiable	room(brenda)&room(esteban)&room(beth)&(![X]:(room(X)=>(X='brenda'\|X='esteban'\|X='beth')))& (((((~tall(esteban))\|(~hate(esteban,heather))))<=>((hate(brenda,heather) & hate(heather,brenda))))& (((hate(joseph,esteban))&(hate(esteban,anna)))=>((hate(joseph,esteban) & hate(esteban,joseph))))& (~((hate(joseph,brenda) & hate(brenda,joseph)))=>((hate(esteban,heather))&(hate(esteban,laura))))& (((tall(esteban))&(brave(beth)))=>(?[X,Y]:((~hate(heather,X))&(is_a_client_of_Google(Y))&(taller(X,Y)))))& (((hate(esteban,heather))\|(~hate(esteban,joseph))))& ((?[X,Y]:(~room(X)&~room(Y)&(X!=beth&Y!=beth)&(X!=Y))))& (~brave(beth))& (hate(laura,beth))& (((hate(brenda,anna))\|(~(tall(brenda)&european(brenda)))))& (~((hate(heather,esteban))\|(~brave(esteban)))))	room(brenda)&room(esteban)&room(beth)&(![X]:(room(X)=>(X='brenda'\|X='esteban'\|X='beth')))& ((~(rich(brenda)&tall(brenda)&person(brenda)))&(hate(brenda,joseph)))	neutral	contradiction	contradiction
Matthew, Don are the only persons in the room. If “Don is the tallest in the room” then “Don neither is not a tall rich quiet european nor is not an amateur astronomer” otherwise “Don is the least tall in the room”. “Don is not liked by Jane” unless “someone who is liked by Marjorie is taller than someone who is not a rich tall quiet european”. “Only one person in the room does not own a microscope” if “Marjorie and Robert like each other” and vice versa. Don is the least rich in the room. Robert is a client of Don. Don is the tallest in the room. Don is the least quiet in the room. Marjorie and Jane like each other. Don is a rich quiet person and does not like Robert.	It is not the case that 'Don is a rich quiet person or is not a creative person or both'.	contradiction	-	room(matthew)&room(don)&(![X]:(room(X)=>(X='matthew'\|X='don')))& ((((![X]:(taller(X,don)))=>(~((~(tall(don)&rich(don)&quiet(don)&european(don)))\|(is_not_an_amateur_astronomer(don)))))\|((~(![X]:(taller(X,don))))=>(![X]:(taller(don,X)))))& (~(?[X,Y]:((like(X,marjorie))&(~(rich(Y)&tall(Y)&quiet(Y)&european(Y)))&(taller(X,Y))))=>(~like(don,jane)))& (((like(marjorie,robert) & like(robert,marjorie)))<=>(((?[X]:(room(X)&does_not_own_a_microscope(X)))&(![X,Y]:((does_not_own_a_microscope(X)&does_not_own_a_microscope(Y))=>(X=Y))))))& (![X]:(richer(don,X)))& (client(don,robert))& (![X]:(taller(X,don)))& (![X]:(quieter(don,X)))& ((like(marjorie,jane) & like(jane,marjorie)))& ((rich(don)&quiet(don)&person(don))&(~like(robert,don))))	room(matthew)&room(don)&(![X]:(room(X)=>(X='matthew'\|X='don')))& (~(((rich(don)&quiet(don)&person(don))\|(~(creative(don)&person(don))))))	entailment	entailment	contradiction
Deann, Albert, Nina, Lori are the only persons in the room. Albert is quieter than Traci and is a happy european. Albert who is not liked by Traci, does not hate Traci. Everyone outside the room who does not play a musical instrument hates Traci. Traci is a sibling of Albert. Albert is not creative and plays a musical instrument.	Albert neither is not quiet, not happy nor is a creative quiet tall person.	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(person_type, type, ( person: $i > $o)). tff(paul_type, type, ( paul: $i)). tff(tall_type, type, ( tall: $i > $o)). tff(quiet_type, type, ( quiet: $i > $o)). tff(creative_type, type, ( creative: $i > $o)). tff(preda_type, type, ( preda: $i > $o)). tff(sibling_type, type, ( sibling: ( $i * $i ) > $o)). tff(lucy_type, type, ( lucy: $i)). tff(hate_type, type, ( hate: ( $i * $i ) > $o)). tff(like_type, type, ( like: ( $i * $i ) > $o)). tff(european_type, type, ( european: $i > $o)). tff(happy_type, type, ( happy: $i > $o)). tff(quieter_type, type, ( quieter: ( $i * $i ) > $o)). tff(alice_type, type, ( alice: $i)). tff(fred_type, type, ( fred: $i)). tff(mary_type, type, ( mary: $i)). tff(1,plain, ((~creative(paul)) <=> (~creative(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'\|)))) & (((((quieter(lucy, paul) & (happy(paul) & european(paul))) & ((~like(paul, lucy)) & (~hate(lucy, paul)))) & ![X: $i] : ((~room(X)) => ((~preda(X)) => hate(lucy, X)))) & sibling(paul, lucy)) & ((~creative(paul)) & preda(paul)))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)) \| (X = \|'alice'\|)))) & (~(((~quiet(paul)) & (~happy(paul))) \| (((creative(paul) & quiet(paul)) & tall(paul)) & person(paul))))))) <=> (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & quieter(lucy, paul) & happy(paul) & european(paul) & (~like(paul, lucy)) & (~hate(lucy, paul)) & ![X: $i] : (room(X) \| hate(lucy, X) \| preda(X)) & sibling(paul, lucy) & (~creative(paul)) & preda(paul))) \| (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~(((~quiet(paul)) & (~happy(paul))) \| (creative(paul) & quiet(paul) & tall(paul) & person(paul)))))))), inference(rewrite,[status(thm)],[])). tff(3,axiom,(~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)) \| (X = \|'alice'\|)))) & (((((quieter(lucy, paul) & (happy(paul) & european(paul))) & ((~like(paul, lucy)) & (~hate(lucy, paul)))) & ![X: $i] : ((~room(X)) => ((~preda(X)) => hate(lucy, X)))) & sibling(paul, lucy)) & ((~creative(paul)) & preda(paul)))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)) \| (X = \|'alice'\|)))) & (~(((~quiet(paul)) & (~happy(paul))) \| (((creative(paul) & quiet(paul)) & tall(paul)) & person(paul))))))), file('/mnt/tmpfs//5050607963222448738464507.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(lucy, paul) & happy(paul) & european(paul) & (~like(paul, lucy)) & (~hate(lucy, paul)) & ![X: $i] : (room(X) \| hate(lucy, X) \| preda(X)) & sibling(paul, lucy) & (~creative(paul)) & preda(paul))) \| (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~(((~quiet(paul)) & (~happy(paul))) \| (creative(paul) & quiet(paul) & tall(paul) & person(paul))))))), inference(modus_ponens,[status(thm)],[3, 2])). tff(5,plain, (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & quieter(lucy, paul) & happy(paul) & european(paul) & (~like(paul, lucy)) & (~hate(lucy, paul)) & ![X: $i] : (room(X) \| hate(lucy, X) \| preda(X)) & sibling(paul, lucy) & (~creative(paul)) & preda(paul)), inference(or_elim,[status(thm)],[4])). tff(6,plain, (~creative(paul)), inference(and_elim,[status(thm)],[5])). tff(7,plain, (~creative(paul)), inference(modus_ponens,[status(thm)],[6, 1])). tff(8,plain, (((~creative(paul)) \| (~quiet(paul)) \| (~tall(paul)) \| (~person(paul))) \| creative(paul)), inference(tautology,[status(thm)],[])). tff(9,plain, ((~creative(paul)) \| (~quiet(paul)) \| (~tall(paul)) \| (~person(paul))), inference(unit_resolution,[status(thm)],[8, 7])). tff(10,plain, (happy(paul) <=> happy(paul)), inference(rewrite,[status(thm)],[])). tff(11,plain, (happy(paul)), inference(and_elim,[status(thm)],[5])). tff(12,plain, (happy(paul)), inference(modus_ponens,[status(thm)],[11, 10])). tff(13,plain, ((happy(paul) \| quiet(paul)) \| (~happy(paul))), inference(tautology,[status(thm)],[])). tff(14,plain, (happy(paul) \| quiet(paul)), inference(unit_resolution,[status(thm)],[13, 12])). tff(15,plain, (room(alice) <=> room(alice)), inference(rewrite,[status(thm)],[])). tff(16,plain, (room(alice)), inference(and_elim,[status(thm)],[5])). tff(17,plain, (room(alice)), inference(modus_ponens,[status(thm)],[16, 15])). tff(18,plain, (room(fred) <=> room(fred)), inference(rewrite,[status(thm)],[])). tff(19,plain, (room(fred)), inference(and_elim,[status(thm)],[5])). tff(20,plain, (room(fred)), inference(modus_ponens,[status(thm)],[19, 18])). tff(21,plain, (room(paul) <=> room(paul)), inference(rewrite,[status(thm)],[])). tff(22,plain, (room(paul)), inference(and_elim,[status(thm)],[5])). tff(23,plain, (room(paul)), inference(modus_ponens,[status(thm)],[22, 21])). tff(24,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(25,plain, (room(mary)), inference(and_elim,[status(thm)],[5])). tff(26,plain, (room(mary)), inference(modus_ponens,[status(thm)],[25, 24])). tff(27,plain, (((~(happy(paul) \| quiet(paul))) \| (~((~creative(paul)) \| (~quiet(paul)) \| (~tall(paul)) \| (~person(paul)))) \| (~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)))) \| (~(happy(paul) \| quiet(paul))) \| (~((~creative(paul)) \| (~quiet(paul)) \| (~tall(paul)) \| (~person(paul)))))), inference(rewrite,[status(thm)],[])). tff(28,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(29,plain, ((creative(paul) & quiet(paul) & tall(paul) & person(paul)) <=> (~((~creative(paul)) \| (~quiet(paul)) \| (~tall(paul)) \| (~person(paul))))), inference(rewrite,[status(thm)],[])). tff(30,plain, (((~quiet(paul)) & (~happy(paul))) <=> (~(happy(paul) \| quiet(paul)))), inference(rewrite,[status(thm)],[])). tff(31,plain, ((((~quiet(paul)) & (~happy(paul))) \| (creative(paul) & quiet(paul) & tall(paul) & person(paul)) \| (~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~room(alice)) \| (~((X!0 = \|'alice'\|) \| (X!0 = \|'fred'\|) \| (X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0))))) <=> ((~(happy(paul) \| quiet(paul))) \| (~((~creative(paul)) \| (~quiet(paul)) \| (~tall(paul)) \| (~person(paul)))) \| (~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)],[30, 29, 28])). tff(32,plain, ((((~quiet(paul)) & (~happy(paul))) \| (creative(paul) & quiet(paul) & tall(paul) & person(paul)) \| (~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)))) \| (~(happy(paul) \| quiet(paul))) \| (~((~creative(paul)) \| (~quiet(paul)) \| (~tall(paul)) \| (~person(paul)))))), inference(transitivity,[status(thm)],[31, 27])). tff(33,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~room(alice)) \| (~((X!0 = \|'alice'\|) \| (X!0 = \|'fred'\|) \| (X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0)))) \| (((~quiet(paul)) & (~happy(paul))) \| (creative(paul) & quiet(paul) & tall(paul) & person(paul)))) <=> (((~quiet(paul)) & (~happy(paul))) \| (creative(paul) & quiet(paul) & tall(paul) & person(paul)) \| (~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(34,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~room(alice)) \| (~((X!0 = \|'alice'\|) \| (X!0 = \|'fred'\|) \| (X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0)))) \| (((~quiet(paul)) & (~happy(paul))) \| (creative(paul) & quiet(paul) & tall(paul) & person(paul)))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~room(alice)) \| (~((X!0 = \|'alice'\|) \| (X!0 = \|'fred'\|) \| (X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0)))) \| (((~quiet(paul)) & (~happy(paul))) \| (creative(paul) & quiet(paul) & tall(paul) & person(paul))))), inference(monotonicity,[status(thm)],[28])). tff(35,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~room(alice)) \| (~((X!0 = \|'alice'\|) \| (X!0 = \|'fred'\|) \| (X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0)))) \| (((~quiet(paul)) & (~happy(paul))) \| (creative(paul) & quiet(paul) & tall(paul) & person(paul)))) <=> (((~quiet(paul)) & (~happy(paul))) \| (creative(paul) & quiet(paul) & tall(paul) & person(paul)) \| (~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)],[34, 33])). tff(36,plain, ((room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~(((~quiet(paul)) & (~happy(paul))) \| (creative(paul) & quiet(paul) & tall(paul) & person(paul))))) <=> (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~(((~quiet(paul)) & (~happy(paul))) \| (creative(paul) & quiet(paul) & tall(paul) & person(paul)))))), inference(rewrite,[status(thm)],[])). tff(37,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~(((~quiet(paul)) & (~happy(paul))) \| (creative(paul) & quiet(paul) & tall(paul) & person(paul)))))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~(((~quiet(paul)) & (~happy(paul))) \| (creative(paul) & quiet(paul) & tall(paul) & person(paul))))))), inference(monotonicity,[status(thm)],[36])). tff(38,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~(((~quiet(paul)) & (~happy(paul))) \| (creative(paul) & quiet(paul) & tall(paul) & person(paul)))))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~(((~quiet(paul)) & (~happy(paul))) \| (creative(paul) & quiet(paul) & tall(paul) & person(paul))))))), inference(rewrite,[status(thm)],[])). tff(39,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~(((~quiet(paul)) & (~happy(paul))) \| (creative(paul) & quiet(paul) & tall(paul) & person(paul)))))), inference(or_elim,[status(thm)],[4])). tff(40,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~(((~quiet(paul)) & (~happy(paul))) \| (creative(paul) & quiet(paul) & tall(paul) & person(paul)))))), inference(modus_ponens,[status(thm)],[39, 37])). tff(41,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~(((~quiet(paul)) & (~happy(paul))) \| (creative(paul) & quiet(paul) & tall(paul) & person(paul)))))), inference(modus_ponens,[status(thm)],[40, 38])). tff(42,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~(((~quiet(paul)) & (~happy(paul))) \| (creative(paul) & quiet(paul) & tall(paul) & person(paul)))))), inference(modus_ponens,[status(thm)],[41, 37])). 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 (and (not (quiet paul)) (not (happy paul))) (and (creative paul) (quiet paul) (tall paul) (person 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(deann)&room(albert)&room(nina)&room(lori)&(![X]:(room(X)=>(X='deann'\|X='albert'\|X='nina'\|X='lori')))& (((quieter(traci,albert))&(happy(albert)&european(albert)))& ((~like(albert,traci))&(~hate(traci,albert)))& (![X]:(~room(X)=>(((does_not_play_a_musical_instrument(X))=>(hate(traci,X))))))& (sibling(albert,traci))& ((~creative(albert))&(plays_a_musical_instrument(albert))))	room(deann)&room(albert)&room(nina)&room(lori)&(![X]:(room(X)=>(X='deann'\|X='albert'\|X='nina'\|X='lori')))& (~((~quiet(albert)&~happy(albert))\|(creative(albert)&quiet(albert)&tall(albert)&person(albert))))	neutral	contradiction	neutral
Betty, Ricardo, Eric, Donald are the only persons in the room. Donald is the richest in the room. Betty plays a string instrument and is a sibling of Essie. Betty is not hated by Essie or is a client of Essie or both. Donald is not rich, not creative and likes Essie. Someone outside the room who is a client of Essie plays a string instrument. Betty is hated by Essie. Someone outside the room who is a creative european is not a creative rich tourist.	Someone who is not a tall rich quiet brave person is a client of someone who is not Ricardo.	entailment	% SZS status Unsatisfiable % SZS output start Proof tff(richer_type, type, ( richer: ( $i * $i ) > $o)). tff(alice_type, type, ( alice: $i)). tff(lucy_type, type, ( lucy: $i)). tff(rich_type, type, ( rich: $i > $o)). tff(person_type, type, ( person: $i > $o)). tff(brave_type, type, ( brave: $i > $o)). tff(quiet_type, type, ( quiet: $i > $o)). tff(tall_type, type, ( tall: $i > $o)). tff(client_type, type, ( client: ( $i * $i ) > $o)). tff(paul_type, type, ( paul: $i)). 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(european_type, type, ( european: $i > $o)). tff(creative_type, type, ( creative: $i > $o)). tff(tourist_type, type, ( tourist: $i > $o)). tff(hate_type, type, ( hate: ( $i * $i ) > $o)). tff(mary_type, type, ( mary: $i)). tff(predb_type, type, ( predb: $i > $o)). tff(like_type, type, ( like: ( $i * $i ) > $o)). tff(sibling_type, type, ( sibling: ( $i * $i ) > $o)). tff(fred_type, type, ( fred: $i)). tff(john_type, type, ( john: $i)). tff(susan_type, type, ( susan: $i)). tff(1,assumption,(~((X!2 = \|'alice'\|) \| (X!2 = \|'fred'\|) \| (X!2 = \|'paul'\|) \| (X!2 = \|'mary'\|) \| (~room(X!2)))), introduced(assumption)). tff(2,plain, (((X!2 = \|'alice'\|) \| (X!2 = \|'fred'\|) \| (X!2 = \|'paul'\|) \| (X!2 = \|'mary'\|) \| (~room(X!2))) \| room(X!2)), inference(tautology,[status(thm)],[])). tff(3,plain, (room(X!2)), inference(unit_resolution,[status(thm)],[2, 1])). tff(4,plain, (((X!2 = \|'alice'\|) \| (X!2 = \|'fred'\|) \| (X!2 = \|'paul'\|) \| (X!2 = \|'mary'\|) \| (~room(X!2))) \| (~(X!2 = \|'mary'\|))), inference(tautology,[status(thm)],[])). tff(5,plain, (~(X!2 = \|'mary'\|)), inference(unit_resolution,[status(thm)],[4, 1])). tff(6,plain, (((X!2 = \|'alice'\|) \| (X!2 = \|'fred'\|) \| (X!2 = \|'paul'\|) \| (X!2 = \|'mary'\|) \| (~room(X!2))) \| (~(X!2 = \|'paul'\|))), inference(tautology,[status(thm)],[])). tff(7,plain, (~(X!2 = \|'paul'\|)), inference(unit_resolution,[status(thm)],[6, 1])). tff(8,plain, (((X!2 = \|'alice'\|) \| (X!2 = \|'fred'\|) \| (X!2 = \|'paul'\|) \| (X!2 = \|'mary'\|) \| (~room(X!2))) \| (~(X!2 = \|'fred'\|))), inference(tautology,[status(thm)],[])). tff(9,plain, (~(X!2 = \|'fred'\|)), inference(unit_resolution,[status(thm)],[8, 1])). tff(10,plain, (((X!2 = \|'alice'\|) \| (X!2 = \|'fred'\|) \| (X!2 = \|'paul'\|) \| (X!2 = \|'mary'\|) \| (~room(X!2))) \| (~(X!2 = \|'alice'\|))), inference(tautology,[status(thm)],[])). tff(11,plain, (~(X!2 = \|'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'\|)))) & ((((((![X: $i] : richer(X, alice) & (predb(mary) & sibling(lucy, mary))) & ((~hate(mary, lucy)) \| client(lucy, mary))) & (((~rich(alice)) & (~creative(alice))) & like(lucy, alice))) & ?[X: $i] : ((~room(X)) => (client(lucy, X) => predb(X)))) & hate(mary, lucy)) & ?[X: $i] : ((~room(X)) => ((creative(X) & european(X)) => (~((creative(X) & rich(X)) & tourist(X))))))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)) \| (X = \|'alice'\|)))) & ?[X: $i, Y: $i] : (((~((((tall(X) & rich(X)) & quiet(X)) & brave(X)) & person(X))) & (~(Y = paul))) & 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] : richer(X, alice) & predb(mary) & sibling(lucy, mary) & ((~hate(mary, lucy)) \| client(lucy, mary)) & (~rich(alice)) & (~creative(alice)) & like(lucy, alice) & ?[X: $i] : (room(X) \| predb(X) \| (~client(lucy, X))) & hate(mary, lucy) & ?[X: $i] : (room(X) \| (~(creative(X) & rich(X) & tourist(X))) \| (~(creative(X) & european(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] : ((~(tall(X) & rich(X) & quiet(X) & brave(X) & person(X))) & (~(Y = paul)) & client(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'\|)))) & ((((((![X: $i] : richer(X, alice) & (predb(mary) & sibling(lucy, mary))) & ((~hate(mary, lucy)) \| client(lucy, mary))) & (((~rich(alice)) & (~creative(alice))) & like(lucy, alice))) & ?[X: $i] : ((~room(X)) => (client(lucy, X) => predb(X)))) & hate(mary, lucy)) & ?[X: $i] : ((~room(X)) => ((creative(X) & european(X)) => (~((creative(X) & rich(X)) & tourist(X))))))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)) \| (X = \|'alice'\|)))) & ?[X: $i, Y: $i] : (((~((((tall(X) & rich(X)) & quiet(X)) & brave(X)) & person(X))) & (~(Y = paul))) & client(X, Y))))), file('/mnt/tmpfs//594003562760700312754394.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))) & ![X: $i] : richer(X, alice) & predb(mary) & sibling(lucy, mary) & ((~hate(mary, lucy)) \| client(lucy, mary)) & (~rich(alice)) & (~creative(alice)) & like(lucy, alice) & ?[X: $i] : (room(X) \| predb(X) \| (~client(lucy, X))) & hate(mary, lucy) & ?[X: $i] : (room(X) \| (~(creative(X) & rich(X) & tourist(X))) \| (~(creative(X) & european(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] : ((~(tall(X) & rich(X) & quiet(X) & brave(X) & person(X))) & (~(Y = paul)) & client(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))) & ![X: $i] : richer(X, alice) & predb(mary) & sibling(lucy, mary) & ((~hate(mary, lucy)) \| client(lucy, mary)) & (~rich(alice)) & (~creative(alice)) & like(lucy, alice) & ?[X: $i] : (room(X) \| predb(X) \| (~client(lucy, X))) & hate(mary, lucy) & ?[X: $i] : (room(X) \| (~(creative(X) & rich(X) & tourist(X))) \| (~(creative(X) & european(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!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(24,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(25,plain, ((~![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| (X!2 = \|'alice'\|) \| (X!2 = \|'fred'\|) \| (X!2 = \|'paul'\|) \| (X!2 = \|'mary'\|) \| (~room(X!2))), inference(modus_ponens,[status(thm)],[24, 23])). tff(26,plain, ($false), inference(unit_resolution,[status(thm)],[25, 22, 11, 9, 7, 5, 3])). tff(27,plain,((X!2 = \|'alice'\|) \| (X!2 = \|'fred'\|) \| (X!2 = \|'paul'\|) \| (X!2 = \|'mary'\|) \| (~room(X!2))), 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!2 = \|'alice'\|) \| (X!2 = \|'fred'\|) \| (X!2 = \|'paul'\|) \| (X!2 = \|'mary'\|) \| (~room(X!2)))) \| ![X: $i, Y: $i] : ((Y = paul) \| (~((~rich(X)) \| (~tall(X)) \| (~quiet(X)) \| (~brave(X)) \| (~person(X)))) \| (~client(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] : ((Y = paul) \| (~((~rich(X)) \| (~tall(X)) \| (~quiet(X)) \| (~brave(X)) \| (~person(X)))) \| (~client(X, Y))))), inference(rewrite,[status(thm)],[])). tff(41,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] : ((Y = paul) \| (~((~rich(X)) \| (~tall(X)) \| (~quiet(X)) \| (~brave(X)) \| (~person(X)))) \| (~client(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] : ((Y = paul) \| (~((~rich(X)) \| (~tall(X)) \| (~quiet(X)) \| (~brave(X)) \| (~person(X)))) \| (~client(X, Y))))), inference(rewrite,[status(thm)],[])). tff(42,plain, (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((tall(X) & rich(X) & quiet(X) & brave(X) & person(X)) <=> (~((~rich(X)) \| (~tall(X)) \| (~quiet(X)) \| (~brave(X)) \| (~person(X))))), ((~(tall(X) & rich(X) & quiet(X) & brave(X) & person(X))) <=> (~(~((~rich(X)) \| (~tall(X)) \| (~quiet(X)) \| (~brave(X)) \| (~person(X))))))), rewrite((~(~((~rich(X)) \| (~tall(X)) \| (~quiet(X)) \| (~brave(X)) \| (~person(X))))) <=> ((~rich(X)) \| (~tall(X)) \| (~quiet(X)) \| (~brave(X)) \| (~person(X)))), ((~(tall(X) & rich(X) & quiet(X) & brave(X) & person(X))) <=> ((~rich(X)) \| (~tall(X)) \| (~quiet(X)) \| (~brave(X)) \| (~person(X))))), (((~(tall(X) & rich(X) & quiet(X) & brave(X) & person(X))) & (~(Y = paul)) & client(X, Y)) <=> (((~rich(X)) \| (~tall(X)) \| (~quiet(X)) \| (~brave(X)) \| (~person(X))) & (~(Y = paul)) & client(X, Y)))), rewrite((((~rich(X)) \| (~tall(X)) \| (~quiet(X)) \| (~brave(X)) \| (~person(X))) & (~(Y = paul)) & client(X, Y)) <=> (~((Y = paul) \| (~((~rich(X)) \| (~tall(X)) \| (~quiet(X)) \| (~brave(X)) \| (~person(X)))) \| (~client(X, Y))))), (((~(tall(X) & rich(X) & quiet(X) & brave(X) & person(X))) & (~(Y = paul)) & client(X, Y)) <=> (~((Y = paul) \| (~((~rich(X)) \| (~tall(X)) \| (~quiet(X)) \| (~brave(X)) \| (~person(X)))) \| (~client(X, Y)))))), ((~((~(tall(X) & rich(X) & quiet(X) & brave(X) & person(X))) & (~(Y = paul)) & client(X, Y))) <=> (~(~((Y = paul) \| (~((~rich(X)) \| (~tall(X)) \| (~quiet(X)) \| (~brave(X)) \| (~person(X)))) \| (~client(X, Y))))))), rewrite((~(~((Y = paul) \| (~((~rich(X)) \| (~tall(X)) \| (~quiet(X)) \| (~brave(X)) \| (~person(X)))) \| (~client(X, Y))))) <=> ((Y = paul) \| (~((~rich(X)) \| (~tall(X)) \| (~quiet(X)) \| (~brave(X)) \| (~person(X)))) \| (~client(X, Y)))), ((~((~(tall(X) & rich(X) & quiet(X) & brave(X) & person(X))) & (~(Y = paul)) & client(X, Y))) <=> ((Y = paul) \| (~((~rich(X)) \| (~tall(X)) \| (~quiet(X)) \| (~brave(X)) \| (~person(X)))) \| (~client(X, Y)))))), inference(bind,[status(th)],[])). tff(43,plain, (![X: $i, Y: $i] : (~((~(tall(X) & rich(X) & quiet(X) & brave(X) & person(X))) & (~(Y = paul)) & client(X, Y))) <=> ![X: $i, Y: $i] : ((Y = paul) \| (~((~rich(X)) \| (~tall(X)) \| (~quiet(X)) \| (~brave(X)) \| (~person(X)))) \| (~client(X, Y)))), inference(quant_intro,[status(thm)],[42])). tff(44,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(45,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] : (~((~(tall(X) & rich(X) & quiet(X) & brave(X) & person(X))) & (~(Y = paul)) & client(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] : ((Y = paul) \| (~((~rich(X)) \| (~tall(X)) \| (~quiet(X)) \| (~brave(X)) \| (~person(X)))) \| (~client(X, Y))))), inference(monotonicity,[status(thm)],[44, 43])). tff(46,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] : (~((~(tall(X) & rich(X) & quiet(X) & brave(X) & person(X))) & (~(Y = paul)) & client(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] : ((Y = paul) \| (~((~rich(X)) \| (~tall(X)) \| (~quiet(X)) \| (~brave(X)) \| (~person(X)))) \| (~client(X, Y))))), inference(transitivity,[status(thm)],[45, 41])). tff(47,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] : (~((~(tall(X) & rich(X) & quiet(X) & brave(X) & person(X))) & (~(Y = paul)) & client(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] : (~((~(tall(X) & rich(X) & quiet(X) & brave(X) & person(X))) & (~(Y = paul)) & client(X, Y))))), inference(rewrite,[status(thm)],[])). tff(48,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] : (~((~(tall(X) & rich(X) & quiet(X) & brave(X) & person(X))) & (~(Y = paul)) & client(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] : (~((~(tall(X) & rich(X) & quiet(X) & brave(X) & person(X))) & (~(Y = paul)) & client(X, Y))))), inference(monotonicity,[status(thm)],[44])). tff(49,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] : (~((~(tall(X) & rich(X) & quiet(X) & brave(X) & person(X))) & (~(Y = paul)) & client(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] : (~((~(tall(X) & rich(X) & quiet(X) & brave(X) & person(X))) & (~(Y = paul)) & client(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] : ((~(tall(X) & rich(X) & quiet(X) & brave(X) & person(X))) & (~(Y = paul)) & 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] : ((~(tall(X) & rich(X) & quiet(X) & brave(X) & person(X))) & (~(Y = paul)) & client(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] : ((~(tall(X) & rich(X) & quiet(X) & brave(X) & person(X))) & (~(Y = paul)) & 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] : ((~(tall(X) & rich(X) & quiet(X) & brave(X) & person(X))) & (~(Y = paul)) & client(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] : ((~(tall(X) & rich(X) & quiet(X) & brave(X) & person(X))) & (~(Y = paul)) & 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] : ((~(tall(X) & rich(X) & quiet(X) & brave(X) & person(X))) & (~(Y = paul)) & client(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] : ((~(tall(X) & rich(X) & quiet(X) & brave(X) & person(X))) & (~(Y = paul)) & client(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] : ((~(tall(X) & rich(X) & quiet(X) & brave(X) & person(X))) & (~(Y = paul)) & client(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] : ((~(tall(X) & rich(X) & quiet(X) & brave(X) & person(X))) & (~(Y = paul)) & client(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] : ((~(tall(X) & rich(X) & quiet(X) & brave(X) & person(X))) & (~(Y = paul)) & client(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!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 (not (and (tall X) (rich X) (quiet X) (brave X) (person X))) (not (= Y paul)) (client X Y)))) (refl (~ (not a!1) (not a!1)))))) (a!8 (exists ((X $i) (Y $i)) (and (not (and (tall X) (rich X) (quiet X) (brave X) (person X))) (not (= Y paul)) (client X Y)))) (a!9 (forall ((X $i) (Y $i)) (let ((a!1 (and (not (and (tall X) (rich X) (quiet X) (brave X) (person X))) (not (= Y paul)) (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(betty)&room(ricardo)&room(eric)&room(donald)&(![X]:(room(X)=>(X='betty'\|X='ricardo'\|X='eric'\|X='donald')))& ((![X]:(richer(X,donald)))& ((plays_a_string_instrument(betty))&(sibling(essie,betty)))& (((~hate(betty,essie))\|(client(essie,betty))))& ((~rich(donald)&~creative(donald))&(like(essie,donald)))& (?[X]:(~room(X)=>(((client(essie,X))=>(plays_a_string_instrument(X))))))& (hate(betty,essie))& (?[X]:(~room(X)=>(((creative(X)&european(X))=>(~(creative(X)&rich(X)&tourist(X))))))))	room(betty)&room(ricardo)&room(eric)&room(donald)&(![X]:(room(X)=>(X='betty'\|X='ricardo'\|X='eric'\|X='donald')))& (?[X,Y]:((~(tall(X)&rich(X)&quiet(X)&brave(X)&person(X)))&(Y!=ricardo)&(client(X,Y))))	contradiction	neutral	entailment
Ginger, Jan are the only persons in the room. "Steve is richer than Jan" if "Jan bakes bread at home". "Ginger is the least rich in the room" if "Ginger is the quietest in the room". Ginger is the least rich in the room. Jan is liked by Julie or is not liked by Julie or both. More than one person outside the room is not a quiet rich happy tall tourist. More than one person outside the room is a client of Steve. It is not the case that 'Steve is richer than Jan'. Jan is liked by Julie or is taller than Julie or both.	Jan neither is not a tall creative happy quiet tourist nor does not bake bread at home.	contradiction	-	room(ginger)&room(jan)&(![X]:(room(X)=>(X='ginger'\|X='jan')))& (((bakes_bread_at_home(jan))=>(richer(jan,steve)))& ((![X]:(quieter(X,ginger)))=>(![X]:(richer(ginger,X))))& (![X]:(richer(ginger,X)))& (((like(jan,julie))\|(~like(jan,julie))))& ((?[X,Y]:(~room(X)&~room(Y)&(~(quiet(X)&rich(X)&happy(X)&tall(X)&tourist(X))&~(quiet(Y)&rich(Y)&happy(Y)&tall(Y)&tourist(Y)))&(X!=Y))))& ((?[X,Y]:(~room(X)&~room(Y)&(client(steve,X)&client(steve,Y))&(X!=Y))))& (~(richer(jan,steve)))& (((like(jan,julie))\|(taller(julie,jan)))))	room(ginger)&room(jan)&(![X]:(room(X)=>(X='ginger'\|X='jan')))& (~((~(tall(jan)&creative(jan)&happy(jan)&quiet(jan)&tourist(jan)))\|(does_not_bake_bread_at_home(jan))))	contradiction	neutral	neutral
Curtis, William, Mia, Robert are the only persons in the room. William who is hated by Carroll, is not hated by Curtis. Robert is the quietest in the room. It is not the case that 'it is not the case that 'it is not the case that 'Mia is a rich brave european or is not a rich happy person or both'''. Robert and William are respectively quiet and rich. Curtis who does not hate Curtis, does not hate Carroll. Mia and Curtis are not brave, not quiet. Someone in the room is not a brave european. Curtis who is hated by Carroll, is richer than Curtis. Only one person in the room is quieter than Curtis.	William who is quieter than Curtis, is richer than Curtis.	contradiction	-	room(curtis)&room(william)&room(mia)&room(robert)&(![X]:(room(X)=>(X='curtis'\|X='william'\|X='mia'\|X='robert')))& (((hate(william,carroll))&(~hate(william,curtis)))& (![X]:(quieter(X,robert)))& (~(~(~(((rich(mia)&brave(mia)&european(mia))\|(~(rich(mia)&happy(mia)&person(mia))))))))& ((quiet(robert))&(rich(william)))& ((~hate(curtis,curtis))&(~hate(carroll,curtis)))& (~brave(mia)&~quiet(mia)&~brave(curtis)&~quiet(curtis))& (?[X]:(room(X)=>(~(brave(X)&european(X)))))& ((hate(curtis,carroll))&(richer(curtis,curtis)))& (((?[X]:(room(X)&quieter(curtis,X)))&(![X,Y]:((quieter(curtis,X)&quieter(curtis,Y))=>(X=Y))))))	room(curtis)&room(william)&room(mia)&room(robert)&(![X]:(room(X)=>(X='curtis'\|X='william'\|X='mia'\|X='robert')))& ((quieter(curtis,william))&(richer(curtis,william)))	entailment	entailment	contradiction
Agnes, Paul, Thomas are the only persons in the room. If "Jeffrey is a client of Agnes" then "more than one person in the room is hated by Kimberly". If "Agnes neither is liked by Jeffrey nor likes Jeffrey" then "everyone in the room who is a client of Denise does not collect vintage stamps". "Paul collects vintage stamps or hates Jeffrey or both" if "only one person outside the room hates Marie". If "Paul is the tallest in the room" then "Agnes who is hated by Denise, does not collect vintage stamps". If "someone who is not liked by Jeffrey is richer than someone who is not tall, not quiet" then "only one person outside the room does not travel domestically frequently". Kimberly and Marie hate each other. Someone outside the room who is not quiet collects vintage stamps. Agnes is taller than Denise and hates Jeffrey. Paul is taller than Denise or is a client of Kimberly or both. Everyone in the room is liked by Marie. Someone in the room who is hated by Kimberly hates Denise. Agnes does not hate Denise or hates Denise or both.	Agnes who likes Jeffrey, is not a tall quiet person.	contradiction	-	room(agnes)&room(paul)&room(thomas)&(![X]:(room(X)=>(X='agnes'\|X='paul'\|X='thomas')))& (((client(agnes,jeffrey))=>((?[X,Y]:(room(X)&room(Y)&(hate(X,kimberly)&hate(Y,kimberly))&(X!=Y)))))& ((~((like(agnes,jeffrey))\|(like(jeffrey,agnes))))=>(![X]:(room(X)=>(((client(denise,X))=>(does_not_collect_vintage_stamps(X)))))))& ((((?[X]:(~room(X)&hate(marie,X)))&(![X,Y]:((hate(marie,X)&hate(marie,Y))=>(X=Y)))))=>(((collects_vintage_stamps(paul))\|(hate(jeffrey,paul)))))& ((![X]:(taller(X,paul)))=>((hate(agnes,denise))&(does_not_collect_vintage_stamps(agnes))))& ((?[X,Y]:((~like(X,jeffrey))&(~tall(Y)&~quiet(Y))&(richer(X,Y))))=>(((?[X]:(~room(X)&does_not_travel_domestically_frequently(X)))&(![X,Y]:((does_not_travel_domestically_frequently(X)&does_not_travel_domestically_frequently(Y))=>(X=Y))))))& ((hate(kimberly,marie) & hate(marie,kimberly)))& (?[X]:(~room(X)=>(((~quiet(X))=>(collects_vintage_stamps(X))))))& ((taller(denise,agnes))&(hate(jeffrey,agnes)))& (((taller(denise,paul))\|(client(kimberly,paul))))& (![X]:(room(X)=>(like(X,marie))))& (?[X]:(room(X)=>(((hate(X,kimberly))=>(hate(denise,X))))))& (((~hate(denise,agnes))\|(hate(denise,agnes)))))	room(agnes)&room(paul)&room(thomas)&(![X]:(room(X)=>(X='agnes'\|X='paul'\|X='thomas')))& ((like(jeffrey,agnes))&(~(tall(agnes)&quiet(agnes)&person(agnes))))	contradiction	neutral	contradiction
Alyson, Francine, Sandra, Maritza are the only persons in the room. Someone who does not have a piercing is quieter than someone who is not Maritza. More than one person in the room does not hate Stacy. Maritza and Francine are respectively quiet and creative. Stacy is quieter than Maritza. Everyone in the room is hated by Maritza. Maritza and Francine hate each other. Maritza is not a happy quiet tourist and is not a quiet european. Sandra is hated by Maritza and is not happy. Francine is the quietest in the room. Francine is a quiet creative european or is a quiet happy tourist or both. Alyson is hated by Maritza and is not quiet.	Francine is not hated by Maritza or is a creative quiet rich happy person or both.	neutral	% SZS status Satisfiable	room(alyson)&room(francine)&room(sandra)&room(maritza)&(![X]:(room(X)=>(X='alyson'\|X='francine'\|X='sandra'\|X='maritza')))& ((?[X,Y]:((does_not_have_a_piercing(X))&(Y!=maritza)&(quieter(X,Y))))& ((?[X,Y]:(room(X)&room(Y)&(~hate(stacy,X)&~hate(stacy,Y))&(X!=Y))))& ((quiet(maritza))&(creative(francine)))& (quieter(maritza,stacy))& (![X]:(room(X)=>(hate(X,maritza))))& ((hate(maritza,francine) & hate(francine,maritza)))& ((~(happy(maritza)&quiet(maritza)&tourist(maritza)))&(~(quiet(maritza)&european(maritza))))& ((hate(sandra,maritza))&(~happy(sandra)))& (![X]:(quieter(X,francine)))& (((quiet(francine)&creative(francine)&european(francine))\|(quiet(francine)&happy(francine)&tourist(francine))))& ((hate(alyson,maritza))&(~quiet(alyson))))	room(alyson)&room(francine)&room(sandra)&room(maritza)&(![X]:(room(X)=>(X='alyson'\|X='francine'\|X='sandra'\|X='maritza')))& (((~hate(francine,maritza))\|(creative(francine)&quiet(francine)&rich(francine)&happy(francine)&person(francine))))	contradiction	entailment	contradiction
Betty is the only person in the room. “Betty is not quiet or is quieter than Justin or both” only if “no one outside the room who is not a quiet person does not like Estelle”. Everyone outside the room who enjoys landscape photography is a quiet person. More than one person outside the room does not like Ana. More than one person outside the room is not Betty.	Betty neither is not a rich tall person nor is a quiet person.	contradiction	-	room(betty)&(![X]:(room(X)=>(X='betty')))& (((((~quiet(betty))\|(quieter(justin,betty))))=>(~?[X]:(~room(X)=>(((~(quiet(X)&person(X)))=>(~like(estelle,X)))))))& (![X]:(~room(X)=>(((enjoys_landscape_photography(X))=>(quiet(X)&person(X))))))& ((?[X,Y]:(~room(X)&~room(Y)&(~like(ana,X)&~like(ana,Y))&(X!=Y))))& ((?[X,Y]:(~room(X)&~room(Y)&(X!=betty&Y!=betty)&(X!=Y)))))	room(betty)&(![X]:(room(X)=>(X='betty')))& (~((~(rich(betty)&tall(betty)&person(betty)))\|(quiet(betty)&person(betty))))	neutral	contradiction	neutral
Nicole, Michael, Scott, Neil are the only persons in the room. “Someone in the room is not a brave creative european” if “John is richer than Michael” and vice versa. John is richer than Michael. Only one person outside the room is not a creative person. It is not the case that 'Neil is a tall happy european'.	Nicole is not a creative european and is a rich happy european.	contradiction	-	room(nicole)&room(michael)&room(scott)&room(neil)&(![X]:(room(X)=>(X='nicole'\|X='michael'\|X='scott'\|X='neil')))& (((richer(michael,john))<=>(?[X]:(room(X)=>(~(brave(X)&creative(X)&european(X))))))& (richer(michael,john))& (((?[X]:(~room(X)&~(creative(X)&person(X))))&(![X,Y]:((~(creative(X)&person(X))&~(creative(Y)&person(Y)))=>(X=Y)))))& (~(tall(neil)&happy(neil)&european(neil))))	room(nicole)&room(michael)&room(scott)&room(neil)&(![X]:(room(X)=>(X='nicole'\|X='michael'\|X='scott'\|X='neil')))& ((~(creative(nicole)&european(nicole)))&(rich(nicole)&happy(nicole)&european(nicole)))	contradiction	neutral	contradiction
Albert, Robert, Stacey, Judith are the only persons in the room. If "Stacey is the least tall in the room" then "Robert and Stacey are respectively tall and happy" otherwise "no one outside the room is not creative". "Ron is taller than Albert" if "Albert neither is a creative happy tall tourist nor bakes bread at home" and vice versa. "Someone who is not tall is taller than someone who is a happy creative tourist" if "Albert and Stacey are respectively creative and tall". If "Robert likes Ron or is liked by Ron or both" then "Albert and Robert are respectively tall and creative". Someone outside the room is taller than Ron. Robert is the tallest in the room. Albert and Robert are respectively happy and creative. Albert is the least tall in the room. Stacey neither is liked by Ron nor does not bake bread at home. Robert is not a creative tourist and is liked by Ron.	Someone who does not hate Ron is taller than someone who is not creative, not tall.	contradiction	-	room(albert)&room(robert)&room(stacey)&room(judith)&(![X]:(room(X)=>(X='albert'\|X='robert'\|X='stacey'\|X='judith')))& ((((![X]:(taller(stacey,X)))=>((tall(robert))&(happy(stacey))))\|((~(![X]:(taller(stacey,X))))=>(~?[X]:(~room(X)=>(~creative(X))))))& ((~((creative(albert)&happy(albert)&tall(albert)&tourist(albert))\|(bakes_bread_at_home(albert))))<=>(taller(albert,ron)))& (((creative(albert))&(tall(stacey)))=>(?[X,Y]:((~tall(X))&(happy(Y)&creative(Y)&tourist(Y))&(taller(X,Y)))))& ((((like(ron,robert))\|(like(robert,ron))))=>((tall(albert))&(creative(robert))))& (?[X]:(~room(X)=>(taller(ron,X))))& (![X]:(taller(X,robert)))& ((happy(albert))&(creative(robert)))& (![X]:(taller(albert,X)))& (~((like(stacey,ron))\|(does_not_bake_bread_at_home(stacey))))& ((~(creative(robert)&tourist(robert)))&(like(robert,ron))))	room(albert)&room(robert)&room(stacey)&room(judith)&(![X]:(room(X)=>(X='albert'\|X='robert'\|X='stacey'\|X='judith')))& (?[X,Y]:((~hate(ron,X))&(~creative(Y)&~tall(Y))&(taller(X,Y))))	entailment	neutral	neutral
Alex, Samantha, Dorothy are the only persons in the room. Alex is the least rich in the room if Fernando is richer than Samantha and vice versa. Dorothy enjoys pottery and is not brave if Samantha and Dorothy are respectively brave and rich. Alex and Samantha are respectively rich and brave. More than one person in the room is a rich tourist. Dorothy enjoys pottery and is not brave. Everyone outside the room who is not a rich tourist is not Alex. James is richer than Samantha. Fernando is richer than Dorothy. More than one person outside the room is richer than Fernando.	Alex is not Samantha or is a rich brave tourist or both.	entailment	% SZS status Unsatisfiable % SZS output start Proof tff(room_type, type, ( room: $i > $o)). tff(tptp_fun_X_5_type, type, ( tptp_fun_X_5: $i)). tff(tptp_fun__mary__type, type, ( tptp_fun__mary_: $i)). tff(tptp_fun__paul__type, type, ( tptp_fun__paul_: $i)). tff(tptp_fun__fred__type, type, ( tptp_fun__fred_: $i)). tff(brave_type, type, ( brave: $i > $o)). tff(mary_type, type, ( mary: $i)). tff(tourist_type, type, ( tourist: $i > $o)). tff(rich_type, type, ( rich: $i > $o)). tff(paul_type, type, ( paul: $i)). tff(fred_type, type, ( fred: $i)). tff(alice_type, type, ( alice: $i)). tff(john_type, type, ( john: $i)). tff(susan_type, type, ( susan: $i)). tff(lucy_type, type, ( lucy: $i)). tff(richer_type, type, ( richer: ( $i * $i ) > $o)). tff(predb_type, type, ( predb: $i > $o)). tff(1,plain, ((~(mary = paul)) <=> (~(mary = paul))), 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//92456001231200294619708.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, ((((((((((((((((((((((~(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)],[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))), 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))), 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))), 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))), 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))), 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))), 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))), 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))), 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))), 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))), 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))), 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))), 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))), 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))), inference(and_elim,[status(thm)],[35])). tff(37,plain, (((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))), inference(and_elim,[status(thm)],[36])). tff(38,plain, ((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))), inference(and_elim,[status(thm)],[37])). tff(39,plain, (((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))), inference(and_elim,[status(thm)],[38])). tff(40,plain, ((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))), inference(and_elim,[status(thm)],[39])). tff(41,plain, (((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))), inference(and_elim,[status(thm)],[40])). tff(42,plain, ((~(mary = paul)) & (~(mary = fred))), inference(and_elim,[status(thm)],[41])). tff(43,plain, (~(mary = paul)), inference(and_elim,[status(thm)],[42])). tff(44,plain, (~(mary = paul)), inference(modus_ponens,[status(thm)],[43, 1])). tff(45,plain, (((~(mary = paul)) \| (~((~rich(mary)) \| (~tourist(mary)) \| (~brave(mary))))) \| (mary = paul)), inference(tautology,[status(thm)],[])). tff(46,plain, ((~(mary = paul)) \| (~((~rich(mary)) \| (~tourist(mary)) \| (~brave(mary))))), inference(unit_resolution,[status(thm)],[45, 44])). tff(47,plain, (room(fred) <=> room(fred)), inference(rewrite,[status(thm)],[])). tff(48,plain, ((~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)))) & (((((((((richer(paul, john) <=> ![X: $i] : richer(mary, X)) & ((brave(paul) & rich(fred)) => (predb(fred) & (~brave(fred))))) & (rich(mary) & brave(paul))) & ?[X: $i, Y: $i] : (((room(X) & room(Y)) & (((rich(X) & tourist(X)) & rich(Y)) & tourist(Y))) & (~(X = Y)))) & (predb(fred) & (~brave(fred)))) & ![X: $i] : ((~room(X)) => ((~(rich(X) & tourist(X))) => (~(X = mary))))) & richer(paul, susan)) & richer(fred, john)) & ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & (richer(john, X) & richer(john, Y))) & (~(X = Y))))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)))) & ((~(mary = paul)) \| ((rich(mary) & brave(mary)) & tourist(mary)))))) <=> (~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (richer(paul, john) <=> ![X: $i] : richer(mary, X)) & ((~(brave(paul) & rich(fred))) \| (predb(fred) & (~brave(fred)))) & rich(mary) & brave(paul) & ?[X: $i, Y: $i] : (room(X) & room(Y) & rich(X) & tourist(X) & rich(Y) & tourist(Y) & (~(X = Y))) & predb(fred) & (~brave(fred)) & (room(mary) \| (rich(mary) & tourist(mary))) & richer(paul, susan) & richer(fred, john) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & richer(john, X) & richer(john, Y) & (~(X = Y))))) \| (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((~(mary = paul)) \| (rich(mary) & brave(mary) & tourist(mary))))))), inference(rewrite,[status(thm)],[])). tff(49,axiom,(~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)))) & (((((((((richer(paul, john) <=> ![X: $i] : richer(mary, X)) & ((brave(paul) & rich(fred)) => (predb(fred) & (~brave(fred))))) & (rich(mary) & brave(paul))) & ?[X: $i, Y: $i] : (((room(X) & room(Y)) & (((rich(X) & tourist(X)) & rich(Y)) & tourist(Y))) & (~(X = Y)))) & (predb(fred) & (~brave(fred)))) & ![X: $i] : ((~room(X)) => ((~(rich(X) & tourist(X))) => (~(X = mary))))) & richer(paul, susan)) & richer(fred, john)) & ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & (richer(john, X) & richer(john, Y))) & (~(X = Y))))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)))) & ((~(mary = paul)) \| ((rich(mary) & brave(mary)) & tourist(mary)))))), file('/mnt/tmpfs//92456001231200294619708.p','negated')). tff(50,plain, (~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (richer(paul, john) <=> ![X: $i] : richer(mary, X)) & ((~(brave(paul) & rich(fred))) \| (predb(fred) & (~brave(fred)))) & rich(mary) & brave(paul) & ?[X: $i, Y: $i] : (room(X) & room(Y) & rich(X) & tourist(X) & rich(Y) & tourist(Y) & (~(X = Y))) & predb(fred) & (~brave(fred)) & (room(mary) \| (rich(mary) & tourist(mary))) & richer(paul, susan) & richer(fred, john) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & richer(john, X) & richer(john, Y) & (~(X = Y))))) \| (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((~(mary = paul)) \| (rich(mary) & brave(mary) & tourist(mary)))))), inference(modus_ponens,[status(thm)],[49, 48])). tff(51,plain, (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (richer(paul, john) <=> ![X: $i] : richer(mary, X)) & ((~(brave(paul) & rich(fred))) \| (predb(fred) & (~brave(fred)))) & rich(mary) & brave(paul) & ?[X: $i, Y: $i] : (room(X) & room(Y) & rich(X) & tourist(X) & rich(Y) & tourist(Y) & (~(X = Y))) & predb(fred) & (~brave(fred)) & (room(mary) \| (rich(mary) & tourist(mary))) & richer(paul, susan) & richer(fred, john) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & richer(john, X) & richer(john, Y) & (~(X = Y)))), inference(or_elim,[status(thm)],[50])). tff(52,plain, (room(fred)), inference(and_elim,[status(thm)],[51])). tff(53,plain, (room(fred)), inference(modus_ponens,[status(thm)],[52, 47])). tff(54,plain, (room(paul) <=> room(paul)), inference(rewrite,[status(thm)],[])). tff(55,plain, (room(paul)), inference(and_elim,[status(thm)],[51])). tff(56,plain, (room(paul)), inference(modus_ponens,[status(thm)],[55, 54])). tff(57,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(58,plain, (room(mary)), inference(and_elim,[status(thm)],[51])). tff(59,plain, (room(mary)), inference(modus_ponens,[status(thm)],[58, 57])). tff(60,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!5 = \|'fred'\|) \| (X!5 = \|'paul'\|) \| (X!5 = \|'mary'\|) \| (~room(X!5)))) \| (~((~(mary = paul)) \| (~((~rich(mary)) \| (~tourist(mary)) \| (~brave(mary))))))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!5 = \|'fred'\|) \| (X!5 = \|'paul'\|) \| (X!5 = \|'mary'\|) \| (~room(X!5)))) \| (~((~(mary = paul)) \| (~((~rich(mary)) \| (~tourist(mary)) \| (~brave(mary)))))))), inference(rewrite,[status(thm)],[])). tff(61,plain, ((~((~(mary = paul)) \| (rich(mary) & brave(mary) & tourist(mary)))) <=> (~((~(mary = paul)) \| (~((~rich(mary)) \| (~tourist(mary)) \| (~brave(mary))))))), inference(rewrite,[status(thm)],[])). tff(62,plain, ((~((X!5 = \|'fred'\|) \| (X!5 = \|'paul'\|) \| (X!5 = \|'mary'\|) \| (~room(X!5)))) <=> (~((X!5 = \|'fred'\|) \| (X!5 = \|'paul'\|) \| (X!5 = \|'mary'\|) \| (~room(X!5))))), inference(rewrite,[status(thm)],[])). tff(63,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!5 = \|'fred'\|) \| (X!5 = \|'paul'\|) \| (X!5 = \|'mary'\|) \| (~room(X!5)))) \| (~((~(mary = paul)) \| (rich(mary) & brave(mary) & tourist(mary))))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!5 = \|'fred'\|) \| (X!5 = \|'paul'\|) \| (X!5 = \|'mary'\|) \| (~room(X!5)))) \| (~((~(mary = paul)) \| (~((~rich(mary)) \| (~tourist(mary)) \| (~brave(mary)))))))), inference(monotonicity,[status(thm)],[62, 61])). tff(64,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!5 = \|'fred'\|) \| (X!5 = \|'paul'\|) \| (X!5 = \|'mary'\|) \| (~room(X!5)))) \| (~((~(mary = paul)) \| (rich(mary) & brave(mary) & tourist(mary))))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!5 = \|'fred'\|) \| (X!5 = \|'paul'\|) \| (X!5 = \|'mary'\|) \| (~room(X!5)))) \| (~((~(mary = paul)) \| (~((~rich(mary)) \| (~tourist(mary)) \| (~brave(mary)))))))), inference(transitivity,[status(thm)],[63, 60])). tff(65,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!5 = \|'fred'\|) \| (X!5 = \|'paul'\|) \| (X!5 = \|'mary'\|) \| (~room(X!5)))) \| (~((~(mary = paul)) \| (rich(mary) & brave(mary) & tourist(mary))))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!5 = \|'fred'\|) \| (X!5 = \|'paul'\|) \| (X!5 = \|'mary'\|) \| (~room(X!5)))) \| (~((~(mary = paul)) \| (rich(mary) & brave(mary) & tourist(mary)))))), inference(rewrite,[status(thm)],[])). tff(66,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!5 = \|'fred'\|) \| (X!5 = \|'paul'\|) \| (X!5 = \|'mary'\|) \| (~room(X!5)))) \| (~((~(mary = paul)) \| (rich(mary) & brave(mary) & tourist(mary))))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!5 = \|'fred'\|) \| (X!5 = \|'paul'\|) \| (X!5 = \|'mary'\|) \| (~room(X!5)))) \| (~((~(mary = paul)) \| (rich(mary) & brave(mary) & tourist(mary)))))), inference(monotonicity,[status(thm)],[62])). tff(67,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!5 = \|'fred'\|) \| (X!5 = \|'paul'\|) \| (X!5 = \|'mary'\|) \| (~room(X!5)))) \| (~((~(mary = paul)) \| (rich(mary) & brave(mary) & tourist(mary))))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!5 = \|'fred'\|) \| (X!5 = \|'paul'\|) \| (X!5 = \|'mary'\|) \| (~room(X!5)))) \| (~((~(mary = paul)) \| (rich(mary) & brave(mary) & tourist(mary)))))), inference(transitivity,[status(thm)],[66, 65])). tff(68,plain, ((room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((~(mary = paul)) \| (rich(mary) & brave(mary) & tourist(mary)))) <=> (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((~(mary = paul)) \| (rich(mary) & brave(mary) & tourist(mary))))), inference(rewrite,[status(thm)],[])). tff(69,plain, ((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((~(mary = paul)) \| (rich(mary) & brave(mary) & tourist(mary))))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((~(mary = paul)) \| (rich(mary) & brave(mary) & tourist(mary)))))), inference(monotonicity,[status(thm)],[68])). tff(70,plain, ((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((~(mary = paul)) \| (rich(mary) & brave(mary) & tourist(mary))))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((~(mary = paul)) \| (rich(mary) & brave(mary) & tourist(mary)))))), inference(rewrite,[status(thm)],[])). tff(71,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((~(mary = paul)) \| (rich(mary) & brave(mary) & tourist(mary))))), inference(or_elim,[status(thm)],[50])). tff(72,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((~(mary = paul)) \| (rich(mary) & brave(mary) & tourist(mary))))), inference(modus_ponens,[status(thm)],[71, 69])). tff(73,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((~(mary = paul)) \| (rich(mary) & brave(mary) & tourist(mary))))), inference(modus_ponens,[status(thm)],[72, 70])). tff(74,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((~(mary = paul)) \| (rich(mary) & brave(mary) & tourist(mary))))), inference(modus_ponens,[status(thm)],[73, 69])). 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!5 \|'fred'\|) (= X!5 \|'paul'\|) (= X!5 \|'mary'\|) (not (room X!5))))) (a!6 (or (not (= mary paul)) (and (rich mary) (brave mary) (tourist mary))))) (let ((a!7 (~ (not (and (room mary) (room paul) (room fred) a!4 a!6)) (or (not (room mary)) (not (room paul)) (not (room fred)) a!5 (not a!6))))) (nnf-neg a!1 a!2 a!3 (sk (~ (not a!4) a!5)) (refl (~ (not a!6) (not a!6))) a!7)))	room(alex)&room(samantha)&room(dorothy)&(![X]:(room(X)=>(X='alex'\|X='samantha'\|X='dorothy')))& (((richer(samantha,fernando))<=>(![X]:(richer(alex,X))))& (((brave(samantha))&(rich(dorothy)))=>((enjoys_pottery(dorothy))&(~brave(dorothy))))& ((rich(alex))&(brave(samantha)))& ((?[X,Y]:(room(X)&room(Y)&(rich(X)&tourist(X)&rich(Y)&tourist(Y))&(X!=Y))))& ((enjoys_pottery(dorothy))&(~brave(dorothy)))& (![X]:(~room(X)=>(((~(rich(X)&tourist(X)))=>(X!=alex)))))& (richer(samantha,james))& (richer(dorothy,fernando))& ((?[X,Y]:(~room(X)&~room(Y)&(richer(fernando,X)&richer(fernando,Y))&(X!=Y)))))	room(alex)&room(samantha)&room(dorothy)&(![X]:(room(X)=>(X='alex'\|X='samantha'\|X='dorothy')))& (((alex!=samantha)\|(rich(alex)&brave(alex)&tourist(alex))))	contradiction	entailment	entailment
Ryan, Christopher, Juan, Effie are the only persons in the room. Only one person outside the room is hated by Mary. Christopher and Ryan hate each other. Effie does not hate Williams and does not hate Mary. Ryan is the least tall in the room.	It is not the case that 'Ryan who is taller than Mary, hates Mary'.	entailment	% SZS status Unsatisfiable % SZS output start Proof tff(tptp_fun__mary__type, type, ( tptp_fun__mary_: $i)). tff(tptp_fun_X_1_type, type, ( tptp_fun_X_1: $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(room_type, type, ( room: $i > $o)). tff(hate_type, type, ( hate: ( $i * $i ) > $o)). tff(mary_type, type, ( mary: $i)). tff(susan_type, type, ( susan: $i)). tff(taller_type, type, ( taller: ( $i * $i ) > $o)). tff(alice_type, type, ( alice: $i)). tff(john_type, type, ( john: $i)). tff(paul_type, type, ( paul: $i)). tff(fred_type, type, ( fred: $i)). tff(lucy_type, type, ( lucy: $i)). tff(1,assumption,(~taller(mary, susan)), introduced(assumption)). tff(2,plain, (^[X: $i] : refl(taller(mary, X) <=> taller(mary, X))), inference(bind,[status(th)],[])). tff(3,plain, (![X: $i] : taller(mary, X) <=> ![X: $i] : taller(mary, X)), inference(quant_intro,[status(thm)],[2])). tff(4,plain, (![X: $i] : taller(mary, X) <=> ![X: $i] : taller(mary, X)), 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'\|)))) & ((((?[X: $i] : ((~room(X)) & hate(X, susan)) & ![X: $i, Y: $i] : ((hate(X, susan) & hate(Y, susan)) => (X = Y))) & (hate(paul, mary) & hate(mary, paul))) & ((~hate(john, alice)) & (~hate(susan, alice)))) & ![X: $i] : taller(mary, X))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)) \| (X = \|'alice'\|)))) & (~(taller(susan, mary) & hate(susan, mary)))))) <=> (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) \| (X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|)) & ?[X: $i] : ((~room(X)) & hate(X, susan)) & ![X: $i, Y: $i] : ((~(hate(X, susan) & hate(Y, susan))) \| (X = Y)) & hate(paul, mary) & hate(mary, paul) & (~hate(john, alice)) & (~hate(susan, alice)) & ![X: $i] : taller(mary, X))) \| (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) \| (X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|)) & (~(taller(susan, mary) & hate(susan, mary))))))), 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'\|)))) & ((((?[X: $i] : ((~room(X)) & hate(X, susan)) & ![X: $i, Y: $i] : ((hate(X, susan) & hate(Y, susan)) => (X = Y))) & (hate(paul, mary) & hate(mary, paul))) & ((~hate(john, alice)) & (~hate(susan, alice)))) & ![X: $i] : taller(mary, X))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)) \| (X = \|'alice'\|)))) & (~(taller(susan, mary) & hate(susan, mary)))))), file('/mnt/tmpfs//3402331071354162466887529.p','negated')). tff(7,plain, (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) \| (X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|)) & ?[X: $i] : ((~room(X)) & hate(X, susan)) & ![X: $i, Y: $i] : ((~(hate(X, susan) & hate(Y, susan))) \| (X = Y)) & hate(paul, mary) & hate(mary, paul) & (~hate(john, alice)) & (~hate(susan, alice)) & ![X: $i] : taller(mary, X))) \| (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) \| (X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|)) & (~(taller(susan, mary) & hate(susan, mary)))))), inference(modus_ponens,[status(thm)],[6, 5])). tff(8,plain, (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) \| (X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|)) & ?[X: $i] : ((~room(X)) & hate(X, susan)) & ![X: $i, Y: $i] : ((~(hate(X, susan) & hate(Y, susan))) \| (X = Y)) & hate(paul, mary) & hate(mary, paul) & (~hate(john, alice)) & (~hate(susan, alice)) & ![X: $i] : taller(mary, X)), inference(or_elim,[status(thm)],[7])). tff(9,plain, (![X: $i] : taller(mary, X)), inference(and_elim,[status(thm)],[8])). tff(10,plain, (![X: $i] : taller(mary, X)), inference(modus_ponens,[status(thm)],[9, 4])). tff(11,plain,( ![X: $i] : taller(mary, X)), inference(skolemize,[status(sab)],[10])). tff(12,plain, (![X: $i] : taller(mary, X)), inference(modus_ponens,[status(thm)],[11, 3])). tff(13,plain, ((~![X: $i] : taller(mary, X)) \| taller(mary, susan)), inference(quant_inst,[status(thm)],[])). tff(14,plain, ($false), inference(unit_resolution,[status(thm)],[13, 12, 1])). tff(15,plain,(taller(mary, susan)), inference(lemma,lemma(discharge,[]))). tff(16,plain, ((~(susan = mary)) <=> (~(susan = mary))), inference(rewrite,[status(thm)],[])). tff(17,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//3402331071354162466887529.p','b14')). tff(18,plain, (((((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))) & (~(lucy = alice))) & (~(lucy = john))), inference(and_elim,[status(thm)],[17])). tff(19,plain, ((((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))) & (~(lucy = alice))), inference(and_elim,[status(thm)],[18])). tff(20,plain, (((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))), inference(and_elim,[status(thm)],[19])). tff(21,plain, ((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))), 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))), 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))), 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))), 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))), 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))), 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))), 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))), inference(and_elim,[status(thm)],[27])). tff(29,plain, (~(susan = mary)), inference(and_elim,[status(thm)],[28])). tff(30,plain, (~(susan = mary)), inference(modus_ponens,[status(thm)],[29, 16])). tff(31,plain, (![X: $i, Y: $i] : ((X = Y) \| (~taller(Y, X)) \| (~taller(X, Y))) <=> ![X: $i, Y: $i] : ((X = Y) \| (~taller(Y, X)) \| (~taller(X, Y)))), inference(rewrite,[status(thm)],[])). tff(32,plain, (![X: $i, Y: $i] : ((X = Y) \| (~taller(Y, X)) \| (~taller(X, Y))) <=> ![X: $i, Y: $i] : ((X = Y) \| (~taller(Y, X)) \| (~taller(X, Y)))), inference(rewrite,[status(thm)],[])). tff(33,plain, (^[X: $i, Y: $i] : trans(monotonicity(rewrite((taller(X, Y) => (~taller(Y, X))) <=> ((~taller(Y, X)) \| (~taller(X, Y)))), (((~(X = Y)) => (taller(X, Y) => (~taller(Y, X)))) <=> ((~(X = Y)) => ((~taller(Y, X)) \| (~taller(X, Y)))))), rewrite(((~(X = Y)) => ((~taller(Y, X)) \| (~taller(X, Y)))) <=> ((X = Y) \| (~taller(Y, X)) \| (~taller(X, Y)))), (((~(X = Y)) => (taller(X, Y) => (~taller(Y, X)))) <=> ((X = Y) \| (~taller(Y, X)) \| (~taller(X, Y)))))), inference(bind,[status(th)],[])). tff(34,plain, (![X: $i, Y: $i] : ((~(X = Y)) => (taller(X, Y) => (~taller(Y, X)))) <=> ![X: $i, Y: $i] : ((X = Y) \| (~taller(Y, X)) \| (~taller(X, Y)))), inference(quant_intro,[status(thm)],[33])). tff(35,axiom,(![X: $i, Y: $i] : ((~(X = Y)) => (taller(X, Y) => (~taller(Y, X))))), file('/mnt/tmpfs//3402331071354162466887529.p','b10')). tff(36,plain, (![X: $i, Y: $i] : ((X = Y) \| (~taller(Y, X)) \| (~taller(X, Y)))), inference(modus_ponens,[status(thm)],[35, 34])). tff(37,plain, (![X: $i, Y: $i] : ((X = Y) \| (~taller(Y, X)) \| (~taller(X, Y)))), inference(modus_ponens,[status(thm)],[36, 32])). tff(38,plain,( ![X: $i, Y: $i] : ((X = Y) \| (~taller(Y, X)) \| (~taller(X, Y)))), inference(skolemize,[status(sab)],[37])). tff(39,plain, (![X: $i, Y: $i] : ((X = Y) \| (~taller(Y, X)) \| (~taller(X, Y)))), inference(modus_ponens,[status(thm)],[38, 31])). tff(40,plain, (((~![X: $i, Y: $i] : ((X = Y) \| (~taller(Y, X)) \| (~taller(X, Y)))) \| ((susan = mary) \| (~taller(susan, mary)) \| (~taller(mary, susan)))) <=> ((~![X: $i, Y: $i] : ((X = Y) \| (~taller(Y, X)) \| (~taller(X, Y)))) \| (susan = mary) \| (~taller(susan, mary)) \| (~taller(mary, susan)))), inference(rewrite,[status(thm)],[])). tff(41,plain, (((susan = mary) \| (~taller(mary, susan)) \| (~taller(susan, mary))) <=> ((susan = mary) \| (~taller(susan, mary)) \| (~taller(mary, susan)))), inference(rewrite,[status(thm)],[])). tff(42,plain, (((~![X: $i, Y: $i] : ((X = Y) \| (~taller(Y, X)) \| (~taller(X, Y)))) \| ((susan = mary) \| (~taller(mary, susan)) \| (~taller(susan, mary)))) <=> ((~![X: $i, Y: $i] : ((X = Y) \| (~taller(Y, X)) \| (~taller(X, Y)))) \| ((susan = mary) \| (~taller(susan, mary)) \| (~taller(mary, susan))))), inference(monotonicity,[status(thm)],[41])). tff(43,plain, (((~![X: $i, Y: $i] : ((X = Y) \| (~taller(Y, X)) \| (~taller(X, Y)))) \| ((susan = mary) \| (~taller(mary, susan)) \| (~taller(susan, mary)))) <=> ((~![X: $i, Y: $i] : ((X = Y) \| (~taller(Y, X)) \| (~taller(X, Y)))) \| (susan = mary) \| (~taller(susan, mary)) \| (~taller(mary, susan)))), inference(transitivity,[status(thm)],[42, 40])). tff(44,plain, ((~![X: $i, Y: $i] : ((X = Y) \| (~taller(Y, X)) \| (~taller(X, Y)))) \| ((susan = mary) \| (~taller(mary, susan)) \| (~taller(susan, mary)))), inference(quant_inst,[status(thm)],[])). tff(45,plain, ((~![X: $i, Y: $i] : ((X = Y) \| (~taller(Y, X)) \| (~taller(X, Y)))) \| (susan = mary) \| (~taller(susan, mary)) \| (~taller(mary, susan))), inference(modus_ponens,[status(thm)],[44, 43])). tff(46,plain, ((~taller(susan, mary)) \| (~taller(mary, susan))), inference(unit_resolution,[status(thm)],[45, 39, 30])). tff(47,plain, (~taller(susan, mary)), inference(unit_resolution,[status(thm)],[46, 15])). tff(48,plain, (((~taller(susan, mary)) \| (~hate(susan, mary))) \| taller(susan, mary)), inference(tautology,[status(thm)],[])). tff(49,plain, ((~taller(susan, mary)) \| (~hate(susan, mary))), 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)],[8])). 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)],[8])). 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)],[8])). 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)],[8])). tff(61,plain, (room(mary)), inference(modus_ponens,[status(thm)],[60, 59])). tff(62,plain, (((~((~taller(susan, mary)) \| (~hate(susan, mary)))) \| (~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~room(alice)) \| (~((~room(X!1)) \| (X!1 = \|'alice'\|) \| (X!1 = \|'fred'\|) \| (X!1 = \|'paul'\|) \| (X!1 = \|'mary'\|)))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~room(alice)) \| (~((~room(X!1)) \| (X!1 = \|'alice'\|) \| (X!1 = \|'fred'\|) \| (X!1 = \|'paul'\|) \| (X!1 = \|'mary'\|))) \| (~((~taller(susan, mary)) \| (~hate(susan, mary)))))), inference(rewrite,[status(thm)],[])). tff(63,plain, ((~((~room(X!1)) \| (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'\|)))), inference(rewrite,[status(thm)],[])). tff(64,plain, ((taller(susan, mary) & hate(susan, mary)) <=> (~((~taller(susan, mary)) \| (~hate(susan, mary))))), inference(rewrite,[status(thm)],[])). tff(65,plain, (((taller(susan, mary) & hate(susan, mary)) \| (~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~room(alice)) \| (~((~room(X!1)) \| (X!1 = \|'alice'\|) \| (X!1 = \|'fred'\|) \| (X!1 = \|'paul'\|) \| (X!1 = \|'mary'\|)))) <=> ((~((~taller(susan, mary)) \| (~hate(susan, mary)))) \| (~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~room(alice)) \| (~((~room(X!1)) \| (X!1 = \|'alice'\|) \| (X!1 = \|'fred'\|) \| (X!1 = \|'paul'\|) \| (X!1 = \|'mary'\|))))), inference(monotonicity,[status(thm)],[64, 63])). tff(66,plain, (((taller(susan, mary) & hate(susan, mary)) \| (~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~room(alice)) \| (~((~room(X!1)) \| (X!1 = \|'alice'\|) \| (X!1 = \|'fred'\|) \| (X!1 = \|'paul'\|) \| (X!1 = \|'mary'\|)))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~room(alice)) \| (~((~room(X!1)) \| (X!1 = \|'alice'\|) \| (X!1 = \|'fred'\|) \| (X!1 = \|'paul'\|) \| (X!1 = \|'mary'\|))) \| (~((~taller(susan, mary)) \| (~hate(susan, mary)))))), inference(transitivity,[status(thm)],[65, 62])). tff(67,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~room(alice)) \| (~((~room(X!1)) \| (X!1 = \|'alice'\|) \| (X!1 = \|'fred'\|) \| (X!1 = \|'paul'\|) \| (X!1 = \|'mary'\|))) \| (taller(susan, mary) & hate(susan, mary))) <=> ((taller(susan, mary) & hate(susan, mary)) \| (~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~room(alice)) \| (~((~room(X!1)) \| (X!1 = \|'alice'\|) \| (X!1 = \|'fred'\|) \| (X!1 = \|'paul'\|) \| (X!1 = \|'mary'\|))))), inference(rewrite,[status(thm)],[])). tff(68,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~room(alice)) \| (~((~room(X!1)) \| (X!1 = \|'alice'\|) \| (X!1 = \|'fred'\|) \| (X!1 = \|'paul'\|) \| (X!1 = \|'mary'\|))) \| (taller(susan, mary) & hate(susan, mary))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~room(alice)) \| (~((~room(X!1)) \| (X!1 = \|'alice'\|) \| (X!1 = \|'fred'\|) \| (X!1 = \|'paul'\|) \| (X!1 = \|'mary'\|))) \| (taller(susan, mary) & hate(susan, mary)))), inference(monotonicity,[status(thm)],[63])). tff(69,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~room(alice)) \| (~((~room(X!1)) \| (X!1 = \|'alice'\|) \| (X!1 = \|'fred'\|) \| (X!1 = \|'paul'\|) \| (X!1 = \|'mary'\|))) \| (taller(susan, mary) & hate(susan, mary))) <=> ((taller(susan, mary) & hate(susan, mary)) \| (~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~room(alice)) \| (~((~room(X!1)) \| (X!1 = \|'alice'\|) \| (X!1 = \|'fred'\|) \| (X!1 = \|'paul'\|) \| (X!1 = \|'mary'\|))))), inference(transitivity,[status(thm)],[68, 67])). tff(70,plain, ((room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) \| (X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|)) & (~(taller(susan, mary) & hate(susan, mary)))) <=> (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) \| (X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|)) & (~(taller(susan, mary) & hate(susan, mary))))), inference(rewrite,[status(thm)],[])). tff(71,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) \| (X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|)) & (~(taller(susan, mary) & hate(susan, mary))))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) \| (X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|)) & (~(taller(susan, mary) & hate(susan, mary)))))), inference(monotonicity,[status(thm)],[70])). tff(72,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) \| (X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|)) & (~(taller(susan, mary) & hate(susan, mary))))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) \| (X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|)) & (~(taller(susan, mary) & hate(susan, mary)))))), inference(rewrite,[status(thm)],[])). tff(73,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) \| (X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|)) & (~(taller(susan, mary) & hate(susan, mary))))), inference(or_elim,[status(thm)],[7])). tff(74,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) \| (X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|)) & (~(taller(susan, mary) & hate(susan, mary))))), inference(modus_ponens,[status(thm)],[73, 71])). tff(75,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) \| (X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|)) & (~(taller(susan, mary) & hate(susan, mary))))), inference(modus_ponens,[status(thm)],[74, 72])). tff(76,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) \| (X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|)) & (~(taller(susan, mary) & hate(susan, mary))))), inference(modus_ponens,[status(thm)],[75, 71])). 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 (not (room X)) (= X \|'alice'\|) (= X \|'fred'\|) (= X \|'paul'\|) (= X \|'mary'\|)))) (a!6 (not (or (not (room X!1)) (= X!1 \|'alice'\|) (= X!1 \|'fred'\|) (= X!1 \|'paul'\|) (= X!1 \|'mary'\|)))) (a!7 (refl (~ (and (taller susan mary) (hate susan mary)) (and (taller susan mary) (hate susan mary)))))) (let ((a!8 (and (room mary) (room paul) (room fred) (room alice) a!5 (not (and (taller susan mary) (hate susan mary)))))) (let ((a!9 (~ (not a!8) (or (not (room mary)) (not (room paul)) (not (room fred)) (not (room alice)) a!6 (and (taller susan mary) (hate susan mary)))))) (nnf-neg a!1 a!2 a!3 a!4 (sk (~ (not a!5) a!6)) a!7 a!9))))	room(ryan)&room(christopher)&room(juan)&room(effie)&(![X]:(room(X)=>(X='ryan'\|X='christopher'\|X='juan'\|X='effie')))& ((((?[X]:(~room(X)&hate(X,mary)))&(![X,Y]:((hate(X,mary)&hate(Y,mary))=>(X=Y)))))& ((hate(christopher,ryan) & hate(ryan,christopher)))& ((~hate(williams,effie))&(~hate(mary,effie)))& (![X]:(taller(ryan,X))))	room(ryan)&room(christopher)&room(juan)&room(effie)&(![X]:(room(X)=>(X='ryan'\|X='christopher'\|X='juan'\|X='effie')))& (~((taller(mary,ryan))&(hate(mary,ryan))))	contradiction	entailment	contradiction
James is the only person in the room. If James is the richest in the room then James is richer than James and is a brave tourist. Everyone outside the room who is not James is hated by Thomas. James is the least rich in the room. James neither is a rich brave tourist nor is hated by Patricia.	Someone who is richer than James is quieter than someone who is hated by Thomas.	neutral	% SZS status Satisfiable	room(james)&(![X]:(room(X)=>(X='james')))& (((![X]:(richer(X,james)))=>((richer(james,james))&(brave(james)&tourist(james))))& (![X]:(~room(X)=>(((X!=james)=>(hate(X,thomas))))))& (![X]:(richer(james,X)))& (~((rich(james)&brave(james)&tourist(james))\|(hate(james,patricia)))))	room(james)&(![X]:(room(X)=>(X='james')))& (?[X,Y]:((richer(james,X))&(hate(Y,thomas))&(quieter(X,Y))))	neutral	neutral	entailment
At least one of the following is true:. -Marilyn is a rich european or is not liked by Blaine or both. -Marilyn is not a happy rich tourist or does not practice archery or both.	Marilyn practices archery and is a tall rich creative quiet happy european.	neutral	% SZS status Satisfiable	room(marilyn)&(![X]:(room(X)=>(X='marilyn')))& (((((rich(marilyn)&european(marilyn))\|(~like(marilyn,blaine))))\| (((~(happy(marilyn)&rich(marilyn)&tourist(marilyn)))\|(does_not_practice_archery(marilyn))))))	room(marilyn)&(![X]:(room(X)=>(X='marilyn')))& ((practices_archery(marilyn))&(tall(marilyn)&rich(marilyn)&creative(marilyn)&quiet(marilyn)&happy(marilyn)&european(marilyn)))	contradiction	neutral	contradiction
Thomas, Francesrick are the only persons in the room. Only one person outside the room is liked by Terry. Everyone outside the room who is not creative, not happy is taller than Terry.	It is not the case that 'Francesrick either is not a creative person or likes Thad'.	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(paul_type, type, ( paul: $i)). tff(happy_type, type, ( happy: $i > $o)). tff(creative_type, type, ( creative: $i > $o)). tff(taller_type, type, ( taller: ( $i * $i ) > $o)). tff(susan_type, type, ( susan: $i)). tff(like_type, type, ( like: ( $i * $i ) > $o)). tff(mary_type, type, ( mary: $i)). tff(lucy_type, type, ( lucy: $i)). tff(person_type, type, ( person: $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)) & like(X, susan)) & ![X: $i, Y: $i] : ((like(X, susan) & like(Y, susan)) => (X = Y))) & ![X: $i] : ((~room(X)) => (((~creative(X)) & (~happy(X))) => taller(susan, X))))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = \|'mary'\|) \| (X = \|'paul'\|)))) & (~(((~(creative(paul) & person(paul))) \| like(lucy, paul)) & (~((~(creative(paul) & person(paul))) \| like(lucy, paul)))))))) <=> (~((~(room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ?[X: $i] : ((~room(X)) & like(X, susan)) & ![X: $i, Y: $i] : ((~(like(X, susan) & like(Y, susan))) \| (X = Y)) & ![X: $i] : (room(X) \| taller(susan, X) \| (~((~creative(X)) & (~happy(X))))))) \| (room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))))))), inference(rewrite,[status(thm)],[])). tff(3,axiom,(~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = \|'mary'\|) \| (X = \|'paul'\|)))) & ((?[X: $i] : ((~room(X)) & like(X, susan)) & ![X: $i, Y: $i] : ((like(X, susan) & like(Y, susan)) => (X = Y))) & ![X: $i] : ((~room(X)) => (((~creative(X)) & (~happy(X))) => taller(susan, X))))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = \|'mary'\|) \| (X = \|'paul'\|)))) & (~(((~(creative(paul) & person(paul))) \| like(lucy, paul)) & (~((~(creative(paul) & person(paul))) \| like(lucy, paul)))))))), file('/mnt/tmpfs//810963892634399796848158.p','negated')). tff(4,plain, (~((~(room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ?[X: $i] : ((~room(X)) & like(X, susan)) & ![X: $i, Y: $i] : ((~(like(X, susan) & like(Y, susan))) \| (X = Y)) & ![X: $i] : (room(X) \| taller(susan, X) \| (~((~creative(X)) & (~happy(X))))))) \| (room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))))), inference(modus_ponens,[status(thm)],[3, 2])). tff(5,plain, (room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ?[X: $i] : ((~room(X)) & like(X, susan)) & ![X: $i, Y: $i] : ((~(like(X, susan) & like(Y, susan))) \| (X = Y)) & ![X: $i] : (room(X) \| taller(susan, X) \| (~((~creative(X)) & (~happy(X)))))), inference(or_elim,[status(thm)],[4])). tff(6,plain, (room(paul)), inference(and_elim,[status(thm)],[5])). tff(7,plain, (room(paul)), inference(modus_ponens,[status(thm)],[6, 1])). tff(8,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(9,plain, (room(mary)), inference(and_elim,[status(thm)],[5])). tff(10,plain, (room(mary)), inference(modus_ponens,[status(thm)],[9, 8])). tff(11,plain, ((~((X!1 = \|'paul'\|) \| (X!1 = \|'mary'\|) \| (~room(X!1)))) <=> (~((X!1 = \|'paul'\|) \| (X!1 = \|'mary'\|) \| (~room(X!1))))), inference(rewrite,[status(thm)],[])). tff(12,plain, (((~room(mary)) \| (~room(paul)) \| (~((X!1 = \|'paul'\|) \| (X!1 = \|'mary'\|) \| (~room(X!1))))) <=> ((~room(mary)) \| (~room(paul)) \| (~((X!1 = \|'paul'\|) \| (X!1 = \|'mary'\|) \| (~room(X!1)))))), 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!1 \|'paul'\|) (= X!1 \|'mary'\|) (not (room X!1)))))) (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(thomas)&room(francesrick)&(![X]:(room(X)=>(X='thomas'\|X='francesrick')))& ((((?[X]:(~room(X)&like(X,terry)))&(![X,Y]:((like(X,terry)&like(Y,terry))=>(X=Y)))))& (![X]:(~room(X)=>(((~creative(X)&~happy(X))=>(taller(terry,X)))))))	room(thomas)&room(francesrick)&(![X]:(room(X)=>(X='thomas'\|X='francesrick')))& (~((((~(creative(francesrick)&person(francesrick)))\|(like(thad,francesrick)))&(~((~(creative(francesrick)&person(francesrick)))\|(like(thad,francesrick)))))))	entailment	entailment	entailment
Michael, Gregory, Joshua, Amy are the only persons in the room. If everyone outside the room is not Joshua then Amy is the least rich in the room. Juanita is a client of Michael. Amy who is a brave rich quiet tourist, is not Michael. It is not the case that 'someone who collects rare minerals like someone who is not Michael'. More than one person in the room does not collect rare minerals.	Michael who is not rich, is not a happy creative quiet tourist.	contradiction	-	room(michael)&room(gregory)&room(joshua)&room(amy)&(![X]:(room(X)=>(X='michael'\|X='gregory'\|X='joshua'\|X='amy')))& (((![X]:(~room(X)=>(X!=joshua)))=>(![X]:(richer(amy,X))))& (client(michael,juanita))& ((brave(amy)&rich(amy)&quiet(amy)&tourist(amy))&(amy!=michael))& (~(?[X,Y]:((collects_rare_minerals(X))&(Y!=michael)&(like(X,Y)))))& ((?[X,Y]:(room(X)&room(Y)&(does_not_collect_rare_minerals(X)&does_not_collect_rare_minerals(Y))&(X!=Y)))))	room(michael)&room(gregory)&room(joshua)&room(amy)&(![X]:(room(X)=>(X='michael'\|X='gregory'\|X='joshua'\|X='amy')))& ((~rich(michael))&(~(happy(michael)&creative(michael)&quiet(michael)&tourist(michael))))	entailment	neutral	neutral
Richard is a tall rich creative person and is liked by Veronica. Richard is a tall european or is a creative european or both.	Richard is a rich european or hates Veronica 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(hate_type, type, ( hate: ( $i * $i ) > $o)). tff(mary_type, type, ( mary: $i)). tff(susan_type, type, ( susan: $i)). tff(rich_type, type, ( rich: $i > $o)). tff(european_type, type, ( european: $i > $o)). tff(tall_type, type, ( tall: $i > $o)). tff(creative_type, type, ( creative: $i > $o)). tff(like_type, type, ( like: ( $i * $i ) > $o)). tff(person_type, type, ( person: $i > $o)). tff(fred_type, type, ( fred: $i)). tff(paul_type, type, ( paul: $i)). tff(1,assumption,(~european(mary)), introduced(assumption)). tff(2,plain, (((~tall(mary)) \| (~european(mary))) \| european(mary)), inference(tautology,[status(thm)],[])). tff(3,plain, ((~tall(mary)) \| (~european(mary))), inference(unit_resolution,[status(thm)],[2, 1])). tff(4,plain, (((~creative(mary)) \| (~european(mary))) \| european(mary)), inference(tautology,[status(thm)],[])). tff(5,plain, ((~creative(mary)) \| (~european(mary))), inference(unit_resolution,[status(thm)],[4, 1])). tff(6,plain, (((~((~tall(mary)) \| (~european(mary)))) \| (~((~creative(mary)) \| (~european(mary))))) <=> ((~((~tall(mary)) \| (~european(mary)))) \| (~((~creative(mary)) \| (~european(mary)))))), inference(rewrite,[status(thm)],[])). tff(7,plain, ((creative(mary) & european(mary)) <=> (~((~creative(mary)) \| (~european(mary))))), inference(rewrite,[status(thm)],[])). tff(8,plain, ((tall(mary) & european(mary)) <=> (~((~tall(mary)) \| (~european(mary))))), inference(rewrite,[status(thm)],[])). tff(9,plain, (((tall(mary) & european(mary)) \| (creative(mary) & european(mary))) <=> ((~((~tall(mary)) \| (~european(mary)))) \| (~((~creative(mary)) \| (~european(mary)))))), inference(monotonicity,[status(thm)],[8, 7])). tff(10,plain, (((tall(mary) & european(mary)) \| (creative(mary) & european(mary))) <=> ((~((~tall(mary)) \| (~european(mary)))) \| (~((~creative(mary)) \| (~european(mary)))))), inference(transitivity,[status(thm)],[9, 6])). tff(11,plain, (((tall(mary) & european(mary)) \| (creative(mary) & european(mary))) <=> ((tall(mary) & european(mary)) \| (creative(mary) & european(mary)))), inference(rewrite,[status(thm)],[])). tff(12,plain, ((~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)))) & (((((tall(mary) & rich(mary)) & creative(mary)) & person(mary)) & like(mary, susan)) & ((tall(mary) & european(mary)) \| (creative(mary) & european(mary))))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)))) & ((rich(mary) & european(mary)) \| hate(susan, mary))))) <=> (~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & tall(mary) & rich(mary) & creative(mary) & person(mary) & like(mary, susan) & ((tall(mary) & european(mary)) \| (creative(mary) & european(mary))))) \| (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((rich(mary) & european(mary)) \| hate(susan, mary)))))), inference(rewrite,[status(thm)],[])). tff(13,axiom,(~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)))) & (((((tall(mary) & rich(mary)) & creative(mary)) & person(mary)) & like(mary, susan)) & ((tall(mary) & european(mary)) \| (creative(mary) & european(mary))))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)))) & ((rich(mary) & european(mary)) \| hate(susan, mary))))), file('/mnt/tmpfs//130226098803814570552871.p','negated')). tff(14,plain, (~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & tall(mary) & rich(mary) & creative(mary) & person(mary) & like(mary, susan) & ((tall(mary) & european(mary)) \| (creative(mary) & european(mary))))) \| (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((rich(mary) & european(mary)) \| hate(susan, mary))))), inference(modus_ponens,[status(thm)],[13, 12])). tff(15,plain, (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & tall(mary) & rich(mary) & creative(mary) & person(mary) & like(mary, susan) & ((tall(mary) & european(mary)) \| (creative(mary) & european(mary)))), inference(or_elim,[status(thm)],[14])). tff(16,plain, ((tall(mary) & european(mary)) \| (creative(mary) & european(mary))), inference(and_elim,[status(thm)],[15])). tff(17,plain, ((tall(mary) & european(mary)) \| (creative(mary) & european(mary))), inference(modus_ponens,[status(thm)],[16, 11])). tff(18,plain, ((tall(mary) & european(mary)) \| (creative(mary) & european(mary))), inference(modus_ponens,[status(thm)],[17, 11])). tff(19,plain, ((tall(mary) & european(mary)) \| (creative(mary) & european(mary))), inference(modus_ponens,[status(thm)],[18, 11])). tff(20,plain, ((tall(mary) & european(mary)) \| (creative(mary) & european(mary))), inference(modus_ponens,[status(thm)],[19, 11])). tff(21,plain, ((~((~tall(mary)) \| (~european(mary)))) \| (~((~creative(mary)) \| (~european(mary))))), inference(modus_ponens,[status(thm)],[20, 10])). tff(22,plain, ($false), inference(unit_resolution,[status(thm)],[21, 5, 3])). tff(23,plain,(european(mary)), inference(lemma,lemma(discharge,[]))). tff(24,plain, (rich(mary) <=> rich(mary)), inference(rewrite,[status(thm)],[])). tff(25,plain, (rich(mary)), inference(and_elim,[status(thm)],[15])). tff(26,plain, (rich(mary)), inference(modus_ponens,[status(thm)],[25, 24])). tff(27,plain, ((~((~european(mary)) \| (~rich(mary)))) \| (~european(mary)) \| (~rich(mary))), inference(tautology,[status(thm)],[])). tff(28,plain, ((~((~european(mary)) \| (~rich(mary)))) \| (~european(mary))), inference(unit_resolution,[status(thm)],[27, 26])). tff(29,plain, (~((~european(mary)) \| (~rich(mary)))), inference(unit_resolution,[status(thm)],[28, 23])). tff(30,plain, (((~((~european(mary)) \| (~rich(mary)))) \| hate(susan, mary)) \| ((~european(mary)) \| (~rich(mary)))), inference(tautology,[status(thm)],[])). tff(31,plain, ((~((~european(mary)) \| (~rich(mary)))) \| hate(susan, mary)), inference(unit_resolution,[status(thm)],[30, 29])). tff(32,plain, (room(fred) <=> room(fred)), inference(rewrite,[status(thm)],[])). tff(33,plain, (room(fred)), inference(and_elim,[status(thm)],[15])). tff(34,plain, (room(fred)), inference(modus_ponens,[status(thm)],[33, 32])). tff(35,plain, (room(paul) <=> room(paul)), inference(rewrite,[status(thm)],[])). tff(36,plain, (room(paul)), inference(and_elim,[status(thm)],[15])). tff(37,plain, (room(paul)), inference(modus_ponens,[status(thm)],[36, 35])). tff(38,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(39,plain, (room(mary)), inference(and_elim,[status(thm)],[15])). tff(40,plain, (room(mary)), inference(modus_ponens,[status(thm)],[39, 38])). tff(41,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!0 = \|'fred'\|) \| (X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0)))) \| (~((~((~european(mary)) \| (~rich(mary)))) \| hate(susan, mary)))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!0 = \|'fred'\|) \| (X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0)))) \| (~((~((~european(mary)) \| (~rich(mary)))) \| hate(susan, mary))))), inference(rewrite,[status(thm)],[])). tff(42,plain, ((~((rich(mary) & european(mary)) \| hate(susan, mary))) <=> (~((~((~european(mary)) \| (~rich(mary)))) \| hate(susan, mary)))), inference(rewrite,[status(thm)],[])). tff(43,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(44,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!0 = \|'fred'\|) \| (X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0)))) \| (~((rich(mary) & european(mary)) \| hate(susan, mary)))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!0 = \|'fred'\|) \| (X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0)))) \| (~((~((~european(mary)) \| (~rich(mary)))) \| hate(susan, mary))))), inference(monotonicity,[status(thm)],[43, 42])). tff(45,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!0 = \|'fred'\|) \| (X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0)))) \| (~((rich(mary) & european(mary)) \| hate(susan, mary)))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!0 = \|'fred'\|) \| (X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0)))) \| (~((~((~european(mary)) \| (~rich(mary)))) \| hate(susan, mary))))), inference(transitivity,[status(thm)],[44, 41])). tff(46,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!0 = \|'fred'\|) \| (X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0)))) \| (~((rich(mary) & european(mary)) \| hate(susan, mary)))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!0 = \|'fred'\|) \| (X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0)))) \| (~((rich(mary) & european(mary)) \| hate(susan, mary))))), inference(rewrite,[status(thm)],[])). tff(47,plain, (((rich(mary) & european(mary)) \| hate(susan, mary)) <=> ((rich(mary) & european(mary)) \| hate(susan, mary))), inference(rewrite,[status(thm)],[])). tff(48,plain, ((~((rich(mary) & european(mary)) \| hate(susan, mary))) <=> (~((rich(mary) & european(mary)) \| hate(susan, mary)))), inference(monotonicity,[status(thm)],[47])). tff(49,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!0 = \|'fred'\|) \| (X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0)))) \| (~((rich(mary) & european(mary)) \| hate(susan, mary)))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!0 = \|'fred'\|) \| (X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0)))) \| (~((rich(mary) & european(mary)) \| hate(susan, mary))))), inference(monotonicity,[status(thm)],[43, 48])). tff(50,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!0 = \|'fred'\|) \| (X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0)))) \| (~((rich(mary) & european(mary)) \| hate(susan, mary)))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!0 = \|'fred'\|) \| (X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0)))) \| (~((rich(mary) & european(mary)) \| hate(susan, mary))))), inference(transitivity,[status(thm)],[49, 46])). tff(51,plain, ((room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((rich(mary) & european(mary)) \| hate(susan, mary))) <=> (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((rich(mary) & european(mary)) \| hate(susan, mary)))), inference(rewrite,[status(thm)],[])). tff(52,plain, ((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((rich(mary) & european(mary)) \| hate(susan, mary)))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((rich(mary) & european(mary)) \| hate(susan, mary))))), inference(monotonicity,[status(thm)],[51])). tff(53,plain, ((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((rich(mary) & european(mary)) \| hate(susan, mary)))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((rich(mary) & european(mary)) \| hate(susan, mary))))), inference(rewrite,[status(thm)],[])). tff(54,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((rich(mary) & european(mary)) \| hate(susan, mary)))), inference(or_elim,[status(thm)],[14])). tff(55,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((rich(mary) & european(mary)) \| hate(susan, mary)))), inference(modus_ponens,[status(thm)],[54, 52])). tff(56,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((rich(mary) & european(mary)) \| hate(susan, mary)))), inference(modus_ponens,[status(thm)],[55, 53])). tff(57,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((rich(mary) & european(mary)) \| hate(susan, mary)))), inference(modus_ponens,[status(thm)],[56, 52])). 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))))) (a!6 (not (or (and (rich mary) (european mary)) (hate susan mary))))) (let ((a!7 (and (room mary) (room paul) (room fred) a!4 (or (and (rich mary) (european mary)) (hate susan mary))))) (let ((a!8 (~ (not a!7) (or (not (room mary)) (not (room paul)) (not (room fred)) a!5 a!6)))) (nnf-neg a!1 a!2 a!3 (sk (~ (not a!4) a!5)) (refl (~ a!6 a!6)) a!8))))	room(richard)&room(curt)&room(donald)&(![X]:(room(X)=>(X='richard'\|X='curt'\|X='donald')))& (((tall(richard)&rich(richard)&creative(richard)&person(richard))&(like(richard,veronica)))& (((tall(richard)&european(richard))\|(creative(richard)&european(richard)))))	room(richard)&room(curt)&room(donald)&(![X]:(room(X)=>(X='richard'\|X='curt'\|X='donald')))& (((rich(richard)&european(richard))\|(hate(veronica,richard))))	contradiction	contradiction	neutral
Matthew, George, Jodi are the only persons in the room. If 'Jodi is the least quiet in the room' then 'someone who does not enjoy snowboarding is a sibling of someone who enjoys snowboarding'. Matthew hates Curtis or enjoys snowboarding or both. Matthew and Curtis hate each other.	Matthew neither is a sibling of Curtis nor is not hated by Curtis.	neutral	% SZS status Satisfiable	room(matthew)&room(george)&room(jodi)&(![X]:(room(X)=>(X='matthew'\|X='george'\|X='jodi')))& (((![X]:(quieter(jodi,X)))=>(?[X,Y]:((does_not_enjoy_snowboarding(X))&(enjoys_snowboarding(Y))&(sibling(X,Y)))))& (((hate(curtis,matthew))\|(enjoys_snowboarding(matthew))))& ((hate(matthew,curtis) & hate(curtis,matthew))))	room(matthew)&room(george)&room(jodi)&(![X]:(room(X)=>(X='matthew'\|X='george'\|X='jodi')))& (~((sibling(curtis,matthew))\|(~hate(matthew,curtis))))	entailment	contradiction	entailment
Stephanie, Sharon, Monica, Nancy are the only persons in the room. "Stephanie is the quietest in the room" only if "it is not the case that 'Denise and Sharon like each other'". If "Sharon is the tallest in the room" then "more than one person outside the room hates Alberta" otherwise "everyone outside the room who is a sibling of Denise is a sibling of Alberta". "Stephanie and Monica are not a tall person" if "Stephanie can play the guitar or is a brave person or both". "Sharon either is not quiet or is hated by Denise" if "Sharon and Monica are respectively tall and quiet" and vice versa. Someone outside the room who likes Alberta is not a tall european. More than one person outside the room is liked by Alberta. Stephanie hates Denise and does not can play the guitar. Alberta is taller than Stephanie. Monica neither is not a creative tall quiet european nor does not hate Denise. Stephanie is a creative european or is liked by Alberta or both. More than one person outside the room uses contact lenses. It is not the case that 'Denise and Sharon like each other'.	Sharon is not a creative brave tall quiet european or hates Rafaela or both.	entailment	% SZS status Unsatisfiable % SZS output start Proof tff(room_type, type, ( room: $i > $o)). tff(tptp_fun_X_6_type, type, ( tptp_fun_X_6: $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(paul_type, type, ( paul: $i)). tff(brave_type, type, ( brave: $i > $o)). tff(creative_type, type, ( creative: $i > $o)). tff(tall_type, type, ( tall: $i > $o)). tff(hate_type, type, ( hate: ( $i * $i ) > $o)). tff(susan_type, type, ( susan: $i)). tff(quiet_type, type, ( quiet: $i > $o)). tff(fred_type, type, ( fred: $i)). tff(lucy_type, type, ( lucy: $i)). tff(like_type, type, ( like: ( $i * $i ) > $o)). tff(predb_type, type, ( predb: $i > $o)). tff(john_type, type, ( john: $i)). tff(mary_type, type, ( mary: $i)). tff(taller_type, type, ( taller: ( $i * $i ) > $o)). tff(preda_type, type, ( preda: $i > $o)). tff(person_type, type, ( person: $i > $o)). tff(quieter_type, type, ( quieter: ( $i * $i ) > $o)). tff(alice_type, type, ( alice: $i)). tff(sibling_type, type, ( sibling: ( $i * $i ) > $o)). tff(1,plain, (quiet(fred) <=> quiet(fred)), 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] : quieter(X, mary) => (~(like(lucy, paul) & like(paul, lucy)))) & ((![X: $i] : taller(X, paul) => ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & (hate(john, X) & hate(john, Y))) & (~(X = Y)))) \| ((~![X: $i] : taller(X, paul)) => ![X: $i] : ((~room(X)) => (sibling(lucy, X) => sibling(john, X)))))) & ((preda(mary) \| (brave(mary) & person(mary))) => ((~(tall(mary) & person(mary))) & (~(tall(fred) & person(fred)))))) & ((tall(paul) & quiet(fred)) <=> (((~quiet(paul)) \| hate(paul, lucy)) & (~((~quiet(paul)) \| hate(paul, lucy)))))) & ?[X: $i] : ((~room(X)) => (like(john, X) => (~(tall(X) & european(X)))))) & ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & (like(X, john) & like(Y, john))) & (~(X = Y)))) & (hate(lucy, mary) & (~preda(mary)))) & taller(mary, john)) & (~((~(((creative(fred) & tall(fred)) & quiet(fred)) & european(fred))) \| (~hate(lucy, fred))))) & ((creative(mary) & european(mary)) \| like(mary, john))) & ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & (predb(X) & predb(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'\|)))) & ((~((((creative(paul) & brave(paul)) & tall(paul)) & quiet(paul)) & european(paul))) \| hate(susan, paul))))) <=> (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((~(like(lucy, paul) & like(paul, lucy))) \| (~![X: $i] : quieter(X, mary))) & ((~(preda(mary) \| (brave(mary) & person(mary)))) \| ((~(tall(mary) & person(mary))) & (~(tall(fred) & person(fred))))) & (~(tall(paul) & quiet(fred))) & ?[X: $i] : (room(X) \| (~(tall(X) & european(X))) \| (~like(john, X))) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & like(X, john) & like(Y, john) & (~(X = Y))) & hate(lucy, mary) & (~preda(mary)) & taller(mary, john) & (~((~hate(lucy, fred)) \| (~(creative(fred) & tall(fred) & quiet(fred) & european(fred))))) & ((creative(mary) & european(mary)) \| like(mary, john)) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & predb(X) & predb(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))) & ((~(creative(paul) & brave(paul) & tall(paul) & quiet(paul) & european(paul))) \| hate(susan, paul)))))), inference(rewrite,[status(thm)],[])). tff(3,axiom,(~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)) \| (X = \|'alice'\|)))) & ((((((((((((![X: $i] : quieter(X, mary) => (~(like(lucy, paul) & like(paul, lucy)))) & ((![X: $i] : taller(X, paul) => ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & (hate(john, X) & hate(john, Y))) & (~(X = Y)))) \| ((~![X: $i] : taller(X, paul)) => ![X: $i] : ((~room(X)) => (sibling(lucy, X) => sibling(john, X)))))) & ((preda(mary) \| (brave(mary) & person(mary))) => ((~(tall(mary) & person(mary))) & (~(tall(fred) & person(fred)))))) & ((tall(paul) & quiet(fred)) <=> (((~quiet(paul)) \| hate(paul, lucy)) & (~((~quiet(paul)) \| hate(paul, lucy)))))) & ?[X: $i] : ((~room(X)) => (like(john, X) => (~(tall(X) & european(X)))))) & ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & (like(X, john) & like(Y, john))) & (~(X = Y)))) & (hate(lucy, mary) & (~preda(mary)))) & taller(mary, john)) & (~((~(((creative(fred) & tall(fred)) & quiet(fred)) & european(fred))) \| (~hate(lucy, fred))))) & ((creative(mary) & european(mary)) \| like(mary, john))) & ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & (predb(X) & predb(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'\|)))) & ((~((((creative(paul) & brave(paul)) & tall(paul)) & quiet(paul)) & european(paul))) \| hate(susan, paul))))), file('/mnt/tmpfs//7520999298238670359633365.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(lucy, paul) & like(paul, lucy))) \| (~![X: $i] : quieter(X, mary))) & ((~(preda(mary) \| (brave(mary) & person(mary)))) \| ((~(tall(mary) & person(mary))) & (~(tall(fred) & person(fred))))) & (~(tall(paul) & quiet(fred))) & ?[X: $i] : (room(X) \| (~(tall(X) & european(X))) \| (~like(john, X))) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & like(X, john) & like(Y, john) & (~(X = Y))) & hate(lucy, mary) & (~preda(mary)) & taller(mary, john) & (~((~hate(lucy, fred)) \| (~(creative(fred) & tall(fred) & quiet(fred) & european(fred))))) & ((creative(mary) & european(mary)) \| like(mary, john)) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & predb(X) & predb(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))) & ((~(creative(paul) & brave(paul) & tall(paul) & quiet(paul) & european(paul))) \| hate(susan, paul))))), inference(modus_ponens,[status(thm)],[3, 2])). tff(5,plain, (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((~(like(lucy, paul) & like(paul, lucy))) \| (~![X: $i] : quieter(X, mary))) & ((~(preda(mary) \| (brave(mary) & person(mary)))) \| ((~(tall(mary) & person(mary))) & (~(tall(fred) & person(fred))))) & (~(tall(paul) & quiet(fred))) & ?[X: $i] : (room(X) \| (~(tall(X) & european(X))) \| (~like(john, X))) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & like(X, john) & like(Y, john) & (~(X = Y))) & hate(lucy, mary) & (~preda(mary)) & taller(mary, john) & (~((~hate(lucy, fred)) \| (~(creative(fred) & tall(fred) & quiet(fred) & european(fred))))) & ((creative(mary) & european(mary)) \| like(mary, john)) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & predb(X) & predb(Y) & (~(X = Y))) & (~(like(lucy, paul) & like(paul, lucy)))), inference(or_elim,[status(thm)],[4])). tff(6,plain, (~((~hate(lucy, fred)) \| (~(creative(fred) & tall(fred) & quiet(fred) & european(fred))))), inference(and_elim,[status(thm)],[5])). tff(7,plain, (creative(fred) & tall(fred) & quiet(fred) & european(fred)), inference(or_elim,[status(thm)],[6])). tff(8,plain, (quiet(fred)), inference(and_elim,[status(thm)],[7])). tff(9,plain, (quiet(fred)), inference(modus_ponens,[status(thm)],[8, 1])). tff(10,plain, ((~(~((~tall(paul)) \| (~quiet(fred))))) <=> ((~tall(paul)) \| (~quiet(fred)))), inference(rewrite,[status(thm)],[])). tff(11,plain, ((tall(paul) & quiet(fred)) <=> (~((~tall(paul)) \| (~quiet(fred))))), inference(rewrite,[status(thm)],[])). tff(12,plain, ((~(tall(paul) & quiet(fred))) <=> (~(~((~tall(paul)) \| (~quiet(fred)))))), inference(monotonicity,[status(thm)],[11])). tff(13,plain, ((~(tall(paul) & quiet(fred))) <=> ((~tall(paul)) \| (~quiet(fred)))), inference(transitivity,[status(thm)],[12, 10])). tff(14,plain, ((~(tall(paul) & quiet(fred))) <=> (~(tall(paul) & quiet(fred)))), inference(rewrite,[status(thm)],[])). tff(15,plain, (~(tall(paul) & quiet(fred))), inference(and_elim,[status(thm)],[5])). tff(16,plain, (~(tall(paul) & quiet(fred))), inference(modus_ponens,[status(thm)],[15, 14])). tff(17,plain, ((~tall(paul)) \| (~quiet(fred))), inference(modus_ponens,[status(thm)],[16, 13])). tff(18,plain, (~tall(paul)), inference(unit_resolution,[status(thm)],[17, 9])). tff(19,plain, (((~quiet(paul)) \| hate(susan, paul) \| (~tall(paul)) \| (~creative(paul)) \| (~brave(paul)) \| (~european(paul))) \| tall(paul)), inference(tautology,[status(thm)],[])). tff(20,plain, ((~quiet(paul)) \| hate(susan, paul) \| (~tall(paul)) \| (~creative(paul)) \| (~brave(paul)) \| (~european(paul))), inference(unit_resolution,[status(thm)],[19, 18])). tff(21,plain, (room(alice) <=> room(alice)), inference(rewrite,[status(thm)],[])). tff(22,plain, (room(alice)), inference(and_elim,[status(thm)],[5])). tff(23,plain, (room(alice)), inference(modus_ponens,[status(thm)],[22, 21])). tff(24,plain, (room(fred) <=> room(fred)), inference(rewrite,[status(thm)],[])). tff(25,plain, (room(fred)), inference(and_elim,[status(thm)],[5])). tff(26,plain, (room(fred)), inference(modus_ponens,[status(thm)],[25, 24])). tff(27,plain, (room(paul) <=> room(paul)), inference(rewrite,[status(thm)],[])). tff(28,plain, (room(paul)), inference(and_elim,[status(thm)],[5])). tff(29,plain, (room(paul)), inference(modus_ponens,[status(thm)],[28, 27])). tff(30,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(31,plain, (room(mary)), inference(and_elim,[status(thm)],[5])). tff(32,plain, (room(mary)), inference(modus_ponens,[status(thm)],[31, 30])). tff(33,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~room(alice)) \| (~((X!6 = \|'alice'\|) \| (X!6 = \|'fred'\|) \| (X!6 = \|'paul'\|) \| (X!6 = \|'mary'\|) \| (~room(X!6)))) \| (~((~quiet(paul)) \| hate(susan, paul) \| (~tall(paul)) \| (~creative(paul)) \| (~brave(paul)) \| (~european(paul))))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~room(alice)) \| (~((X!6 = \|'alice'\|) \| (X!6 = \|'fred'\|) \| (X!6 = \|'paul'\|) \| (X!6 = \|'mary'\|) \| (~room(X!6)))) \| (~((~quiet(paul)) \| hate(susan, paul) \| (~tall(paul)) \| (~creative(paul)) \| (~brave(paul)) \| (~european(paul)))))), inference(rewrite,[status(thm)],[])). tff(34,plain, ((~((~(creative(paul) & brave(paul) & tall(paul) & quiet(paul) & european(paul))) \| hate(susan, paul))) <=> (~((~quiet(paul)) \| hate(susan, paul) \| (~tall(paul)) \| (~creative(paul)) \| (~brave(paul)) \| (~european(paul))))), inference(rewrite,[status(thm)],[])). tff(35,plain, ((~((X!6 = \|'alice'\|) \| (X!6 = \|'fred'\|) \| (X!6 = \|'paul'\|) \| (X!6 = \|'mary'\|) \| (~room(X!6)))) <=> (~((X!6 = \|'alice'\|) \| (X!6 = \|'fred'\|) \| (X!6 = \|'paul'\|) \| (X!6 = \|'mary'\|) \| (~room(X!6))))), inference(rewrite,[status(thm)],[])). tff(36,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~room(alice)) \| (~((X!6 = \|'alice'\|) \| (X!6 = \|'fred'\|) \| (X!6 = \|'paul'\|) \| (X!6 = \|'mary'\|) \| (~room(X!6)))) \| (~((~(creative(paul) & brave(paul) & tall(paul) & quiet(paul) & european(paul))) \| hate(susan, paul)))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~room(alice)) \| (~((X!6 = \|'alice'\|) \| (X!6 = \|'fred'\|) \| (X!6 = \|'paul'\|) \| (X!6 = \|'mary'\|) \| (~room(X!6)))) \| (~((~quiet(paul)) \| hate(susan, paul) \| (~tall(paul)) \| (~creative(paul)) \| (~brave(paul)) \| (~european(paul)))))), inference(monotonicity,[status(thm)],[35, 34])). tff(37,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~room(alice)) \| (~((X!6 = \|'alice'\|) \| (X!6 = \|'fred'\|) \| (X!6 = \|'paul'\|) \| (X!6 = \|'mary'\|) \| (~room(X!6)))) \| (~((~(creative(paul) & brave(paul) & tall(paul) & quiet(paul) & european(paul))) \| hate(susan, paul)))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~room(alice)) \| (~((X!6 = \|'alice'\|) \| (X!6 = \|'fred'\|) \| (X!6 = \|'paul'\|) \| (X!6 = \|'mary'\|) \| (~room(X!6)))) \| (~((~quiet(paul)) \| hate(susan, paul) \| (~tall(paul)) \| (~creative(paul)) \| (~brave(paul)) \| (~european(paul)))))), inference(transitivity,[status(thm)],[36, 33])). tff(38,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~room(alice)) \| (~((X!6 = \|'alice'\|) \| (X!6 = \|'fred'\|) \| (X!6 = \|'paul'\|) \| (X!6 = \|'mary'\|) \| (~room(X!6)))) \| (~((~(creative(paul) & brave(paul) & tall(paul) & quiet(paul) & european(paul))) \| hate(susan, paul)))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~room(alice)) \| (~((X!6 = \|'alice'\|) \| (X!6 = \|'fred'\|) \| (X!6 = \|'paul'\|) \| (X!6 = \|'mary'\|) \| (~room(X!6)))) \| (~((~(creative(paul) & brave(paul) & tall(paul) & quiet(paul) & european(paul))) \| hate(susan, paul))))), inference(rewrite,[status(thm)],[])). tff(39,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~room(alice)) \| (~((X!6 = \|'alice'\|) \| (X!6 = \|'fred'\|) \| (X!6 = \|'paul'\|) \| (X!6 = \|'mary'\|) \| (~room(X!6)))) \| (~((~(creative(paul) & brave(paul) & tall(paul) & quiet(paul) & european(paul))) \| hate(susan, paul)))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~room(alice)) \| (~((X!6 = \|'alice'\|) \| (X!6 = \|'fred'\|) \| (X!6 = \|'paul'\|) \| (X!6 = \|'mary'\|) \| (~room(X!6)))) \| (~((~(creative(paul) & brave(paul) & tall(paul) & quiet(paul) & european(paul))) \| hate(susan, paul))))), inference(monotonicity,[status(thm)],[35])). tff(40,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~room(alice)) \| (~((X!6 = \|'alice'\|) \| (X!6 = \|'fred'\|) \| (X!6 = \|'paul'\|) \| (X!6 = \|'mary'\|) \| (~room(X!6)))) \| (~((~(creative(paul) & brave(paul) & tall(paul) & quiet(paul) & european(paul))) \| hate(susan, paul)))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~room(alice)) \| (~((X!6 = \|'alice'\|) \| (X!6 = \|'fred'\|) \| (X!6 = \|'paul'\|) \| (X!6 = \|'mary'\|) \| (~room(X!6)))) \| (~((~(creative(paul) & brave(paul) & tall(paul) & quiet(paul) & european(paul))) \| hate(susan, paul))))), inference(transitivity,[status(thm)],[39, 38])). tff(41,plain, ((room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((~(creative(paul) & brave(paul) & tall(paul) & quiet(paul) & european(paul))) \| hate(susan, paul))) <=> (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((~(creative(paul) & brave(paul) & tall(paul) & quiet(paul) & european(paul))) \| hate(susan, paul)))), inference(rewrite,[status(thm)],[])). tff(42,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((~(creative(paul) & brave(paul) & tall(paul) & quiet(paul) & european(paul))) \| hate(susan, paul)))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((~(creative(paul) & brave(paul) & tall(paul) & quiet(paul) & european(paul))) \| hate(susan, paul))))), inference(monotonicity,[status(thm)],[41])). tff(43,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((~(creative(paul) & brave(paul) & tall(paul) & quiet(paul) & european(paul))) \| hate(susan, paul)))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((~(creative(paul) & brave(paul) & tall(paul) & quiet(paul) & european(paul))) \| hate(susan, paul))))), inference(rewrite,[status(thm)],[])). tff(44,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((~(creative(paul) & brave(paul) & tall(paul) & quiet(paul) & european(paul))) \| hate(susan, paul)))), inference(or_elim,[status(thm)],[4])). tff(45,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((~(creative(paul) & brave(paul) & tall(paul) & quiet(paul) & european(paul))) \| hate(susan, paul)))), inference(modus_ponens,[status(thm)],[44, 42])). tff(46,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((~(creative(paul) & brave(paul) & tall(paul) & quiet(paul) & european(paul))) \| hate(susan, paul)))), inference(modus_ponens,[status(thm)],[45, 43])). tff(47,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((~(creative(paul) & brave(paul) & tall(paul) & quiet(paul) & european(paul))) \| hate(susan, 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 (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!6 \|'alice'\|) (= X!6 \|'fred'\|) (= X!6 \|'paul'\|) (= X!6 \|'mary'\|) (not (room X!6))))) (a!7 (or (not (and (creative paul) (brave paul) (tall paul) (quiet paul) (european paul))) (hate susan paul)))) (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(stephanie)&room(sharon)&room(monica)&room(nancy)&(![X]:(room(X)=>(X='stephanie'\|X='sharon'\|X='monica'\|X='nancy')))& (((![X]:(quieter(X,stephanie)))=>(~((like(denise,sharon) & like(sharon,denise)))))& (((![X]:(taller(X,sharon)))=>((?[X,Y]:(~room(X)&~room(Y)&(hate(alberta,X)&hate(alberta,Y))&(X!=Y)))))\|((~(![X]:(taller(X,sharon))))=>(![X]:(~room(X)=>(((sibling(denise,X))=>(sibling(alberta,X))))))))& ((((can_play_the_guitar(stephanie))\|(brave(stephanie)&person(stephanie))))=>(~(tall(stephanie)&person(stephanie))&~(tall(monica)&person(monica))))& (((tall(sharon))&(quiet(monica)))<=>((((~quiet(sharon))\|(hate(sharon,denise)))&(~((~quiet(sharon))\|(hate(sharon,denise)))))))& (?[X]:(~room(X)=>(((like(alberta,X))=>(~(tall(X)&european(X)))))))& ((?[X,Y]:(~room(X)&~room(Y)&(like(X,alberta)&like(Y,alberta))&(X!=Y))))& ((hate(denise,stephanie))&(does_not_can_play_the_guitar(stephanie)))& (taller(stephanie,alberta))& (~((~(creative(monica)&tall(monica)&quiet(monica)&european(monica)))\|(~hate(denise,monica))))& (((creative(stephanie)&european(stephanie))\|(like(stephanie,alberta))))& ((?[X,Y]:(~room(X)&~room(Y)&(uses_contact_lenses(X)&uses_contact_lenses(Y))&(X!=Y))))& (~((like(denise,sharon) & like(sharon,denise)))))	room(stephanie)&room(sharon)&room(monica)&room(nancy)&(![X]:(room(X)=>(X='stephanie'\|X='sharon'\|X='monica'\|X='nancy')))& (((~(creative(sharon)&brave(sharon)&tall(sharon)&quiet(sharon)&european(sharon)))\|(hate(rafaela,sharon))))	entailment	neutral	neutral
Nancy, Steven, Amy, Gustavo are the only persons in the room. At most one of the following is true:. -Only one person outside the room does not enjoy mountain biking. -Nancy who does not enjoy mountain biking, does enjoy mountain biking.	Steven does not enjoy mountain biking or does enjoy mountain biking or both.	entailment	% SZS status Unsatisfiable % SZS output start Proof tff(preda_type, type, ( preda: $i > $o)). tff(paul_type, type, ( paul: $i)). tff(tptp_fun__alice__type, type, ( tptp_fun__alice_: $i)). tff(tptp_fun__fred__type, type, ( tptp_fun__fred_: $i)). tff(tptp_fun__paul__type, type, ( tptp_fun__paul_: $i)). tff(tptp_fun__mary__type, type, ( tptp_fun__mary_: $i)). tff(room_type, type, ( room: $i > $o)). tff(alice_type, type, ( alice: $i)). tff(fred_type, type, ( fred: $i)). tff(mary_type, type, ( mary: $i)). tff(1,plain, ((~$true) <=> $false), inference(rewrite,[status(thm)],[])). tff(2,plain, (((room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) \| (X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|))) => (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) \| (X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|)))) <=> $true), inference(rewrite,[status(thm)],[])). tff(3,plain, (((room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) \| (X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|))) & $true) <=> (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) \| (X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|)))), inference(rewrite,[status(thm)],[])). tff(4,plain, (((~preda(paul)) \| preda(paul)) <=> $true), inference(rewrite,[status(thm)],[])). tff(5,plain, (((room(mary) & room(paul) & room(fred) & room(alice)) & ![X: $i] : ((~room(X)) \| (X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|))) <=> (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) \| (X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|)))), inference(rewrite,[status(thm)],[])). tff(6,plain, (^[X: $i] : trans(monotonicity(trans(monotonicity(rewrite((((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)) <=> ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|))), (((((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)) \| (X = \|'alice'\|)) <=> (((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|)) \| (X = \|'alice'\|)))), rewrite((((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|)) \| (X = \|'alice'\|)) <=> ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|))), (((((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)) \| (X = \|'alice'\|)) <=> ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|)))), ((room(X) => ((((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)) \| (X = \|'alice'\|))) <=> (room(X) => ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|))))), rewrite((room(X) => ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|))) <=> ((~room(X)) \| (X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|))), ((room(X) => ((((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)) \| (X = \|'alice'\|))) <=> ((~room(X)) \| (X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|))))), inference(bind,[status(th)],[])). tff(7,plain, (![X: $i] : (room(X) => ((((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)) \| (X = \|'alice'\|))) <=> ![X: $i] : ((~room(X)) \| (X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|))), inference(quant_intro,[status(thm)],[6])). tff(8,plain, (((room(mary) & room(paul) & room(fred)) & room(alice)) <=> (room(mary) & room(paul) & room(fred) & room(alice))), inference(rewrite,[status(thm)],[])). tff(9,plain, (((room(mary) & room(paul)) & room(fred)) <=> (room(mary) & room(paul) & room(fred))), inference(rewrite,[status(thm)],[])). tff(10,plain, ((((room(mary) & room(paul)) & room(fred)) & room(alice)) <=> ((room(mary) & room(paul) & room(fred)) & room(alice))), inference(monotonicity,[status(thm)],[9])). tff(11,plain, ((((room(mary) & room(paul)) & room(fred)) & room(alice)) <=> (room(mary) & room(paul) & room(fred) & room(alice))), inference(transitivity,[status(thm)],[10, 8])). tff(12,plain, (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)) \| (X = \|'alice'\|)))) <=> ((room(mary) & room(paul) & room(fred) & room(alice)) & ![X: $i] : ((~room(X)) \| (X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|)))), inference(monotonicity,[status(thm)],[11, 7])). tff(13,plain, (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)) \| (X = \|'alice'\|)))) <=> (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) \| (X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|)))), inference(transitivity,[status(thm)],[12, 5])). tff(14,plain, ((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)) \| (X = \|'alice'\|)))) & ((~preda(paul)) \| preda(paul))) <=> ((room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) \| (X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|))) & $true)), inference(monotonicity,[status(thm)],[13, 4])). 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)) \| preda(paul))) <=> (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) \| (X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|)))), inference(transitivity,[status(thm)],[14, 3])). tff(16,plain, ((~$false) <=> $true), inference(rewrite,[status(thm)],[])). tff(17,plain, (((?[X: $i] : ((~room(X)) & (~preda(X))) & ![X: $i, Y: $i] : ((~((~preda(X)) & (~preda(Y)))) \| (X = Y)) & (~preda(mary))) & preda(mary)) <=> $false), inference(rewrite,[status(thm)],[])). tff(18,plain, (((?[X: $i] : ((~room(X)) & (~preda(X))) & ![X: $i, Y: $i] : ((~((~preda(X)) & (~preda(Y)))) \| (X = Y))) & (~preda(mary))) <=> (?[X: $i] : ((~room(X)) & (~preda(X))) & ![X: $i, Y: $i] : ((~((~preda(X)) & (~preda(Y)))) \| (X = Y)) & (~preda(mary)))), inference(rewrite,[status(thm)],[])). tff(19,plain, ((?[X: $i] : ((~room(X)) & (~preda(X))) & ![X: $i, Y: $i] : (((~preda(X)) & (~preda(Y))) => (X = Y))) <=> (?[X: $i] : ((~room(X)) & (~preda(X))) & ![X: $i, Y: $i] : ((~((~preda(X)) & (~preda(Y)))) \| (X = Y)))), inference(rewrite,[status(thm)],[])). tff(20,plain, (((?[X: $i] : ((~room(X)) & (~preda(X))) & ![X: $i, Y: $i] : (((~preda(X)) & (~preda(Y))) => (X = Y))) & (~preda(mary))) <=> ((?[X: $i] : ((~room(X)) & (~preda(X))) & ![X: $i, Y: $i] : ((~((~preda(X)) & (~preda(Y)))) \| (X = Y))) & (~preda(mary)))), inference(monotonicity,[status(thm)],[19])). tff(21,plain, (((?[X: $i] : ((~room(X)) & (~preda(X))) & ![X: $i, Y: $i] : (((~preda(X)) & (~preda(Y))) => (X = Y))) & (~preda(mary))) <=> (?[X: $i] : ((~room(X)) & (~preda(X))) & ![X: $i, Y: $i] : ((~((~preda(X)) & (~preda(Y)))) \| (X = Y)) & (~preda(mary)))), inference(transitivity,[status(thm)],[20, 18])). tff(22,plain, ((((?[X: $i] : ((~room(X)) & (~preda(X))) & ![X: $i, Y: $i] : (((~preda(X)) & (~preda(Y))) => (X = Y))) & (~preda(mary))) & preda(mary)) <=> ((?[X: $i] : ((~room(X)) & (~preda(X))) & ![X: $i, Y: $i] : ((~((~preda(X)) & (~preda(Y)))) \| (X = Y)) & (~preda(mary))) & preda(mary))), inference(monotonicity,[status(thm)],[21])). tff(23,plain, ((((?[X: $i] : ((~room(X)) & (~preda(X))) & ![X: $i, Y: $i] : (((~preda(X)) & (~preda(Y))) => (X = Y))) & (~preda(mary))) & preda(mary)) <=> $false), inference(transitivity,[status(thm)],[22, 17])). tff(24,plain, ((~(((?[X: $i] : ((~room(X)) & (~preda(X))) & ![X: $i, Y: $i] : (((~preda(X)) & (~preda(Y))) => (X = Y))) & (~preda(mary))) & preda(mary))) <=> (~$false)), inference(monotonicity,[status(thm)],[23])). tff(25,plain, ((~(((?[X: $i] : ((~room(X)) & (~preda(X))) & ![X: $i, Y: $i] : (((~preda(X)) & (~preda(Y))) => (X = Y))) & (~preda(mary))) & preda(mary))) <=> $true), inference(transitivity,[status(thm)],[24, 16])). tff(26,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)) & (~preda(X))) & ![X: $i, Y: $i] : (((~preda(X)) & (~preda(Y))) => (X = Y))) & (~preda(mary))) & preda(mary)))) <=> ((room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) \| (X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|))) & $true)), inference(monotonicity,[status(thm)],[13, 25])). tff(27,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)) & (~preda(X))) & ![X: $i, Y: $i] : (((~preda(X)) & (~preda(Y))) => (X = Y))) & (~preda(mary))) & preda(mary)))) <=> (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) \| (X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|)))), inference(transitivity,[status(thm)],[26, 3])). tff(28,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)) & (~preda(X))) & ![X: $i, Y: $i] : (((~preda(X)) & (~preda(Y))) => (X = Y))) & (~preda(mary))) & preda(mary)))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)) \| (X = \|'alice'\|)))) & ((~preda(paul)) \| preda(paul)))) <=> ((room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) \| (X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|))) => (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) \| (X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|))))), inference(monotonicity,[status(thm)],[27, 15])). tff(29,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)) & (~preda(X))) & ![X: $i, Y: $i] : (((~preda(X)) & (~preda(Y))) => (X = Y))) & (~preda(mary))) & preda(mary)))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)) \| (X = \|'alice'\|)))) & ((~preda(paul)) \| preda(paul)))) <=> $true), inference(transitivity,[status(thm)],[28, 2])). tff(30,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)) & (~preda(X))) & ![X: $i, Y: $i] : (((~preda(X)) & (~preda(Y))) => (X = Y))) & (~preda(mary))) & preda(mary)))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)) \| (X = \|'alice'\|)))) & ((~preda(paul)) \| preda(paul))))) <=> (~$true)), inference(monotonicity,[status(thm)],[29])). tff(31,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)) & (~preda(X))) & ![X: $i, Y: $i] : (((~preda(X)) & (~preda(Y))) => (X = Y))) & (~preda(mary))) & preda(mary)))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)) \| (X = \|'alice'\|)))) & ((~preda(paul)) \| preda(paul))))) <=> $false), inference(transitivity,[status(thm)],[30, 1])). tff(32,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)) & (~preda(X))) & ![X: $i, Y: $i] : (((~preda(X)) & (~preda(Y))) => (X = Y))) & (~preda(mary))) & preda(mary)))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)) \| (X = \|'alice'\|)))) & ((~preda(paul)) \| preda(paul))))), file('/mnt/tmpfs//1901430361840919986976036.p','negated')). tff(33,plain, ($false), inference(modus_ponens,[status(thm)],[32, 31])). % SZS output end Proof	room(nancy)&room(steven)&room(amy)&room(gustavo)&(![X]:(room(X)=>(X='nancy'\|X='steven'\|X='amy'\|X='gustavo')))& (~(((?[X]:(~room(X)&does_not_enjoy_mountain_biking(X)))&(![X,Y]:((does_not_enjoy_mountain_biking(X)&does_not_enjoy_mountain_biking(Y))=>(X=Y))))&(does_not_enjoy_mountain_biking(nancy))&(does_enjoy_mountain_biking(nancy))))	room(nancy)&room(steven)&room(amy)&room(gustavo)&(![X]:(room(X)=>(X='nancy'\|X='steven'\|X='amy'\|X='gustavo')))& (((does_not_enjoy_mountain_biking(steven))\|(does_enjoy_mountain_biking(steven))))	entailment	neutral	neutral
Steven, Chester are the only persons in the room. Keith and Steven hate each other. Steven who is hated by Richard, hates Keith. Steven is the tallest in the room.	Steven is hated by Keith or collects antique jewelry 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(preda_type, type, ( preda: $i > $o)). tff(mary_type, type, ( mary: $i)). tff(hate_type, type, ( hate: ( $i * $i ) > $o)). tff(john_type, type, ( john: $i)). tff(taller_type, type, ( taller: ( $i * $i ) > $o)). tff(fred_type, type, ( fred: $i)). tff(paul_type, type, ( paul: $i)). tff(1,plain, (hate(mary, john) <=> hate(mary, john)), inference(rewrite,[status(thm)],[])). tff(2,plain, ((~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = \|'mary'\|) \| (X = \|'paul'\|)))) & (((hate(john, mary) & hate(mary, john)) & (hate(mary, fred) & hate(john, mary))) & ![X: $i] : taller(X, mary))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = \|'mary'\|) \| (X = \|'paul'\|)))) & (hate(mary, john) \| preda(mary))))) <=> (~((~(room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & hate(john, mary) & hate(mary, john) & hate(mary, fred) & ![X: $i] : taller(X, mary))) \| (room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (hate(mary, john) \| preda(mary)))))), inference(rewrite,[status(thm)],[])). tff(3,axiom,(~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = \|'mary'\|) \| (X = \|'paul'\|)))) & (((hate(john, mary) & hate(mary, john)) & (hate(mary, fred) & hate(john, mary))) & ![X: $i] : taller(X, mary))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = \|'mary'\|) \| (X = \|'paul'\|)))) & (hate(mary, john) \| preda(mary))))), file('/mnt/tmpfs//314022552174321713894611.p','negated')). tff(4,plain, (~((~(room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & hate(john, mary) & hate(mary, john) & hate(mary, fred) & ![X: $i] : taller(X, mary))) \| (room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (hate(mary, john) \| preda(mary))))), inference(modus_ponens,[status(thm)],[3, 2])). tff(5,plain, (room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & hate(john, mary) & hate(mary, john) & hate(mary, fred) & ![X: $i] : taller(X, mary)), inference(or_elim,[status(thm)],[4])). tff(6,plain, (hate(mary, john)), inference(and_elim,[status(thm)],[5])). tff(7,plain, (hate(mary, john)), inference(modus_ponens,[status(thm)],[6, 1])). tff(8,plain, ((hate(mary, john) \| preda(mary)) \| (~hate(mary, john))), inference(tautology,[status(thm)],[])). tff(9,plain, (hate(mary, john) \| preda(mary)), 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!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0)))) \| (~(hate(mary, john) \| preda(mary)))) <=> ((~room(mary)) \| (~room(paul)) \| (~((X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0)))) \| (~(hate(mary, john) \| preda(mary))))), inference(rewrite,[status(thm)],[])). tff(17,plain, ((hate(mary, john) \| preda(mary)) <=> (hate(mary, john) \| preda(mary))), inference(rewrite,[status(thm)],[])). tff(18,plain, ((~(hate(mary, john) \| preda(mary))) <=> (~(hate(mary, john) \| preda(mary)))), inference(monotonicity,[status(thm)],[17])). tff(19,plain, ((~((X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0)))) <=> (~((X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0))))), inference(rewrite,[status(thm)],[])). tff(20,plain, (((~room(mary)) \| (~room(paul)) \| (~((X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0)))) \| (~(hate(mary, john) \| preda(mary)))) <=> ((~room(mary)) \| (~room(paul)) \| (~((X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0)))) \| (~(hate(mary, john) \| preda(mary))))), inference(monotonicity,[status(thm)],[19, 18])). tff(21,plain, (((~room(mary)) \| (~room(paul)) \| (~((X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0)))) \| (~(hate(mary, john) \| preda(mary)))) <=> ((~room(mary)) \| (~room(paul)) \| (~((X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0)))) \| (~(hate(mary, john) \| preda(mary))))), inference(transitivity,[status(thm)],[20, 16])). tff(22,plain, ((room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (hate(mary, john) \| preda(mary))) <=> (room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (hate(mary, john) \| preda(mary)))), inference(rewrite,[status(thm)],[])). tff(23,plain, ((~(room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (hate(mary, john) \| preda(mary)))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (hate(mary, john) \| preda(mary))))), inference(monotonicity,[status(thm)],[22])). tff(24,plain, ((~(room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (hate(mary, john) \| preda(mary)))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (hate(mary, john) \| preda(mary))))), inference(rewrite,[status(thm)],[])). tff(25,plain, (~(room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (hate(mary, john) \| preda(mary)))), inference(or_elim,[status(thm)],[4])). tff(26,plain, (~(room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (hate(mary, john) \| preda(mary)))), inference(modus_ponens,[status(thm)],[25, 23])). tff(27,plain, (~(room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (hate(mary, john) \| preda(mary)))), inference(modus_ponens,[status(thm)],[26, 24])). tff(28,plain, (~(room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (hate(mary, john) \| preda(mary)))), inference(modus_ponens,[status(thm)],[27, 23])). 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))))) (a!5 (~ (not (or (hate mary john) (preda mary))) (not (or (hate mary john) (preda mary)))))) (let ((a!6 (not (and (room mary) (room paul) a!3 (or (hate mary john) (preda mary))))) (a!7 (or (not (room mary)) (not (room paul)) a!4 (not (or (hate mary john) (preda mary)))))) (nnf-neg a!1 a!2 (sk (~ (not a!3) a!4)) (refl a!5) (~ a!6 a!7))))	room(steven)&room(chester)&(![X]:(room(X)=>(X='steven'\|X='chester')))& (((hate(keith,steven) & hate(steven,keith)))& ((hate(steven,richard))&(hate(keith,steven)))& (![X]:(taller(X,steven))))	room(steven)&room(chester)&(![X]:(room(X)=>(X='steven'\|X='chester')))& (((hate(steven,keith))\|(collects_antique_jewelry(steven))))	neutral	neutral	entailment
Earl, Eric, Debra, Willard are the only persons in the room. If “Eric is the least quiet in the room” then “Willard does not hate James or is not hated by James or both” otherwise “more than one person outside the room is not a happy european”. “Willard either hates James or does not enjoy origami” if “Willard and Eric do not hate James”. Willard does not hate James or is not hated by James or both. Eric is the quietest in the room. Eric neither is hated by James nor is not a quiet happy rich person. Eric and Willard are respectively rich and happy. Willard is a happy brave european or hates James or both. More than one person outside the room is not rich. Only one person outside the room does not hate James.	More than one person outside the room is a creative quiet rich happy brave european.	neutral	% SZS status Satisfiable	room(earl)&room(eric)&room(debra)&room(willard)&(![X]:(room(X)=>(X='earl'\|X='eric'\|X='debra'\|X='willard')))& ((((![X]:(quieter(eric,X)))=>(((~hate(james,willard))\|(~hate(willard,james)))))\|((~(![X]:(quieter(eric,X))))=>((?[X,Y]:(~room(X)&~room(Y)&(~(happy(X)&european(X))&~(happy(Y)&european(Y)))&(X!=Y))))))& ((~hate(james,willard)&~hate(james,eric))=>((((hate(james,willard))\|(does_not_enjoy_origami(willard)))&(~((hate(james,willard))\|(does_not_enjoy_origami(willard)))))))& (((~hate(james,willard))\|(~hate(willard,james))))& (![X]:(quieter(X,eric)))& (~((hate(eric,james))\|(~(quiet(eric)&happy(eric)&rich(eric)&person(eric)))))& ((rich(eric))&(happy(willard)))& (((happy(willard)&brave(willard)&european(willard))\|(hate(james,willard))))& ((?[X,Y]:(~room(X)&~room(Y)&(~rich(X)&~rich(Y))&(X!=Y))))& (((?[X]:(~room(X)&~hate(james,X)))&(![X,Y]:((~hate(james,X)&~hate(james,Y))=>(X=Y))))))	room(earl)&room(eric)&room(debra)&room(willard)&(![X]:(room(X)=>(X='earl'\|X='eric'\|X='debra'\|X='willard')))& ((?[X,Y]:(~room(X)&~room(Y)&(creative(X)&quiet(X)&rich(X)&happy(X)&brave(X)&european(X)&creative(Y)&quiet(Y)&rich(Y)&happy(Y)&brave(Y)&european(Y))&(X!=Y))))	neutral	contradiction	neutral
Matthew, Richard are the only persons in the room. Only one of the following is true:. -Richard is the least rich in the room. -Matthew neither is not liked by Chris nor is not rich.	It is not the case that 'Richard who is not Matthew, is richer than Chris'.	neutral	% SZS status Satisfiable	room(matthew)&room(richard)&(![X]:(room(X)=>(X='matthew'\|X='richard')))& (((![X]:(richer(richard,X)))\|(~((~like(matthew,chris))\|(~rich(matthew)))))&~(![X]:(richer(richard,X))&~((~like(matthew,chris))\|(~rich(matthew)))))	room(matthew)&room(richard)&(![X]:(room(X)=>(X='matthew'\|X='richard')))& (~((richard!=matthew)&(richer(chris,richard))))	entailment	entailment	entailment
Lester is the only person in the room. Someone who does not like Regina like someone who is not a brave tall tourist. Only one person outside the room likes Regina. Lester is the richest in the room. Only one person outside the room is a quiet european. Lester is a rich creative quiet brave tall tourist.	Lester is not a rich tall creative european.	entailment	% SZS status Unsatisfiable % SZS output start Proof tff(tptp_fun__mary__type, type, ( tptp_fun__mary_: $i)). tff(tptp_fun_X_4_type, type, ( tptp_fun_X_4: $i)). tff(room_type, type, ( room: $i > $o)). 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(rich_type, type, ( rich: $i > $o)). tff(tptp_fun_X_3_type, type, ( tptp_fun_X_3: $i)). tff(tourist_type, type, ( tourist: $i > $o)). tff(brave_type, type, ( brave: $i > $o)). tff(quiet_type, type, ( quiet: $i > $o)). tff(richer_type, type, ( richer: ( $i * $i ) > $o)). tff(like_type, type, ( like: ( $i * $i ) > $o)). tff(paul_type, type, ( paul: $i)). tff(1,assumption,(mary = X!3), introduced(assumption)). tff(2,plain, (X!3 = mary), inference(symmetry,[status(thm)],[1])). tff(3,plain, (room(X!3) <=> room(mary)), inference(monotonicity,[status(thm)],[2])). tff(4,plain, (room(mary) <=> room(X!3)), inference(symmetry,[status(thm)],[3])). tff(5,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(6,plain, ((~(((room(mary) & ![X: $i] : (room(X) => (X = \|'mary'\|))) & ((((?[X: $i, Y: $i] : (((~like(paul, X)) & (~((brave(Y) & tall(Y)) & tourist(Y)))) & like(X, Y)) & (?[X: $i] : ((~room(X)) & like(paul, X)) & ![X: $i, Y: $i] : ((like(paul, X) & like(paul, Y)) => (X = Y)))) & ![X: $i] : richer(X, mary)) & (?[X: $i] : (((~room(X)) & quiet(X)) & european(X)) & ![X: $i, Y: $i] : ((((quiet(X) & european(X)) & quiet(Y)) & european(Y)) => (X = Y)))) & (((((rich(mary) & creative(mary)) & quiet(mary)) & brave(mary)) & tall(mary)) & tourist(mary)))) => ((room(mary) & ![X: $i] : (room(X) => (X = \|'mary'\|))) & (~(((rich(mary) & tall(mary)) & creative(mary)) & european(mary)))))) <=> (~((~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ?[X: $i, Y: $i] : ((~like(paul, X)) & (~(brave(Y) & tall(Y) & tourist(Y))) & like(X, Y)) & ?[X: $i] : ((~room(X)) & like(paul, X)) & ![X: $i, Y: $i] : ((~(like(paul, X) & like(paul, Y))) \| (X = Y)) & ![X: $i] : richer(X, mary) & ?[X: $i] : ((~room(X)) & quiet(X) & european(X)) & ![X: $i, Y: $i] : ((~(quiet(X) & european(X) & quiet(Y) & european(Y))) \| (X = Y)) & rich(mary) & creative(mary) & quiet(mary) & brave(mary) & tall(mary) & tourist(mary))) \| (room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~(rich(mary) & tall(mary) & creative(mary) & european(mary))))))), inference(rewrite,[status(thm)],[])). tff(7,axiom,(~(((room(mary) & ![X: $i] : (room(X) => (X = \|'mary'\|))) & ((((?[X: $i, Y: $i] : (((~like(paul, X)) & (~((brave(Y) & tall(Y)) & tourist(Y)))) & like(X, Y)) & (?[X: $i] : ((~room(X)) & like(paul, X)) & ![X: $i, Y: $i] : ((like(paul, X) & like(paul, Y)) => (X = Y)))) & ![X: $i] : richer(X, mary)) & (?[X: $i] : (((~room(X)) & quiet(X)) & european(X)) & ![X: $i, Y: $i] : ((((quiet(X) & european(X)) & quiet(Y)) & european(Y)) => (X = Y)))) & (((((rich(mary) & creative(mary)) & quiet(mary)) & brave(mary)) & tall(mary)) & tourist(mary)))) => ((room(mary) & ![X: $i] : (room(X) => (X = \|'mary'\|))) & (~(((rich(mary) & tall(mary)) & creative(mary)) & european(mary)))))), file('/mnt/tmpfs//6774318898430356139294942.p','negated')). tff(8,plain, (~((~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ?[X: $i, Y: $i] : ((~like(paul, X)) & (~(brave(Y) & tall(Y) & tourist(Y))) & like(X, Y)) & ?[X: $i] : ((~room(X)) & like(paul, X)) & ![X: $i, Y: $i] : ((~(like(paul, X) & like(paul, Y))) \| (X = Y)) & ![X: $i] : richer(X, mary) & ?[X: $i] : ((~room(X)) & quiet(X) & european(X)) & ![X: $i, Y: $i] : ((~(quiet(X) & european(X) & quiet(Y) & european(Y))) \| (X = Y)) & rich(mary) & creative(mary) & quiet(mary) & brave(mary) & tall(mary) & tourist(mary))) \| (room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~(rich(mary) & tall(mary) & creative(mary) & european(mary)))))), inference(modus_ponens,[status(thm)],[7, 6])). tff(9,plain, (room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ?[X: $i, Y: $i] : ((~like(paul, X)) & (~(brave(Y) & tall(Y) & tourist(Y))) & like(X, Y)) & ?[X: $i] : ((~room(X)) & like(paul, X)) & ![X: $i, Y: $i] : ((~(like(paul, X) & like(paul, Y))) \| (X = Y)) & ![X: $i] : richer(X, mary) & ?[X: $i] : ((~room(X)) & quiet(X) & european(X)) & ![X: $i, Y: $i] : ((~(quiet(X) & european(X) & quiet(Y) & european(Y))) \| (X = Y)) & rich(mary) & creative(mary) & quiet(mary) & brave(mary) & tall(mary) & tourist(mary)), inference(or_elim,[status(thm)],[8])). tff(10,plain, (room(mary)), inference(and_elim,[status(thm)],[9])). tff(11,plain, (room(mary)), inference(modus_ponens,[status(thm)],[10, 5])). tff(12,plain, (room(X!3)), inference(modus_ponens,[status(thm)],[11, 4])). tff(13,plain, (?[X: $i] : ((~room(X)) & quiet(X) & european(X)) <=> ?[X: $i] : ((~room(X)) & quiet(X) & european(X))), inference(rewrite,[status(thm)],[])). tff(14,plain, (?[X: $i] : ((~room(X)) & quiet(X) & european(X))), inference(and_elim,[status(thm)],[9])). tff(15,plain, (?[X: $i] : ((~room(X)) & quiet(X) & european(X))), inference(modus_ponens,[status(thm)],[14, 13])). tff(16,plain,( (~room(X!3)) & quiet(X!3) & european(X!3)), inference(skolemize,[status(sab)],[15])). tff(17,plain, (~room(X!3)), inference(and_elim,[status(thm)],[16])). tff(18,plain, ($false), inference(unit_resolution,[status(thm)],[17, 12])). tff(19,plain,(~(mary = X!3)), inference(lemma,lemma(discharge,[]))). tff(20,plain, (quiet(mary) <=> quiet(mary)), inference(rewrite,[status(thm)],[])). tff(21,plain, (quiet(mary)), inference(and_elim,[status(thm)],[9])). tff(22,plain, (quiet(mary)), inference(modus_ponens,[status(thm)],[21, 20])). tff(23,plain, (^[X: $i, Y: $i] : refl(((X = Y) \| (~european(Y)) \| (~quiet(X)) \| (~european(X)) \| (~quiet(Y))) <=> ((X = Y) \| (~european(Y)) \| (~quiet(X)) \| (~european(X)) \| (~quiet(Y))))), inference(bind,[status(th)],[])). tff(24,plain, (![X: $i, Y: $i] : ((X = Y) \| (~european(Y)) \| (~quiet(X)) \| (~european(X)) \| (~quiet(Y))) <=> ![X: $i, Y: $i] : ((X = Y) \| (~european(Y)) \| (~quiet(X)) \| (~european(X)) \| (~quiet(Y)))), inference(quant_intro,[status(thm)],[23])). tff(25,plain, (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((quiet(X) & european(X) & quiet(Y) & european(Y)) <=> (~((~european(Y)) \| (~quiet(X)) \| (~european(X)) \| (~quiet(Y))))), ((~(quiet(X) & european(X) & quiet(Y) & european(Y))) <=> (~(~((~european(Y)) \| (~quiet(X)) \| (~european(X)) \| (~quiet(Y))))))), rewrite((~(~((~european(Y)) \| (~quiet(X)) \| (~european(X)) \| (~quiet(Y))))) <=> ((~european(Y)) \| (~quiet(X)) \| (~european(X)) \| (~quiet(Y)))), ((~(quiet(X) & european(X) & quiet(Y) & european(Y))) <=> ((~european(Y)) \| (~quiet(X)) \| (~european(X)) \| (~quiet(Y))))), (((~(quiet(X) & european(X) & quiet(Y) & european(Y))) \| (X = Y)) <=> (((~european(Y)) \| (~quiet(X)) \| (~european(X)) \| (~quiet(Y))) \| (X = Y)))), rewrite((((~european(Y)) \| (~quiet(X)) \| (~european(X)) \| (~quiet(Y))) \| (X = Y)) <=> ((X = Y) \| (~european(Y)) \| (~quiet(X)) \| (~european(X)) \| (~quiet(Y)))), (((~(quiet(X) & european(X) & quiet(Y) & european(Y))) \| (X = Y)) <=> ((X = Y) \| (~european(Y)) \| (~quiet(X)) \| (~european(X)) \| (~quiet(Y)))))), inference(bind,[status(th)],[])). tff(26,plain, (![X: $i, Y: $i] : ((~(quiet(X) & european(X) & quiet(Y) & european(Y))) \| (X = Y)) <=> ![X: $i, Y: $i] : ((X = Y) \| (~european(Y)) \| (~quiet(X)) \| (~european(X)) \| (~quiet(Y)))), inference(quant_intro,[status(thm)],[25])). tff(27,plain, (![X: $i, Y: $i] : ((~(quiet(X) & european(X) & quiet(Y) & european(Y))) \| (X = Y)) <=> ![X: $i, Y: $i] : ((~(quiet(X) & european(X) & quiet(Y) & european(Y))) \| (X = Y))), inference(rewrite,[status(thm)],[])). tff(28,plain, (![X: $i, Y: $i] : ((~(quiet(X) & european(X) & quiet(Y) & european(Y))) \| (X = Y))), inference(and_elim,[status(thm)],[9])). tff(29,plain, (![X: $i, Y: $i] : ((~(quiet(X) & european(X) & quiet(Y) & european(Y))) \| (X = Y))), inference(modus_ponens,[status(thm)],[28, 27])). tff(30,plain,( ![X: $i, Y: $i] : ((~(quiet(X) & european(X) & quiet(Y) & european(Y))) \| (X = Y))), inference(skolemize,[status(sab)],[29])). tff(31,plain, (![X: $i, Y: $i] : ((X = Y) \| (~european(Y)) \| (~quiet(X)) \| (~european(X)) \| (~quiet(Y)))), inference(modus_ponens,[status(thm)],[30, 26])). tff(32,plain, (![X: $i, Y: $i] : ((X = Y) \| (~european(Y)) \| (~quiet(X)) \| (~european(X)) \| (~quiet(Y)))), inference(modus_ponens,[status(thm)],[31, 24])). tff(33,plain, (european(X!3)), inference(and_elim,[status(thm)],[16])). tff(34,plain, (quiet(X!3)), inference(and_elim,[status(thm)],[16])). tff(35,plain, (((~![X: $i, Y: $i] : ((X = Y) \| (~european(Y)) \| (~quiet(X)) \| (~european(X)) \| (~quiet(Y)))) \| ((~european(mary)) \| (~european(X!3)) \| (mary = X!3) \| (~quiet(mary)) \| (~quiet(X!3)))) <=> ((~![X: $i, Y: $i] : ((X = Y) \| (~european(Y)) \| (~quiet(X)) \| (~european(X)) \| (~quiet(Y)))) \| (~european(mary)) \| (~european(X!3)) \| (mary = X!3) \| (~quiet(mary)) \| (~quiet(X!3)))), inference(rewrite,[status(thm)],[])). tff(36,plain, (((mary = X!3) \| (~european(X!3)) \| (~quiet(mary)) \| (~european(mary)) \| (~quiet(X!3))) <=> ((~european(mary)) \| (~european(X!3)) \| (mary = X!3) \| (~quiet(mary)) \| (~quiet(X!3)))), inference(rewrite,[status(thm)],[])). tff(37,plain, (((~![X: $i, Y: $i] : ((X = Y) \| (~european(Y)) \| (~quiet(X)) \| (~european(X)) \| (~quiet(Y)))) \| ((mary = X!3) \| (~european(X!3)) \| (~quiet(mary)) \| (~european(mary)) \| (~quiet(X!3)))) <=> ((~![X: $i, Y: $i] : ((X = Y) \| (~european(Y)) \| (~quiet(X)) \| (~european(X)) \| (~quiet(Y)))) \| ((~european(mary)) \| (~european(X!3)) \| (mary = X!3) \| (~quiet(mary)) \| (~quiet(X!3))))), inference(monotonicity,[status(thm)],[36])). tff(38,plain, (((~![X: $i, Y: $i] : ((X = Y) \| (~european(Y)) \| (~quiet(X)) \| (~european(X)) \| (~quiet(Y)))) \| ((mary = X!3) \| (~european(X!3)) \| (~quiet(mary)) \| (~european(mary)) \| (~quiet(X!3)))) <=> ((~![X: $i, Y: $i] : ((X = Y) \| (~european(Y)) \| (~quiet(X)) \| (~european(X)) \| (~quiet(Y)))) \| (~european(mary)) \| (~european(X!3)) \| (mary = X!3) \| (~quiet(mary)) \| (~quiet(X!3)))), inference(transitivity,[status(thm)],[37, 35])). tff(39,plain, ((~![X: $i, Y: $i] : ((X = Y) \| (~european(Y)) \| (~quiet(X)) \| (~european(X)) \| (~quiet(Y)))) \| ((mary = X!3) \| (~european(X!3)) \| (~quiet(mary)) \| (~european(mary)) \| (~quiet(X!3)))), inference(quant_inst,[status(thm)],[])). tff(40,plain, ((~![X: $i, Y: $i] : ((X = Y) \| (~european(Y)) \| (~quiet(X)) \| (~european(X)) \| (~quiet(Y)))) \| (~european(mary)) \| (~european(X!3)) \| (mary = X!3) \| (~quiet(mary)) \| (~quiet(X!3))), inference(modus_ponens,[status(thm)],[39, 38])). tff(41,plain, ((~european(mary)) \| (mary = X!3)), inference(unit_resolution,[status(thm)],[40, 34, 33, 32, 22])). tff(42,plain, (~european(mary)), inference(unit_resolution,[status(thm)],[41, 19])). tff(43,plain, (((~rich(mary)) \| (~tall(mary)) \| (~creative(mary)) \| (~european(mary))) \| european(mary)), inference(tautology,[status(thm)],[])). tff(44,plain, ((~rich(mary)) \| (~tall(mary)) \| (~creative(mary)) \| (~european(mary))), inference(unit_resolution,[status(thm)],[43, 42])). tff(45,plain, (((~room(mary)) \| (~((~room(X!4)) \| (X!4 = \|'mary'\|))) \| (rich(mary) & tall(mary) & creative(mary) & european(mary))) <=> ((~room(mary)) \| (~((~room(X!4)) \| (X!4 = \|'mary'\|))) \| (~((~rich(mary)) \| (~tall(mary)) \| (~creative(mary)) \| (~european(mary)))))), inference(rewrite,[status(thm)],[])). tff(46,plain, ((room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~(rich(mary) & tall(mary) & creative(mary) & european(mary)))) <=> (room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~(rich(mary) & tall(mary) & creative(mary) & european(mary))))), inference(rewrite,[status(thm)],[])). tff(47,plain, ((~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~(rich(mary) & tall(mary) & creative(mary) & european(mary))))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~(rich(mary) & tall(mary) & creative(mary) & european(mary)))))), inference(monotonicity,[status(thm)],[46])). tff(48,plain, ((~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~(rich(mary) & tall(mary) & creative(mary) & european(mary))))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~(rich(mary) & tall(mary) & creative(mary) & european(mary)))))), inference(rewrite,[status(thm)],[])). tff(49,plain, (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~(rich(mary) & tall(mary) & creative(mary) & european(mary))))), inference(or_elim,[status(thm)],[8])). tff(50,plain, (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~(rich(mary) & tall(mary) & creative(mary) & european(mary))))), inference(modus_ponens,[status(thm)],[49, 47])). tff(51,plain, (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~(rich(mary) & tall(mary) & creative(mary) & european(mary))))), inference(modus_ponens,[status(thm)],[50, 48])). tff(52,plain, (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~(rich(mary) & tall(mary) & creative(mary) & european(mary))))), inference(modus_ponens,[status(thm)],[51, 47])). 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 (refl (~ (and (rich mary) (tall mary) (creative mary) (european mary)) (and (rich mary) (tall mary) (creative mary) (european mary)))))) (let ((a!5 (and (room mary) a!2 (not (and (rich mary) (tall mary) (creative mary) (european mary)))))) (let ((a!6 (~ (not a!5) (or (not (room mary)) a!3 (and (rich mary) (tall mary) (creative mary) (european mary)))))) (nnf-neg a!1 (sk (~ (not a!2) a!3)) a!4 a!6))))	room(lester)&(![X]:(room(X)=>(X='lester')))& ((?[X,Y]:((~like(regina,X))&(~(brave(Y)&tall(Y)&tourist(Y)))&(like(X,Y))))& (((?[X]:(~room(X)&like(regina,X)))&(![X,Y]:((like(regina,X)&like(regina,Y))=>(X=Y)))))& (![X]:(richer(X,lester)))& (((?[X]:(~room(X)&quiet(X)&european(X)))&(![X,Y]:((quiet(X)&european(X)&quiet(Y)&european(Y))=>(X=Y)))))& (rich(lester)&creative(lester)&quiet(lester)&brave(lester)&tall(lester)&tourist(lester)))	room(lester)&(![X]:(room(X)=>(X='lester')))& (~(rich(lester)&tall(lester)&creative(lester)&european(lester)))	contradiction	contradiction	contradiction
Helen neither is not a tall person nor hates Charles. Aletha neither does not own a television nor is not a tall person.	Helen who is not a tall european, is richer than Charles.	neutral	% SZS status Satisfiable	room(helen)&room(aletha)&(![X]:(room(X)=>(X='helen'\|X='aletha')))& ((~((~(tall(helen)&person(helen)))\|(hate(charles,helen))))& (~((does_not_own_a_television(aletha))\|(~(tall(aletha)&person(aletha))))))	room(helen)&room(aletha)&(![X]:(room(X)=>(X='helen'\|X='aletha')))& ((~(tall(helen)&european(helen)))&(richer(charles,helen)))	neutral	contradiction	contradiction
Doris, Jeff, Carl, Robert are the only persons in the room. More than one person outside the room is not Robert. Only one person outside the room is taller than Bradley. Doris hates Bradley or does not enjoy trail running or both.	Doris has a piercing or does not hate Bradley or both.	neutral	% SZS status Satisfiable	room(doris)&room(jeff)&room(carl)&room(robert)&(![X]:(room(X)=>(X='doris'\|X='jeff'\|X='carl'\|X='robert')))& (((?[X,Y]:(~room(X)&~room(Y)&(X!=robert&Y!=robert)&(X!=Y))))& (((?[X]:(~room(X)&taller(bradley,X)))&(![X,Y]:((taller(bradley,X)&taller(bradley,Y))=>(X=Y)))))& (((hate(bradley,doris))\|(does_not_enjoy_trail_running(doris)))))	room(doris)&room(jeff)&room(carl)&room(robert)&(![X]:(room(X)=>(X='doris'\|X='jeff'\|X='carl'\|X='robert')))& (((has_a_piercing(doris))\|(~hate(bradley,doris))))	neutral	entailment	entailment
None of the following is true:. -Michael neither is not tall, not quiet nor is a tall tourist. -Anita neither is not a quiet tourist nor is not quiet, not tall.	Anita is not a quiet tourist.	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(paul_type, type, ( paul: $i)). tff(quiet_type, type, ( quiet: $i > $o)). tff(tall_type, type, ( tall: $i > $o)). tff(mary_type, type, ( mary: $i)). tff(alice_type, type, ( alice: $i)). tff(fred_type, type, ( fred: $i)). tff(1,assumption,(~((~quiet(paul)) \| (~tourist(paul)))), introduced(assumption)). tff(2,plain, (((~quiet(paul)) \| (~tourist(paul))) \| quiet(paul)), inference(tautology,[status(thm)],[])). tff(3,plain, (quiet(paul)), inference(unit_resolution,[status(thm)],[2, 1])). tff(4,plain, ((quiet(paul) \| tall(paul)) \| (~quiet(paul))), inference(tautology,[status(thm)],[])). tff(5,plain, (quiet(paul) \| tall(paul)), inference(unit_resolution,[status(thm)],[4, 3])). tff(6,plain, (((~quiet(paul)) \| (~tourist(paul))) \| tourist(paul)), inference(tautology,[status(thm)],[])). tff(7,plain, (tourist(paul)), inference(unit_resolution,[status(thm)],[6, 1])). tff(8,plain, ((((~quiet(paul)) \| (~tourist(paul))) \| (~(quiet(paul) \| tall(paul)))) <=> ((~quiet(paul)) \| (~tourist(paul)) \| (~(quiet(paul) \| tall(paul))))), inference(rewrite,[status(thm)],[])). tff(9,plain, (((~quiet(paul)) & (~tall(paul))) <=> (~(quiet(paul) \| tall(paul)))), inference(rewrite,[status(thm)],[])). tff(10,plain, ((~(~((~quiet(paul)) \| (~tourist(paul))))) <=> ((~quiet(paul)) \| (~tourist(paul)))), inference(rewrite,[status(thm)],[])). tff(11,plain, ((quiet(paul) & tourist(paul)) <=> (~((~quiet(paul)) \| (~tourist(paul))))), inference(rewrite,[status(thm)],[])). tff(12,plain, ((~(quiet(paul) & tourist(paul))) <=> (~(~((~quiet(paul)) \| (~tourist(paul)))))), inference(monotonicity,[status(thm)],[11])). tff(13,plain, ((~(quiet(paul) & tourist(paul))) <=> ((~quiet(paul)) \| (~tourist(paul)))), inference(transitivity,[status(thm)],[12, 10])). tff(14,plain, (((~(quiet(paul) & tourist(paul))) \| ((~quiet(paul)) & (~tall(paul)))) <=> (((~quiet(paul)) \| (~tourist(paul))) \| (~(quiet(paul) \| tall(paul))))), inference(monotonicity,[status(thm)],[13, 9])). tff(15,plain, (((~(quiet(paul) & tourist(paul))) \| ((~quiet(paul)) & (~tall(paul)))) <=> ((~quiet(paul)) \| (~tourist(paul)) \| (~(quiet(paul) \| tall(paul))))), inference(transitivity,[status(thm)],[14, 8])). tff(16,plain, (((~(quiet(paul) & tourist(paul))) \| ((~quiet(paul)) & (~tall(paul)))) <=> ((~(quiet(paul) & tourist(paul))) \| ((~quiet(paul)) & (~tall(paul))))), inference(rewrite,[status(thm)],[])). tff(17,plain, ((~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)) \| (X = \|'alice'\|)))) & (~((~(((~tall(mary)) & (~quiet(mary))) \| (tall(mary) & tourist(mary)))) \| (~((~(quiet(paul) & tourist(paul))) \| ((~quiet(paul)) & (~tall(paul)))))))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)) \| (X = \|'alice'\|)))) & (~(quiet(paul) & tourist(paul)))))) <=> (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~((~(((~tall(mary)) & (~quiet(mary))) \| (tall(mary) & tourist(mary)))) \| (~((~(quiet(paul) & tourist(paul))) \| ((~quiet(paul)) & (~tall(paul))))))))) \| (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~(quiet(paul) & tourist(paul))))))), inference(rewrite,[status(thm)],[])). tff(18,axiom,(~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)) \| (X = \|'alice'\|)))) & (~((~(((~tall(mary)) & (~quiet(mary))) \| (tall(mary) & tourist(mary)))) \| (~((~(quiet(paul) & tourist(paul))) \| ((~quiet(paul)) & (~tall(paul)))))))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)) \| (X = \|'alice'\|)))) & (~(quiet(paul) & tourist(paul)))))), file('/mnt/tmpfs//3297052140574498422207429.p','negated')). tff(19,plain, (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~((~(((~tall(mary)) & (~quiet(mary))) \| (tall(mary) & tourist(mary)))) \| (~((~(quiet(paul) & tourist(paul))) \| ((~quiet(paul)) & (~tall(paul))))))))) \| (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~(quiet(paul) & tourist(paul)))))), inference(modus_ponens,[status(thm)],[18, 17])). tff(20,plain, (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~((~(((~tall(mary)) & (~quiet(mary))) \| (tall(mary) & tourist(mary)))) \| (~((~(quiet(paul) & tourist(paul))) \| ((~quiet(paul)) & (~tall(paul)))))))), inference(or_elim,[status(thm)],[19])). tff(21,plain, (~((~(((~tall(mary)) & (~quiet(mary))) \| (tall(mary) & tourist(mary)))) \| (~((~(quiet(paul) & tourist(paul))) \| ((~quiet(paul)) & (~tall(paul))))))), inference(and_elim,[status(thm)],[20])). tff(22,plain, ((~(quiet(paul) & tourist(paul))) \| ((~quiet(paul)) & (~tall(paul)))), inference(or_elim,[status(thm)],[21])). tff(23,plain, ((~(quiet(paul) & tourist(paul))) \| ((~quiet(paul)) & (~tall(paul)))), inference(modus_ponens,[status(thm)],[22, 16])). tff(24,plain, ((~quiet(paul)) \| (~tourist(paul)) \| (~(quiet(paul) \| tall(paul)))), inference(modus_ponens,[status(thm)],[23, 15])). tff(25,plain, ($false), inference(unit_resolution,[status(thm)],[24, 7, 3, 5])). tff(26,plain,((~quiet(paul)) \| (~tourist(paul))), inference(lemma,lemma(discharge,[]))). tff(27,plain, (room(alice) <=> room(alice)), inference(rewrite,[status(thm)],[])). tff(28,plain, (room(alice)), inference(and_elim,[status(thm)],[20])). tff(29,plain, (room(alice)), inference(modus_ponens,[status(thm)],[28, 27])). tff(30,plain, (room(fred) <=> room(fred)), inference(rewrite,[status(thm)],[])). tff(31,plain, (room(fred)), inference(and_elim,[status(thm)],[20])). tff(32,plain, (room(fred)), inference(modus_ponens,[status(thm)],[31, 30])). tff(33,plain, (room(paul) <=> room(paul)), inference(rewrite,[status(thm)],[])). tff(34,plain, (room(paul)), inference(and_elim,[status(thm)],[20])). tff(35,plain, (room(paul)), inference(modus_ponens,[status(thm)],[34, 33])). tff(36,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(37,plain, (room(mary)), inference(and_elim,[status(thm)],[20])). tff(38,plain, (room(mary)), inference(modus_ponens,[status(thm)],[37, 36])). tff(39,plain, (((~((~quiet(paul)) \| (~tourist(paul)))) \| (~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)))) \| (~((~quiet(paul)) \| (~tourist(paul)))))), inference(rewrite,[status(thm)],[])). tff(40,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(41,plain, (((quiet(paul) & tourist(paul)) \| (~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~room(alice)) \| (~((X!0 = \|'alice'\|) \| (X!0 = \|'fred'\|) \| (X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0))))) <=> ((~((~quiet(paul)) \| (~tourist(paul)))) \| (~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)],[11, 40])). tff(42,plain, (((quiet(paul) & tourist(paul)) \| (~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)))) \| (~((~quiet(paul)) \| (~tourist(paul)))))), inference(transitivity,[status(thm)],[41, 39])). tff(43,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~room(alice)) \| (~((X!0 = \|'alice'\|) \| (X!0 = \|'fred'\|) \| (X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0)))) \| (quiet(paul) & tourist(paul))) <=> ((quiet(paul) & tourist(paul)) \| (~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(44,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~room(alice)) \| (~((X!0 = \|'alice'\|) \| (X!0 = \|'fred'\|) \| (X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0)))) \| (quiet(paul) & tourist(paul))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~room(alice)) \| (~((X!0 = \|'alice'\|) \| (X!0 = \|'fred'\|) \| (X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0)))) \| (quiet(paul) & tourist(paul)))), inference(monotonicity,[status(thm)],[40])). 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)))) \| (quiet(paul) & tourist(paul))) <=> ((quiet(paul) & tourist(paul)) \| (~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)],[44, 43])). tff(46,plain, ((room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~(quiet(paul) & tourist(paul)))) <=> (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~(quiet(paul) & tourist(paul))))), inference(rewrite,[status(thm)],[])). tff(47,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~(quiet(paul) & tourist(paul))))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~(quiet(paul) & tourist(paul)))))), inference(monotonicity,[status(thm)],[46])). tff(48,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~(quiet(paul) & tourist(paul))))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~(quiet(paul) & tourist(paul)))))), 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))) & (~(quiet(paul) & tourist(paul))))), inference(or_elim,[status(thm)],[19])). tff(50,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~(quiet(paul) & tourist(paul))))), inference(modus_ponens,[status(thm)],[49, 47])). tff(51,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~(quiet(paul) & tourist(paul))))), inference(modus_ponens,[status(thm)],[50, 48])). tff(52,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~(quiet(paul) & tourist(paul))))), inference(modus_ponens,[status(thm)],[51, 47])). 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 (~ (and (quiet paul) (tourist paul)) (and (quiet paul) (tourist paul)))))) (let ((a!8 (and (room mary) (room paul) (room fred) (room alice) a!5 (not (and (quiet paul) (tourist paul)))))) (let ((a!9 (~ (not a!8) (or (not (room mary)) (not (room paul)) (not (room fred)) (not (room alice)) a!6 (and (quiet paul) (tourist paul)))))) (nnf-neg a!1 a!2 a!3 a!4 (sk (~ (not a!5) a!6)) a!7 a!9))))	room(michael)&room(anita)&room(shirley)&room(charles)&(![X]:(room(X)=>(X='michael'\|X='anita'\|X='shirley'\|X='charles')))& (~((~((~tall(michael)&~quiet(michael))\|(tall(michael)&tourist(michael))))\|(~((~(quiet(anita)&tourist(anita)))\|(~quiet(anita)&~tall(anita))))))	room(michael)&room(anita)&room(shirley)&room(charles)&(![X]:(room(X)=>(X='michael'\|X='anita'\|X='shirley'\|X='charles')))& (~(quiet(anita)&tourist(anita)))	contradiction	neutral	contradiction
Dora, Tami, Lura are the only persons in the room. 'No one outside the room hates Marvin' unless 'Marvin is a sibling of Tami'. If 'Lura neither hates Mary nor plays the drums' then 'Lura is the tallest in the room'. Dora neither is not brave nor is not hated by Marvin. Lura and Tami are respectively creative and brave. Someone who hates Marvin hate someone who is not Lura. Tami does not hate Marvin or does not play the drums or both. Dora and Tami are respectively tall and creative. Tami is the tallest in the room. Everyone outside the room who is not creative, not brave, not tall is not hated by Mary.	Someone who is not rich, not quiet, not tall, not creative, not happy is a sibling of someone who is a sibling of Marvin.	neutral	% SZS status Satisfiable	room(dora)&room(tami)&room(lura)&(![X]:(room(X)=>(X='dora'\|X='tami'\|X='lura')))& ((~(sibling(tami,marvin))=>(~?[X]:(~room(X)=>(hate(marvin,X)))))& ((~((hate(mary,lura))\|(plays_the_drums(lura))))=>(![X]:(taller(X,lura))))& (~((~brave(dora))\|(~hate(dora,marvin))))& ((creative(lura))&(brave(tami)))& (?[X,Y]:((hate(marvin,X))&(Y!=lura)&(hate(X,Y))))& (((~hate(marvin,tami))\|(does_not_play_the_drums(tami))))& ((tall(dora))&(creative(tami)))& (![X]:(taller(X,tami)))& (![X]:(~room(X)=>(((~creative(X)&~brave(X)&~tall(X))=>(~hate(X,mary)))))))	room(dora)&room(tami)&room(lura)&(![X]:(room(X)=>(X='dora'\|X='tami'\|X='lura')))& (?[X,Y]:((~rich(X)&~quiet(X)&~tall(X)&~creative(X)&~happy(X))&(sibling(marvin,Y))&(sibling(X,Y))))	neutral	neutral	entailment
Todd, William, Jeff are the only persons in the room. Only one person in the room hates Jamie. More than one person outside the room is hated by Jamie. Todd and William hate each other. William is not hated by Jamie or is not Todd or both. Jamie is a sibling of Jeff.	Todd and Jeff are sibling of Jamie.	neutral	% SZS status Satisfiable	room(todd)&room(william)&room(jeff)&(![X]:(room(X)=>(X='todd'\|X='william'\|X='jeff')))& ((((?[X]:(room(X)&hate(jamie,X)))&(![X,Y]:((hate(jamie,X)&hate(jamie,Y))=>(X=Y)))))& ((?[X,Y]:(~room(X)&~room(Y)&(hate(X,jamie)&hate(Y,jamie))&(X!=Y))))& ((hate(todd,william) & hate(william,todd)))& (((~hate(william,jamie))\|(william!=todd)))& (sibling(jeff,jamie)))	room(todd)&room(william)&room(jeff)&(![X]:(room(X)=>(X='todd'\|X='william'\|X='jeff')))& (sibling(jamie,todd)&sibling(jamie,jeff))	contradiction	entailment	entailment
Carole is the only person in the room. If "more than one person outside the room is not Carole" then "Carole neither is not rich nor does not hate Dana". If "Wilma and Dana hate each other" then "Carole is not hated by Carman" otherwise "Carole is hated by Wilma". "Carole is the richest in the room" unless "someone who hates Carman hate someone who is not hated by Wilma". Everyone outside the room hates Dana. Dana is a client of Carole. More than one person outside the room is hated by Dana. Carole is the least rich in the room. Wilma and Carole hate each other. Someone outside the room who is a client of Dana is not hated by Carman.	Someone who is richer than Wilma hate someone who is not rich.	contradiction	-	room(carole)&(![X]:(room(X)=>(X='carole')))& ((((?[X,Y]:(~room(X)&~room(Y)&(X!=carole&Y!=carole)&(X!=Y))))=>(~((~rich(carole))\|(~hate(dana,carole)))))& ((((hate(wilma,dana) & hate(dana,wilma)))=>(~hate(carole,carman)))\|((~((hate(wilma,dana) & hate(dana,wilma))))=>(hate(carole,wilma))))& (~(?[X,Y]:((hate(carman,X))&(~hate(Y,wilma))&(hate(X,Y))))=>(![X]:(richer(X,carole))))& (![X]:(~room(X)=>(hate(dana,X))))& (client(carole,dana))& ((?[X,Y]:(~room(X)&~room(Y)&(hate(X,dana)&hate(Y,dana))&(X!=Y))))& (![X]:(richer(carole,X)))& ((hate(wilma,carole) & hate(carole,wilma)))& (?[X]:(~room(X)=>(((client(dana,X))=>(~hate(X,carman)))))))	room(carole)&(![X]:(room(X)=>(X='carole')))& (?[X,Y]:((richer(wilma,X))&(~rich(Y))&(hate(X,Y))))	entailment	entailment	neutral
Aileen, Thomas, Arthur, Charles are the only persons in the room. If Arthur does not play the drums or is not Thomas or both then Arthur likes Jorge or is richer than Mary or both. Someone in the room is not a tall creative rich european only if everyone in the room is not liked by Jorge. Thomas is the least rich in the room. Arthur likes Jorge or is richer than Mary or both. Everyone in the room is not liked by Jorge. More than one person in the room is a happy european. Only one person outside the room plays the drums. Jorge is richer than Aileen. Everyone outside the room does not like Mary.	Thomas who is liked by Jorge, is not a tall happy creative person.	contradiction	-	room(aileen)&room(thomas)&room(arthur)&room(charles)&(![X]:(room(X)=>(X='aileen'\|X='thomas'\|X='arthur'\|X='charles')))& (((((does_not_play_the_drums(arthur))\|(arthur!=thomas)))=>(((like(jorge,arthur))\|(richer(mary,arthur)))))& ((?[X]:(room(X)=>(~(tall(X)&creative(X)&rich(X)&european(X)))))=>(![X]:(room(X)=>(~like(X,jorge)))))& (![X]:(richer(thomas,X)))& (((like(jorge,arthur))\|(richer(mary,arthur))))& (![X]:(room(X)=>(~like(X,jorge))))& ((?[X,Y]:(room(X)&room(Y)&(happy(X)&european(X)&happy(Y)&european(Y))&(X!=Y))))& (((?[X]:(~room(X)&plays_the_drums(X)))&(![X,Y]:((plays_the_drums(X)&plays_the_drums(Y))=>(X=Y)))))& (richer(aileen,jorge))& (![X]:(~room(X)=>(~like(mary,X)))))	room(aileen)&room(thomas)&room(arthur)&room(charles)&(![X]:(room(X)=>(X='aileen'\|X='thomas'\|X='arthur'\|X='charles')))& ((like(thomas,jorge))&(~(tall(thomas)&happy(thomas)&creative(thomas)&person(thomas))))	contradiction	neutral	contradiction
Corey, Sherri, Joshua are the only persons in the room. Someone in the room is liked by Ardis. Joshua is liked by Ardis or likes Jerry or both. Joshua and Corey like each other. Ardis is quieter than Joshua. Corey does not like Ardis. Everyone outside the room who enjoys watercolor painting is liked by Jerry.	Corey is not brave, not quiet and likes Ardis.	contradiction	-	room(corey)&room(sherri)&room(joshua)&(![X]:(room(X)=>(X='corey'\|X='sherri'\|X='joshua')))& ((?[X]:(room(X)=>(like(X,ardis))))& (((like(joshua,ardis))\|(like(jerry,joshua))))& ((like(joshua,corey) & like(corey,joshua)))& (quieter(joshua,ardis))& (~like(ardis,corey))& (![X]:(~room(X)=>(((enjoys_watercolor_painting(X))=>(like(X,jerry)))))))	room(corey)&room(sherri)&room(joshua)&(![X]:(room(X)=>(X='corey'\|X='sherri'\|X='joshua')))& ((~brave(corey)&~quiet(corey))&(like(ardis,corey)))	contradiction	contradiction	contradiction
Richarda is the only person in the room. Richarda is the least tall in the room. Richarda is not a happy person. Richarda who is not a happy person, is not hated by Richard.	Richarda neither does enjoy mountain biking nor is not a rich happy tall european.	contradiction	-	room(richarda)&(![X]:(room(X)=>(X='richarda')))& ((![X]:(taller(richarda,X)))& (~(happy(richarda)&person(richarda)))& ((~(happy(richarda)&person(richarda)))&(~hate(richarda,richard))))	room(richarda)&(![X]:(room(X)=>(X='richarda')))& (~((does_enjoy_mountain_biking(richarda))\|(~(rich(richarda)&happy(richarda)&tall(richarda)&european(richarda)))))	neutral	neutral	contradiction
Nathan is the only person in the room. Nathan is liked by Robert or does not play video games or both if only one person in the room is not a rich european and vice versa. If Nathan neither is a quiet european nor is not liked by Robert then Nathan who is quieter than Joann, likes Robert. Nathan is the least rich in the room. Nathan is the quietest in the room. Everyone in the room who watches fantasy movies is not a creative rich tourist. Only one person in the room is a rich european.	Nathan does not watche fantasy movies or is quieter than Jerome or both.	entailment	% SZS status Unsatisfiable % SZS output start Proof tff(tptp_fun__mary__type, type, ( tptp_fun__mary_: $i)). tff(tptp_fun_X_4_type, type, ( tptp_fun_X_4: $i)). tff(room_type, type, ( room: $i > $o)). tff(quieter_type, type, ( quieter: ( $i * $i ) > $o)). tff(mary_type, type, ( mary: $i)). tff(alice_type, type, ( alice: $i)). tff(preda_type, type, ( preda: $i > $o)). tff(european_type, type, ( european: $i > $o)). tff(rich_type, type, ( rich: $i > $o)). tff(tourist_type, type, ( tourist: $i > $o)). tff(creative_type, type, ( creative: $i > $o)). tff(richer_type, type, ( richer: ( $i * $i ) > $o)). tff(like_type, type, ( like: ( $i * $i ) > $o)). tff(fred_type, type, ( fred: $i)). tff(paul_type, type, ( paul: $i)). tff(quiet_type, type, ( quiet: $i > $o)). tff(predb_type, type, ( predb: $i > $o)). tff(1,assumption,(~quieter(alice, mary)), introduced(assumption)). tff(2,plain, (^[X: $i] : refl(quieter(X, mary) <=> quieter(X, mary))), inference(bind,[status(th)],[])). tff(3,plain, (![X: $i] : quieter(X, mary) <=> ![X: $i] : quieter(X, mary)), inference(quant_intro,[status(thm)],[2])). tff(4,plain, (![X: $i] : quieter(X, mary) <=> ![X: $i] : quieter(X, mary)), inference(rewrite,[status(thm)],[])). tff(5,plain, ((~(((room(mary) & ![X: $i] : (room(X) => (X = \|'mary'\|))) & (((((((?[X: $i] : (room(X) & (~(rich(X) & european(X)))) & ![X: $i, Y: $i] : (((~(rich(X) & european(X))) & (~(rich(Y) & european(Y)))) => (X = Y))) <=> (like(mary, fred) \| (~predb(mary)))) & ((~((quiet(mary) & european(mary)) \| (~like(mary, fred)))) => (quieter(paul, mary) & like(fred, mary)))) & ![X: $i] : richer(mary, X)) & ![X: $i] : quieter(X, mary)) & ![X: $i] : (room(X) => (preda(X) => (~((creative(X) & rich(X)) & tourist(X)))))) & (?[X: $i] : ((room(X) & rich(X)) & european(X)) & ![X: $i, Y: $i] : ((((rich(X) & european(X)) & rich(Y)) & european(Y)) => (X = Y))))) => ((room(mary) & ![X: $i] : (room(X) => (X = \|'mary'\|))) & ((~preda(mary)) \| quieter(alice, mary))))) <=> (~((~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ((?[X: $i] : (room(X) & (~(rich(X) & european(X)))) & ![X: $i, Y: $i] : ((~((~(rich(X) & european(X))) & (~(rich(Y) & european(Y))))) \| (X = Y))) <=> (like(mary, fred) \| (~predb(mary)))) & ((quiet(mary) & european(mary)) \| (~like(mary, fred)) \| (quieter(paul, mary) & like(fred, mary))) & ![X: $i] : richer(mary, X) & ![X: $i] : quieter(X, mary) & ![X: $i] : ((~room(X)) \| (~(creative(X) & rich(X) & tourist(X))) \| (~preda(X))) & ?[X: $i] : (room(X) & rich(X) & european(X)) & ![X: $i, Y: $i] : ((~(rich(X) & european(X) & rich(Y) & european(Y))) \| (X = Y)))) \| (room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ((~preda(mary)) \| quieter(alice, mary)))))), inference(rewrite,[status(thm)],[])). tff(6,axiom,(~(((room(mary) & ![X: $i] : (room(X) => (X = \|'mary'\|))) & (((((((?[X: $i] : (room(X) & (~(rich(X) & european(X)))) & ![X: $i, Y: $i] : (((~(rich(X) & european(X))) & (~(rich(Y) & european(Y)))) => (X = Y))) <=> (like(mary, fred) \| (~predb(mary)))) & ((~((quiet(mary) & european(mary)) \| (~like(mary, fred)))) => (quieter(paul, mary) & like(fred, mary)))) & ![X: $i] : richer(mary, X)) & ![X: $i] : quieter(X, mary)) & ![X: $i] : (room(X) => (preda(X) => (~((creative(X) & rich(X)) & tourist(X)))))) & (?[X: $i] : ((room(X) & rich(X)) & european(X)) & ![X: $i, Y: $i] : ((((rich(X) & european(X)) & rich(Y)) & european(Y)) => (X = Y))))) => ((room(mary) & ![X: $i] : (room(X) => (X = \|'mary'\|))) & ((~preda(mary)) \| quieter(alice, mary))))), file('/mnt/tmpfs//1812433221303198791620613.p','negated')). tff(7,plain, (~((~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ((?[X: $i] : (room(X) & (~(rich(X) & european(X)))) & ![X: $i, Y: $i] : ((~((~(rich(X) & european(X))) & (~(rich(Y) & european(Y))))) \| (X = Y))) <=> (like(mary, fred) \| (~predb(mary)))) & ((quiet(mary) & european(mary)) \| (~like(mary, fred)) \| (quieter(paul, mary) & like(fred, mary))) & ![X: $i] : richer(mary, X) & ![X: $i] : quieter(X, mary) & ![X: $i] : ((~room(X)) \| (~(creative(X) & rich(X) & tourist(X))) \| (~preda(X))) & ?[X: $i] : (room(X) & rich(X) & european(X)) & ![X: $i, Y: $i] : ((~(rich(X) & european(X) & rich(Y) & european(Y))) \| (X = Y)))) \| (room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ((~preda(mary)) \| quieter(alice, mary))))), inference(modus_ponens,[status(thm)],[6, 5])). tff(8,plain, (room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ((?[X: $i] : (room(X) & (~(rich(X) & european(X)))) & ![X: $i, Y: $i] : ((~((~(rich(X) & european(X))) & (~(rich(Y) & european(Y))))) \| (X = Y))) <=> (like(mary, fred) \| (~predb(mary)))) & ((quiet(mary) & european(mary)) \| (~like(mary, fred)) \| (quieter(paul, mary) & like(fred, mary))) & ![X: $i] : richer(mary, X) & ![X: $i] : quieter(X, mary) & ![X: $i] : ((~room(X)) \| (~(creative(X) & rich(X) & tourist(X))) \| (~preda(X))) & ?[X: $i] : (room(X) & rich(X) & european(X)) & ![X: $i, Y: $i] : ((~(rich(X) & european(X) & rich(Y) & european(Y))) \| (X = Y))), inference(or_elim,[status(thm)],[7])). tff(9,plain, (![X: $i] : quieter(X, mary)), inference(and_elim,[status(thm)],[8])). tff(10,plain, (![X: $i] : quieter(X, mary)), inference(modus_ponens,[status(thm)],[9, 4])). tff(11,plain,( ![X: $i] : quieter(X, mary)), inference(skolemize,[status(sab)],[10])). tff(12,plain, (![X: $i] : quieter(X, mary)), inference(modus_ponens,[status(thm)],[11, 3])). tff(13,plain, ((~![X: $i] : quieter(X, mary)) \| quieter(alice, mary)), inference(quant_inst,[status(thm)],[])). tff(14,plain, ($false), inference(unit_resolution,[status(thm)],[13, 12, 1])). tff(15,plain,(quieter(alice, mary)), inference(lemma,lemma(discharge,[]))). tff(16,plain, (((~preda(mary)) \| quieter(alice, mary)) \| (~quieter(alice, mary))), inference(tautology,[status(thm)],[])). tff(17,plain, ((~preda(mary)) \| quieter(alice, mary)), inference(unit_resolution,[status(thm)],[16, 15])). tff(18,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(19,plain, (room(mary)), inference(and_elim,[status(thm)],[8])). tff(20,plain, (room(mary)), inference(modus_ponens,[status(thm)],[19, 18])). tff(21,plain, (((~room(mary)) \| (~((~room(X!4)) \| (X!4 = \|'mary'\|))) \| (~((~preda(mary)) \| quieter(alice, mary)))) <=> ((~room(mary)) \| (~((~room(X!4)) \| (X!4 = \|'mary'\|))) \| (~((~preda(mary)) \| quieter(alice, mary))))), inference(rewrite,[status(thm)],[])). tff(22,plain, ((room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ((~preda(mary)) \| quieter(alice, mary))) <=> (room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ((~preda(mary)) \| quieter(alice, mary)))), inference(rewrite,[status(thm)],[])). tff(23,plain, ((~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ((~preda(mary)) \| quieter(alice, mary)))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ((~preda(mary)) \| quieter(alice, mary))))), inference(monotonicity,[status(thm)],[22])). tff(24,plain, ((~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ((~preda(mary)) \| quieter(alice, mary)))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ((~preda(mary)) \| quieter(alice, mary))))), inference(rewrite,[status(thm)],[])). tff(25,plain, (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ((~preda(mary)) \| quieter(alice, mary)))), inference(or_elim,[status(thm)],[7])). tff(26,plain, (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ((~preda(mary)) \| quieter(alice, mary)))), inference(modus_ponens,[status(thm)],[25, 23])). tff(27,plain, (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ((~preda(mary)) \| quieter(alice, mary)))), inference(modus_ponens,[status(thm)],[26, 24])). tff(28,plain, (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ((~preda(mary)) \| quieter(alice, mary)))), inference(modus_ponens,[status(thm)],[27, 23])). 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 (not (or (not (preda mary)) (quieter alice mary))))) (let ((a!5 (and (room mary) a!2 (or (not (preda mary)) (quieter alice mary))))) (let ((a!6 (~ (not a!5) (or (not (room mary)) a!3 a!4)))) (nnf-neg a!1 (sk (~ (not a!2) a!3)) (refl (~ a!4 a!4)) a!6))))	room(nathan)&(![X]:(room(X)=>(X='nathan')))& (((((?[X]:(room(X)&~(rich(X)&european(X))))&(![X,Y]:((~(rich(X)&european(X))&~(rich(Y)&european(Y)))=>(X=Y)))))<=>(((like(nathan,robert))\|(does_not_play_video_games(nathan)))))& ((~((quiet(nathan)&european(nathan))\|(~like(nathan,robert))))=>((quieter(joann,nathan))&(like(robert,nathan))))& (![X]:(richer(nathan,X)))& (![X]:(quieter(X,nathan)))& (![X]:(room(X)=>(((watches_fantasy_movies(X))=>(~(creative(X)&rich(X)&tourist(X)))))))& (((?[X]:(room(X)&rich(X)&european(X)))&(![X,Y]:((rich(X)&european(X)&rich(Y)&european(Y))=>(X=Y))))))	room(nathan)&(![X]:(room(X)=>(X='nathan')))& (((does_not_watche_fantasy_movies(nathan))\|(quieter(jerome,nathan))))	contradiction	entailment	contradiction
It is not the case that 'Robbie is a client of Kenneth or is a sibling of Jose or both'.	Robbie is a sibling of Jose and hates Kenneth.	contradiction	-	room(johanna)&room(robert)&room(robbie)&room(joseph)&(![X]:(room(X)=>(X='johanna'\|X='robert'\|X='robbie'\|X='joseph')))& (~(((client(kenneth,robbie))\|(sibling(jose,robbie)))))	room(johanna)&room(robert)&room(robbie)&room(joseph)&(![X]:(room(X)=>(X='johanna'\|X='robert'\|X='robbie'\|X='joseph')))& ((sibling(jose,robbie))&(hate(kenneth,robbie)))	contradiction	neutral	contradiction
None of the following is true:. -It is not the case that 'Laura is not hated by Grace and hates Grace'. -Laura either likes Grace or is not happy, not tall, not quiet.	It is not the case that 'someone who is liked by Grace like someone who is not hated by Grace'.	neutral	% SZS status Satisfiable	room(laura)&room(jason)&room(tina)&room(michelle)&(![X]:(room(X)=>(X='laura'\|X='jason'\|X='tina'\|X='michelle')))& (~((~((~hate(laura,grace))&(hate(grace,laura))))\|((((like(grace,laura))\|(~happy(laura)&~tall(laura)&~quiet(laura)))&(~((like(grace,laura))\|(~happy(laura)&~tall(laura)&~quiet(laura))))))))	room(laura)&room(jason)&room(tina)&room(michelle)&(![X]:(room(X)=>(X='laura'\|X='jason'\|X='tina'\|X='michelle')))& (~(?[X,Y]:((like(X,grace))&(~hate(Y,grace))&(like(X,Y)))))	entailment	entailment	entailment
Jeri, Robert, Maria, Scott are the only persons in the room. "Jeri is the least quiet in the room" only if "Scott and Maria like each other". Scott and Maria like each other. Ashley is quieter than Robert.	Robert likes Ashley or is not a tall quiet rich person or both.	neutral	% SZS status Satisfiable	room(jeri)&room(robert)&room(maria)&room(scott)&(![X]:(room(X)=>(X='jeri'\|X='robert'\|X='maria'\|X='scott')))& (((![X]:(quieter(jeri,X)))=>((like(scott,maria) & like(maria,scott))))& ((like(scott,maria) & like(maria,scott)))& (quieter(robert,ashley)))	room(jeri)&room(robert)&room(maria)&room(scott)&(![X]:(room(X)=>(X='jeri'\|X='robert'\|X='maria'\|X='scott')))& (((like(ashley,robert))\|(~(tall(robert)&quiet(robert)&rich(robert)&person(robert)))))	neutral	entailment	entailment
Andrew, Mack, Robert, Antonio are the only persons in the room. At least one of the following is true:. -Mack is the least tall in the room. -Mack and Antonio are respectively tall and rich. -Everyone outside the room who does not can play the guitar does not like Bryan.	Andrew who is taller than Bryan, is not tall.	neutral	% SZS status Satisfiable	room(andrew)&room(mack)&room(robert)&room(antonio)&(![X]:(room(X)=>(X='andrew'\|X='mack'\|X='robert'\|X='antonio')))& (((![X]:(taller(mack,X)))\| ((tall(mack))&(rich(antonio)))\| (![X]:(~room(X)=>(((does_not_can_play_the_guitar(X))=>(~like(bryan,X))))))))	room(andrew)&room(mack)&room(robert)&room(antonio)&(![X]:(room(X)=>(X='andrew'\|X='mack'\|X='robert'\|X='antonio')))& ((taller(bryan,andrew))&(~tall(andrew)))	contradiction	neutral	contradiction
Michael, Rosalia are the only persons in the room. Michael is liked by Mandy. Rosalia does not enjoy jogging or does not like James or both. Everyone outside the room is not brave. More than one person outside the room does not like Mandy. Rosalia and Michael are respectively happy and brave.	Rosalia who does not enjoy jogging, does not like Mandy.	neutral	% SZS status Satisfiable	room(michael)&room(rosalia)&(![X]:(room(X)=>(X='michael'\|X='rosalia')))& ((like(michael,mandy))& (((does_not_enjoy_jogging(rosalia))\|(~like(james,rosalia))))& (![X]:(~room(X)=>(~brave(X))))& ((?[X,Y]:(~room(X)&~room(Y)&(~like(mandy,X)&~like(mandy,Y))&(X!=Y))))& ((happy(rosalia))&(brave(michael))))	room(michael)&room(rosalia)&(![X]:(room(X)=>(X='michael'\|X='rosalia')))& ((does_not_enjoy_jogging(rosalia))&(~like(mandy,rosalia)))	contradiction	contradiction	contradiction
Carmen, Lillian are the only persons in the room. Lillian who is not Carmen, is a rich european unless only one person outside the room is not Carmen. Carmen does not collect action figures. Lillian neither is not hated by Virginia nor is taller than Virginia. Someone who does not hate Lillian hate someone who collects action figures. Lillian collects action figures and is not a tall european. Only one person outside the room is a tall european. Carmen is the least rich in the room.	Lillian who is a tall creative person, is not rich.	contradiction	-	room(carmen)&room(lillian)&(![X]:(room(X)=>(X='carmen'\|X='lillian')))& ((~(((?[X]:(~room(X)&X!=carmen))&(![X,Y]:((X!=carmen&Y!=carmen)=>(X=Y)))))=>((lillian!=carmen)&(rich(lillian)&european(lillian))))& (does_not_collect_action_figures(carmen))& (~((~hate(lillian,virginia))\|(taller(virginia,lillian))))& (?[X,Y]:((~hate(lillian,X))&(collects_action_figures(Y))&(hate(X,Y))))& ((collects_action_figures(lillian))&(~(tall(lillian)&european(lillian))))& (((?[X]:(~room(X)&tall(X)&european(X)))&(![X,Y]:((tall(X)&european(X)&tall(Y)&european(Y))=>(X=Y)))))& (![X]:(richer(carmen,X))))	room(carmen)&room(lillian)&(![X]:(room(X)=>(X='carmen'\|X='lillian')))& ((tall(lillian)&creative(lillian)&person(lillian))&(~rich(lillian)))	contradiction	contradiction	contradiction
Andrew is the only person in the room. Andrew is the least quiet in the room. Someone who is a creative person is quieter than someone who is not Andrew. Andrew neither is liked by Frederick nor is quieter than Carol. Andrew neither is not a creative quiet person nor is liked by Carol. Renata and Frederick like each other. Andrew is not a craft beer aficionado or does not like Carol or both. Frederick and Carol like each other.	Andrew is quieter than Frederick and practices digital art.	contradiction	-	room(andrew)&(![X]:(room(X)=>(X='andrew')))& ((![X]:(quieter(andrew,X)))& (?[X,Y]:((creative(X)&person(X))&(Y!=andrew)&(quieter(X,Y))))& (~((like(andrew,frederick))\|(quieter(carol,andrew))))& (~((~(creative(andrew)&quiet(andrew)&person(andrew)))\|(like(andrew,carol))))& ((like(renata,frederick) & like(frederick,renata)))& (((is_not_a_craft_beer_aficionado(andrew))\|(~like(carol,andrew))))& ((like(frederick,carol) & like(carol,frederick))))	room(andrew)&(![X]:(room(X)=>(X='andrew')))& ((quieter(frederick,andrew))&(practices_digital_art(andrew)))	neutral	contradiction	contradiction
Stephanie, Matthew are the only persons in the room. If everyone outside the room is not happy then Stephanie and Joe like each other otherwise no one outside the room who does not have a tattoo likes Ellen. Stephanie is a tall tourist. Stephanie does not like Joe. Stephanie is the least tall in the room.	It is not the case that 'Matthew who is taller than Joe, is not quiet, not tall, not happy'.	entailment	% SZS status Unsatisfiable % SZS output start Proof tff(tall_type, type, ( tall: $i > $o)). tff(fred_type, type, ( fred: $i)). tff(taller_type, type, ( taller: ( $i * $i ) > $o)). tff(mary_type, type, ( mary: $i)). tff(like_type, type, ( like: ( $i * $i ) > $o)). tff(tourist_type, type, ( tourist: $i > $o)). 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(paul_type, type, ( paul: $i)). tff(happy_type, type, ( happy: $i > $o)). tff(quiet_type, type, ( quiet: $i > $o)). tff(alice_type, type, ( alice: $i)). tff(preda_type, type, ( preda: $i > $o)). tff(john_type, type, ( john: $i)). tff(susan_type, type, ( susan: $i)). tff(lucy_type, type, ( lucy: $i)). tff(tptp_fun_X_0_type, type, ( tptp_fun_X_0: $i)). tff(1,assumption,(~taller(mary, fred)), introduced(assumption)). tff(2,plain, (^[X: $i] : refl(taller(mary, X) <=> taller(mary, X))), inference(bind,[status(th)],[])). tff(3,plain, (![X: $i] : taller(mary, X) <=> ![X: $i] : taller(mary, X)), inference(quant_intro,[status(thm)],[2])). tff(4,plain, (![X: $i] : taller(mary, X) <=> ![X: $i] : taller(mary, X)), inference(rewrite,[status(thm)],[])). tff(5,plain, ((~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = \|'mary'\|) \| (X = \|'paul'\|)))) & (((((![X: $i] : ((~room(X)) => (~happy(X))) => (like(mary, fred) & like(fred, mary))) \| ((~![X: $i] : ((~room(X)) => (~happy(X)))) => (~?[X: $i] : ((~room(X)) => ((~preda(X)) => like(alice, X)))))) & (tall(mary) & tourist(mary))) & (~like(fred, mary))) & ![X: $i] : taller(mary, X))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = \|'mary'\|) \| (X = \|'paul'\|)))) & (~(taller(fred, paul) & (((~quiet(paul)) & (~tall(paul))) & (~happy(paul)))))))) <=> (~((~(room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & tall(mary) & tourist(mary) & (~like(fred, mary)) & ![X: $i] : taller(mary, X))) \| (room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~(taller(fred, paul) & (~quiet(paul)) & (~tall(paul)) & (~happy(paul)))))))), inference(rewrite,[status(thm)],[])). tff(6,axiom,(~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = \|'mary'\|) \| (X = \|'paul'\|)))) & (((((![X: $i] : ((~room(X)) => (~happy(X))) => (like(mary, fred) & like(fred, mary))) \| ((~![X: $i] : ((~room(X)) => (~happy(X)))) => (~?[X: $i] : ((~room(X)) => ((~preda(X)) => like(alice, X)))))) & (tall(mary) & tourist(mary))) & (~like(fred, mary))) & ![X: $i] : taller(mary, X))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = \|'mary'\|) \| (X = \|'paul'\|)))) & (~(taller(fred, paul) & (((~quiet(paul)) & (~tall(paul))) & (~happy(paul)))))))), file('/mnt/tmpfs//836017118726898429632910.p','negated')). tff(7,plain, (~((~(room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & tall(mary) & tourist(mary) & (~like(fred, mary)) & ![X: $i] : taller(mary, X))) \| (room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~(taller(fred, paul) & (~quiet(paul)) & (~tall(paul)) & (~happy(paul))))))), inference(modus_ponens,[status(thm)],[6, 5])). tff(8,plain, (room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & tall(mary) & tourist(mary) & (~like(fred, mary)) & ![X: $i] : taller(mary, X)), inference(or_elim,[status(thm)],[7])). tff(9,plain, (![X: $i] : taller(mary, X)), inference(and_elim,[status(thm)],[8])). tff(10,plain, (![X: $i] : taller(mary, X)), inference(modus_ponens,[status(thm)],[9, 4])). tff(11,plain,( ![X: $i] : taller(mary, X)), inference(skolemize,[status(sab)],[10])). tff(12,plain, (![X: $i] : taller(mary, X)), inference(modus_ponens,[status(thm)],[11, 3])). tff(13,plain, ((~![X: $i] : taller(mary, X)) \| taller(mary, fred)), inference(quant_inst,[status(thm)],[])). tff(14,plain, ($false), inference(unit_resolution,[status(thm)],[13, 12, 1])). tff(15,plain,(taller(mary, fred)), inference(lemma,lemma(discharge,[]))). tff(16,plain, (tall(mary) <=> tall(mary)), inference(rewrite,[status(thm)],[])). tff(17,plain, (tall(mary)), inference(and_elim,[status(thm)],[8])). tff(18,plain, (tall(mary)), inference(modus_ponens,[status(thm)],[17, 16])). tff(19,plain, ((~(mary = fred)) <=> (~(mary = fred))), 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//836017118726898429632910.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, (((((((((((((~(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)],[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))), 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))), 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))), 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))), 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))), inference(and_elim,[status(thm)],[53])). tff(55,plain, (((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))), inference(and_elim,[status(thm)],[54])). tff(56,plain, ((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))), inference(and_elim,[status(thm)],[55])). tff(57,plain, (((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))), inference(and_elim,[status(thm)],[56])). tff(58,plain, ((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))), inference(and_elim,[status(thm)],[57])). tff(59,plain, (((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))), inference(and_elim,[status(thm)],[58])). tff(60,plain, ((~(mary = paul)) & (~(mary = fred))), inference(and_elim,[status(thm)],[59])). tff(61,plain, (~(mary = fred)), inference(and_elim,[status(thm)],[60])). tff(62,plain, (~(mary = fred)), inference(modus_ponens,[status(thm)],[61, 19])). tff(63,plain, (^[X: $i, Y: $i] : refl(((X = Y) \| tall(Y) \| (~taller(X, Y)) \| (~tall(X))) <=> ((X = Y) \| tall(Y) \| (~taller(X, Y)) \| (~tall(X))))), inference(bind,[status(th)],[])). tff(64,plain, (![X: $i, Y: $i] : ((X = Y) \| tall(Y) \| (~taller(X, Y)) \| (~tall(X))) <=> ![X: $i, Y: $i] : ((X = Y) \| tall(Y) \| (~taller(X, Y)) \| (~tall(X)))), inference(quant_intro,[status(thm)],[63])). tff(65,plain, (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((taller(X, Y) & tall(X)) <=> (~((~taller(X, Y)) \| (~tall(X))))), ((~(taller(X, Y) & tall(X))) <=> (~(~((~taller(X, Y)) \| (~tall(X))))))), rewrite((~(~((~taller(X, Y)) \| (~tall(X))))) <=> ((~taller(X, Y)) \| (~tall(X)))), ((~(taller(X, Y) & tall(X))) <=> ((~taller(X, Y)) \| (~tall(X))))), (((X = Y) \| tall(Y) \| (~(taller(X, Y) & tall(X)))) <=> ((X = Y) \| tall(Y) \| ((~taller(X, Y)) \| (~tall(X)))))), rewrite(((X = Y) \| tall(Y) \| ((~taller(X, Y)) \| (~tall(X)))) <=> ((X = Y) \| tall(Y) \| (~taller(X, Y)) \| (~tall(X)))), (((X = Y) \| tall(Y) \| (~(taller(X, Y) & tall(X)))) <=> ((X = Y) \| tall(Y) \| (~taller(X, Y)) \| (~tall(X)))))), inference(bind,[status(th)],[])). tff(66,plain, (![X: $i, Y: $i] : ((X = Y) \| tall(Y) \| (~(taller(X, Y) & tall(X)))) <=> ![X: $i, Y: $i] : ((X = Y) \| tall(Y) \| (~taller(X, Y)) \| (~tall(X)))), inference(quant_intro,[status(thm)],[65])). tff(67,plain, (![X: $i, Y: $i] : ((X = Y) \| tall(Y) \| (~(taller(X, Y) & tall(X)))) <=> ![X: $i, Y: $i] : ((X = Y) \| tall(Y) \| (~(taller(X, Y) & tall(X))))), inference(rewrite,[status(thm)],[])). tff(68,plain, (^[X: $i, Y: $i] : trans(monotonicity(rewrite(((taller(X, Y) & tall(X)) => tall(Y)) <=> (tall(Y) \| (~(taller(X, Y) & tall(X))))), (((~(X = Y)) => ((taller(X, Y) & tall(X)) => tall(Y))) <=> ((~(X = Y)) => (tall(Y) \| (~(taller(X, Y) & tall(X))))))), rewrite(((~(X = Y)) => (tall(Y) \| (~(taller(X, Y) & tall(X))))) <=> ((X = Y) \| tall(Y) \| (~(taller(X, Y) & tall(X))))), (((~(X = Y)) => ((taller(X, Y) & tall(X)) => tall(Y))) <=> ((X = Y) \| tall(Y) \| (~(taller(X, Y) & tall(X))))))), inference(bind,[status(th)],[])). tff(69,plain, (![X: $i, Y: $i] : ((~(X = Y)) => ((taller(X, Y) & tall(X)) => tall(Y))) <=> ![X: $i, Y: $i] : ((X = Y) \| tall(Y) \| (~(taller(X, Y) & tall(X))))), inference(quant_intro,[status(thm)],[68])). tff(70,axiom,(![X: $i, Y: $i] : ((~(X = Y)) => ((taller(X, Y) & tall(X)) => tall(Y)))), file('/mnt/tmpfs//836017118726898429632910.p','b9')). tff(71,plain, (![X: $i, Y: $i] : ((X = Y) \| tall(Y) \| (~(taller(X, Y) & tall(X))))), inference(modus_ponens,[status(thm)],[70, 69])). tff(72,plain, (![X: $i, Y: $i] : ((X = Y) \| tall(Y) \| (~(taller(X, Y) & tall(X))))), inference(modus_ponens,[status(thm)],[71, 67])). tff(73,plain,( ![X: $i, Y: $i] : ((X = Y) \| tall(Y) \| (~(taller(X, Y) & tall(X))))), inference(skolemize,[status(sab)],[72])). tff(74,plain, (![X: $i, Y: $i] : ((X = Y) \| tall(Y) \| (~taller(X, Y)) \| (~tall(X)))), inference(modus_ponens,[status(thm)],[73, 66])). tff(75,plain, (![X: $i, Y: $i] : ((X = Y) \| tall(Y) \| (~taller(X, Y)) \| (~tall(X)))), inference(modus_ponens,[status(thm)],[74, 64])). tff(76,plain, (((~![X: $i, Y: $i] : ((X = Y) \| tall(Y) \| (~taller(X, Y)) \| (~tall(X)))) \| ((mary = fred) \| tall(fred) \| (~tall(mary)) \| (~taller(mary, fred)))) <=> ((~![X: $i, Y: $i] : ((X = Y) \| tall(Y) \| (~taller(X, Y)) \| (~tall(X)))) \| (mary = fred) \| tall(fred) \| (~tall(mary)) \| (~taller(mary, fred)))), inference(rewrite,[status(thm)],[])). tff(77,plain, (((mary = fred) \| tall(fred) \| (~taller(mary, fred)) \| (~tall(mary))) <=> ((mary = fred) \| tall(fred) \| (~tall(mary)) \| (~taller(mary, fred)))), inference(rewrite,[status(thm)],[])). tff(78,plain, (((~![X: $i, Y: $i] : ((X = Y) \| tall(Y) \| (~taller(X, Y)) \| (~tall(X)))) \| ((mary = fred) \| tall(fred) \| (~taller(mary, fred)) \| (~tall(mary)))) <=> ((~![X: $i, Y: $i] : ((X = Y) \| tall(Y) \| (~taller(X, Y)) \| (~tall(X)))) \| ((mary = fred) \| tall(fred) \| (~tall(mary)) \| (~taller(mary, fred))))), inference(monotonicity,[status(thm)],[77])). tff(79,plain, (((~![X: $i, Y: $i] : ((X = Y) \| tall(Y) \| (~taller(X, Y)) \| (~tall(X)))) \| ((mary = fred) \| tall(fred) \| (~taller(mary, fred)) \| (~tall(mary)))) <=> ((~![X: $i, Y: $i] : ((X = Y) \| tall(Y) \| (~taller(X, Y)) \| (~tall(X)))) \| (mary = fred) \| tall(fred) \| (~tall(mary)) \| (~taller(mary, fred)))), inference(transitivity,[status(thm)],[78, 76])). tff(80,plain, ((~![X: $i, Y: $i] : ((X = Y) \| tall(Y) \| (~taller(X, Y)) \| (~tall(X)))) \| ((mary = fred) \| tall(fred) \| (~taller(mary, fred)) \| (~tall(mary)))), inference(quant_inst,[status(thm)],[])). tff(81,plain, ((~![X: $i, Y: $i] : ((X = Y) \| tall(Y) \| (~taller(X, Y)) \| (~tall(X)))) \| (mary = fred) \| tall(fred) \| (~tall(mary)) \| (~taller(mary, fred))), inference(modus_ponens,[status(thm)],[80, 79])). tff(82,plain, (tall(fred) \| (~taller(mary, fred))), inference(unit_resolution,[status(thm)],[81, 75, 62, 18])). tff(83,plain, (tall(fred)), inference(unit_resolution,[status(thm)],[82, 15])). tff(84,assumption,(~((X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0)))), introduced(assumption)). tff(85,plain, (((X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0))) \| room(X!0)), inference(tautology,[status(thm)],[])). tff(86,plain, (room(X!0)), inference(unit_resolution,[status(thm)],[85, 84])). tff(87,plain, (((X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0))) \| (~(X!0 = \|'mary'\|))), inference(tautology,[status(thm)],[])). tff(88,plain, (~(X!0 = \|'mary'\|)), inference(unit_resolution,[status(thm)],[87, 84])). tff(89,plain, (((X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0))) \| (~(X!0 = \|'paul'\|))), inference(tautology,[status(thm)],[])). tff(90,plain, (~(X!0 = \|'paul'\|)), inference(unit_resolution,[status(thm)],[89, 84])). tff(91,plain, (^[X: $i] : refl(((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) <=> ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))))), inference(bind,[status(th)],[])). tff(92,plain, (![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) <=> ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))), inference(quant_intro,[status(thm)],[91])). tff(93,plain, (![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) <=> ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))), inference(rewrite,[status(thm)],[])). tff(94,plain, (![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))), inference(and_elim,[status(thm)],[8])). tff(95,plain, (![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))), inference(modus_ponens,[status(thm)],[94, 93])). tff(96,plain,( ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))), inference(skolemize,[status(sab)],[95])). tff(97,plain, (![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))), inference(modus_ponens,[status(thm)],[96, 92])). tff(98,plain, (((~![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| ((X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0)))) <=> ((~![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| (X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0)))), inference(rewrite,[status(thm)],[])). tff(99,plain, ((~![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| ((X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0)))), inference(quant_inst,[status(thm)],[])). tff(100,plain, ((~![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| (X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0))), inference(modus_ponens,[status(thm)],[99, 98])). tff(101,plain, ($false), inference(unit_resolution,[status(thm)],[100, 97, 90, 88, 86])). tff(102,plain,((X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0))), inference(lemma,lemma(discharge,[]))). tff(103,plain, (room(paul) <=> room(paul)), inference(rewrite,[status(thm)],[])). tff(104,plain, (room(paul)), inference(and_elim,[status(thm)],[8])). tff(105,plain, (room(paul)), inference(modus_ponens,[status(thm)],[104, 103])). tff(106,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(107,plain, (room(mary)), inference(and_elim,[status(thm)],[8])). tff(108,plain, (room(mary)), inference(modus_ponens,[status(thm)],[107, 106])). tff(109,plain, (((~room(mary)) \| (~room(paul)) \| (~((X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0)))) \| (taller(fred, paul) & (~quiet(paul)) & (~tall(paul)) & (~happy(paul)))) <=> ((~room(mary)) \| (~room(paul)) \| (~((X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0)))) \| (~(quiet(paul) \| tall(paul) \| happy(paul) \| (~taller(fred, paul)))))), inference(rewrite,[status(thm)],[])). tff(110,plain, ((~((X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0)))) <=> (~((X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0))))), inference(rewrite,[status(thm)],[])). tff(111,plain, (((~room(mary)) \| (~room(paul)) \| (~((X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0)))) \| (taller(fred, paul) & (~quiet(paul)) & (~tall(paul)) & (~happy(paul)))) <=> ((~room(mary)) \| (~room(paul)) \| (~((X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0)))) \| (taller(fred, paul) & (~quiet(paul)) & (~tall(paul)) & (~happy(paul))))), inference(monotonicity,[status(thm)],[110])). tff(112,plain, ((room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~(taller(fred, paul) & (~quiet(paul)) & (~tall(paul)) & (~happy(paul))))) <=> (room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~(taller(fred, paul) & (~quiet(paul)) & (~tall(paul)) & (~happy(paul)))))), inference(rewrite,[status(thm)],[])). tff(113,plain, ((~(room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~(taller(fred, paul) & (~quiet(paul)) & (~tall(paul)) & (~happy(paul)))))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~(taller(fred, paul) & (~quiet(paul)) & (~tall(paul)) & (~happy(paul))))))), inference(monotonicity,[status(thm)],[112])). tff(114,plain, ((~(room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~(taller(fred, paul) & (~quiet(paul)) & (~tall(paul)) & (~happy(paul)))))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~(taller(fred, paul) & (~quiet(paul)) & (~tall(paul)) & (~happy(paul))))))), inference(rewrite,[status(thm)],[])). tff(115,plain, (~(room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~(taller(fred, paul) & (~quiet(paul)) & (~tall(paul)) & (~happy(paul)))))), inference(or_elim,[status(thm)],[7])). tff(116,plain, (~(room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~(taller(fred, paul) & (~quiet(paul)) & (~tall(paul)) & (~happy(paul)))))), inference(modus_ponens,[status(thm)],[115, 113])). tff(117,plain, (~(room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~(taller(fred, paul) & (~quiet(paul)) & (~tall(paul)) & (~happy(paul)))))), inference(modus_ponens,[status(thm)],[116, 114])). tff(118,plain, (~(room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~(taller(fred, paul) & (~quiet(paul)) & (~tall(paul)) & (~happy(paul)))))), inference(modus_ponens,[status(thm)],[117, 113])). 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))))) (a!5 (and (taller fred paul) (not (quiet paul)) (not (tall paul)) (not (happy paul))))) (let ((a!6 (~ (not (and (room mary) (room paul) a!3 (not a!5))) (or (not (room mary)) (not (room paul)) a!4 a!5)))) (nnf-neg a!1 a!2 (sk (~ (not a!3) a!4)) (refl (~ a!5 a!5)) a!6)))	room(stephanie)&room(matthew)&(![X]:(room(X)=>(X='stephanie'\|X='matthew')))& ((((![X]:(~room(X)=>(~happy(X))))=>((like(stephanie,joe) & like(joe,stephanie))))\|((~(![X]:(~room(X)=>(~happy(X)))))=>(~?[X]:(~room(X)=>(((does_not_have_a_tattoo(X))=>(like(ellen,X))))))))& (tall(stephanie)&tourist(stephanie))& (~like(joe,stephanie))& (![X]:(taller(stephanie,X))))	room(stephanie)&room(matthew)&(![X]:(room(X)=>(X='stephanie'\|X='matthew')))& (~((taller(joe,matthew))&(~quiet(matthew)&~tall(matthew)&~happy(matthew))))	contradiction	entailment	neutral
Stephanie, Thomas are the only persons in the room. If “more than one person outside the room is not happy” then “Stephanie either likes Doris or is taller than Beverly”. If “Stephanie is not liked by Beverly” then “someone outside the room enjoys fishing” otherwise “Barbara and Stephanie like each other”. Stephanie is a tall brave creative happy european. Everyone outside the room is not liked by Doris. More than one person outside the room does not like Barbara. Stephanie is the least tall in the room. Someone outside the room who is not a brave person is not liked by Barbara.	Someone who is not tall like someone who is a creative person.	contradiction	-	room(stephanie)&room(thomas)&(![X]:(room(X)=>(X='stephanie'\|X='thomas')))& ((((?[X,Y]:(~room(X)&~room(Y)&(~happy(X)&~happy(Y))&(X!=Y))))=>((((like(doris,stephanie))\|(taller(beverly,stephanie)))&(~((like(doris,stephanie))\|(taller(beverly,stephanie)))))))& (((~like(stephanie,beverly))=>(?[X]:(~room(X)=>(enjoys_fishing(X)))))\|((~(~like(stephanie,beverly)))=>((like(barbara,stephanie) & like(stephanie,barbara)))))& (tall(stephanie)&brave(stephanie)&creative(stephanie)&happy(stephanie)&european(stephanie))& (![X]:(~room(X)=>(~like(X,doris))))& ((?[X,Y]:(~room(X)&~room(Y)&(~like(barbara,X)&~like(barbara,Y))&(X!=Y))))& (![X]:(taller(stephanie,X)))& (?[X]:(~room(X)=>(((~(brave(X)&person(X)))=>(~like(X,barbara)))))))	room(stephanie)&room(thomas)&(![X]:(room(X)=>(X='stephanie'\|X='thomas')))& (?[X,Y]:((~tall(X))&(creative(Y)&person(Y))&(like(X,Y))))	neutral	neutral	entailment
Brett, Gregory, Marjorie, Michelle are the only persons in the room. Marjorie and Gregory are respectively rich and quiet unless only one person in the room hates Jesse. Brett and Marjorie hate each other if Gregory is the richest in the room. Brett and Marjorie hate each other. Gregory and Brett are respectively rich and brave. Gregory who collects rare minerals, hates Barbara. Gregory and Brett are respectively quiet and rich.	Gregory neither is a happy creative brave tall rich european nor hates Barbara.	contradiction	-	room(brett)&room(gregory)&room(marjorie)&room(michelle)&(![X]:(room(X)=>(X='brett'\|X='gregory'\|X='marjorie'\|X='michelle')))& ((~(((?[X]:(room(X)&hate(jesse,X)))&(![X,Y]:((hate(jesse,X)&hate(jesse,Y))=>(X=Y)))))=>((rich(marjorie))&(quiet(gregory))))& ((![X]:(richer(X,gregory)))=>((hate(brett,marjorie) & hate(marjorie,brett))))& ((hate(brett,marjorie) & hate(marjorie,brett)))& ((rich(gregory))&(brave(brett)))& ((collects_rare_minerals(gregory))&(hate(barbara,gregory)))& ((quiet(gregory))&(rich(brett))))	room(brett)&room(gregory)&room(marjorie)&room(michelle)&(![X]:(room(X)=>(X='brett'\|X='gregory'\|X='marjorie'\|X='michelle')))& (~((happy(gregory)&creative(gregory)&brave(gregory)&tall(gregory)&rich(gregory)&european(gregory))\|(hate(barbara,gregory))))	contradiction	neutral	contradiction
Raymond, Jack are the only persons in the room. Raymond who likes Melissa, is not a happy creative person if Raymond either hates Margaret or is not liked by Melissa and vice versa. Raymond is the least tall in the room if more than one person outside the room likes Melissa and vice versa. Raymond does not like Margaret. Melissa and Raymond like each other. Raymond neither enjoys bird watching nor is liked by Margaret. Margaret is taller than Raymond. Raymond neither is a rich creative person nor is a quiet person.	Raymond is not liked by Margaret and is a happy creative person.	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(happy_type, type, ( happy: $i > $o)). tff(mary_type, type, ( mary: $i)). tff(person_type, type, ( person: $i > $o)). tff(creative_type, type, ( creative: $i > $o)). tff(like_type, type, ( like: ( $i * $i ) > $o)). tff(alice_type, type, ( alice: $i)). tff(rich_type, type, ( rich: $i > $o)). tff(quiet_type, type, ( quiet: $i > $o)). tff(taller_type, type, ( taller: ( $i * $i ) > $o)). tff(fred_type, type, ( fred: $i)). tff(predc_type, type, ( predc: $i > $o)). tff(paul_type, type, ( paul: $i)). tff(hate_type, type, ( hate: ( $i * $i ) > $o)). tff(1,plain, (like(alice, mary) <=> like(alice, mary)), inference(rewrite,[status(thm)],[])). tff(2,plain, ((~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = \|'mary'\|) \| (X = \|'paul'\|)))) & (((((((((hate(fred, mary) \| (~like(mary, alice))) & (~(hate(fred, mary) \| (~like(mary, alice))))) <=> (like(alice, mary) & (~((happy(mary) & creative(mary)) & person(mary))))) & (?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & (like(alice, X) & like(alice, Y))) & (~(X = Y))) <=> ![X: $i] : taller(mary, X))) & (~like(fred, mary))) & (like(alice, mary) & like(mary, alice))) & (~(predc(mary) \| like(mary, fred)))) & taller(mary, fred)) & (~(((rich(mary) & creative(mary)) & person(mary)) \| (quiet(mary) & person(mary)))))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = \|'mary'\|) \| (X = \|'paul'\|)))) & ((~like(mary, fred)) & ((happy(mary) & creative(mary)) & person(mary)))))) <=> (~((~(room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~(like(alice, mary) & (~(happy(mary) & creative(mary) & person(mary))))) & (?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & like(alice, X) & like(alice, Y) & (~(X = Y))) <=> ![X: $i] : taller(mary, X)) & (~like(fred, mary)) & like(alice, mary) & like(mary, alice) & (~(predc(mary) \| like(mary, fred))) & taller(mary, fred) & (~((quiet(mary) & person(mary)) \| (rich(mary) & creative(mary) & person(mary)))))) \| (room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~like(mary, fred)) & happy(mary) & creative(mary) & person(mary))))), inference(rewrite,[status(thm)],[])). tff(3,axiom,(~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = \|'mary'\|) \| (X = \|'paul'\|)))) & (((((((((hate(fred, mary) \| (~like(mary, alice))) & (~(hate(fred, mary) \| (~like(mary, alice))))) <=> (like(alice, mary) & (~((happy(mary) & creative(mary)) & person(mary))))) & (?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & (like(alice, X) & like(alice, Y))) & (~(X = Y))) <=> ![X: $i] : taller(mary, X))) & (~like(fred, mary))) & (like(alice, mary) & like(mary, alice))) & (~(predc(mary) \| like(mary, fred)))) & taller(mary, fred)) & (~(((rich(mary) & creative(mary)) & person(mary)) \| (quiet(mary) & person(mary)))))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = \|'mary'\|) \| (X = \|'paul'\|)))) & ((~like(mary, fred)) & ((happy(mary) & creative(mary)) & person(mary)))))), file('/mnt/tmpfs//3188362950136917905314834.p','negated')). tff(4,plain, (~((~(room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~(like(alice, mary) & (~(happy(mary) & creative(mary) & person(mary))))) & (?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & like(alice, X) & like(alice, Y) & (~(X = Y))) <=> ![X: $i] : taller(mary, X)) & (~like(fred, mary)) & like(alice, mary) & like(mary, alice) & (~(predc(mary) \| like(mary, fred))) & taller(mary, fred) & (~((quiet(mary) & person(mary)) \| (rich(mary) & creative(mary) & person(mary)))))) \| (room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~like(mary, fred)) & happy(mary) & creative(mary) & person(mary)))), inference(modus_ponens,[status(thm)],[3, 2])). tff(5,plain, (room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~(like(alice, mary) & (~(happy(mary) & creative(mary) & person(mary))))) & (?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & like(alice, X) & like(alice, Y) & (~(X = Y))) <=> ![X: $i] : taller(mary, X)) & (~like(fred, mary)) & like(alice, mary) & like(mary, alice) & (~(predc(mary) \| like(mary, fred))) & taller(mary, fred) & (~((quiet(mary) & person(mary)) \| (rich(mary) & creative(mary) & person(mary))))), inference(or_elim,[status(thm)],[4])). tff(6,plain, (like(alice, mary)), inference(and_elim,[status(thm)],[5])). tff(7,plain, (like(alice, mary)), inference(modus_ponens,[status(thm)],[6, 1])). tff(8,plain, ((~(~((~like(alice, mary)) \| (~((~happy(mary)) \| (~creative(mary)) \| (~person(mary))))))) <=> ((~like(alice, mary)) \| (~((~happy(mary)) \| (~creative(mary)) \| (~person(mary)))))), inference(rewrite,[status(thm)],[])). tff(9,plain, ((like(alice, mary) & ((~happy(mary)) \| (~creative(mary)) \| (~person(mary)))) <=> (~((~like(alice, mary)) \| (~((~happy(mary)) \| (~creative(mary)) \| (~person(mary))))))), inference(rewrite,[status(thm)],[])). tff(10,plain, ((~(~((~happy(mary)) \| (~creative(mary)) \| (~person(mary))))) <=> ((~happy(mary)) \| (~creative(mary)) \| (~person(mary)))), inference(rewrite,[status(thm)],[])). tff(11,plain, ((happy(mary) & creative(mary) & person(mary)) <=> (~((~happy(mary)) \| (~creative(mary)) \| (~person(mary))))), inference(rewrite,[status(thm)],[])). tff(12,plain, ((~(happy(mary) & creative(mary) & person(mary))) <=> (~(~((~happy(mary)) \| (~creative(mary)) \| (~person(mary)))))), inference(monotonicity,[status(thm)],[11])). tff(13,plain, ((~(happy(mary) & creative(mary) & person(mary))) <=> ((~happy(mary)) \| (~creative(mary)) \| (~person(mary)))), inference(transitivity,[status(thm)],[12, 10])). tff(14,plain, ((like(alice, mary) & (~(happy(mary) & creative(mary) & person(mary)))) <=> (like(alice, mary) & ((~happy(mary)) \| (~creative(mary)) \| (~person(mary))))), inference(monotonicity,[status(thm)],[13])). tff(15,plain, ((like(alice, mary) & (~(happy(mary) & creative(mary) & person(mary)))) <=> (~((~like(alice, mary)) \| (~((~happy(mary)) \| (~creative(mary)) \| (~person(mary))))))), inference(transitivity,[status(thm)],[14, 9])). tff(16,plain, ((~(like(alice, mary) & (~(happy(mary) & creative(mary) & person(mary))))) <=> (~(~((~like(alice, mary)) \| (~((~happy(mary)) \| (~creative(mary)) \| (~person(mary)))))))), inference(monotonicity,[status(thm)],[15])). tff(17,plain, ((~(like(alice, mary) & (~(happy(mary) & creative(mary) & person(mary))))) <=> ((~like(alice, mary)) \| (~((~happy(mary)) \| (~creative(mary)) \| (~person(mary)))))), inference(transitivity,[status(thm)],[16, 8])). tff(18,plain, ((~(like(alice, mary) & (~(happy(mary) & creative(mary) & person(mary))))) <=> (~(like(alice, mary) & (~(happy(mary) & creative(mary) & person(mary)))))), inference(rewrite,[status(thm)],[])). tff(19,plain, (~(like(alice, mary) & (~(happy(mary) & creative(mary) & person(mary))))), inference(and_elim,[status(thm)],[5])). tff(20,plain, (~(like(alice, mary) & (~(happy(mary) & creative(mary) & person(mary))))), inference(modus_ponens,[status(thm)],[19, 18])). tff(21,plain, ((~like(alice, mary)) \| (~((~happy(mary)) \| (~creative(mary)) \| (~person(mary))))), inference(modus_ponens,[status(thm)],[20, 17])). tff(22,plain, (~((~happy(mary)) \| (~creative(mary)) \| (~person(mary)))), inference(unit_resolution,[status(thm)],[21, 7])). tff(23,plain, (((~happy(mary)) \| (~creative(mary)) \| (~person(mary))) \| happy(mary)), inference(tautology,[status(thm)],[])). tff(24,plain, (happy(mary)), inference(unit_resolution,[status(thm)],[23, 22])). tff(25,plain, (((~happy(mary)) \| (~creative(mary)) \| (~person(mary))) \| person(mary)), inference(tautology,[status(thm)],[])). tff(26,plain, (person(mary)), inference(unit_resolution,[status(thm)],[25, 22])). tff(27,plain, (((~happy(mary)) \| (~creative(mary)) \| (~person(mary))) \| creative(mary)), inference(tautology,[status(thm)],[])). tff(28,plain, (creative(mary)), inference(unit_resolution,[status(thm)],[27, 22])). tff(29,plain, ((~like(mary, fred)) <=> (~like(mary, fred))), inference(rewrite,[status(thm)],[])). tff(30,plain, (~(predc(mary) \| like(mary, fred))), inference(and_elim,[status(thm)],[5])). tff(31,plain, (~like(mary, fred)), inference(or_elim,[status(thm)],[30])). tff(32,plain, (~like(mary, fred)), inference(modus_ponens,[status(thm)],[31, 29])). tff(33,plain, (room(paul) <=> room(paul)), inference(rewrite,[status(thm)],[])). tff(34,plain, (room(paul)), inference(and_elim,[status(thm)],[5])). tff(35,plain, (room(paul)), inference(modus_ponens,[status(thm)],[34, 33])). tff(36,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(37,plain, (room(mary)), inference(and_elim,[status(thm)],[5])). tff(38,plain, (room(mary)), inference(modus_ponens,[status(thm)],[37, 36])). tff(39,plain, (((~room(mary)) \| (~room(paul)) \| (~((X!3 = \|'paul'\|) \| (X!3 = \|'mary'\|) \| (~room(X!3)))) \| like(mary, fred) \| (~happy(mary)) \| (~creative(mary)) \| (~person(mary))) <=> (like(mary, fred) \| (~room(mary)) \| (~room(paul)) \| (~((X!3 = \|'paul'\|) \| (X!3 = \|'mary'\|) \| (~room(X!3)))) \| (~happy(mary)) \| (~creative(mary)) \| (~person(mary)))), inference(rewrite,[status(thm)],[])). tff(40,plain, ((~((X!3 = \|'paul'\|) \| (X!3 = \|'mary'\|) \| (~room(X!3)))) <=> (~((X!3 = \|'paul'\|) \| (X!3 = \|'mary'\|) \| (~room(X!3))))), inference(rewrite,[status(thm)],[])). tff(41,plain, (((~room(mary)) \| (~room(paul)) \| (~((X!3 = \|'paul'\|) \| (X!3 = \|'mary'\|) \| (~room(X!3)))) \| like(mary, fred) \| (~happy(mary)) \| (~creative(mary)) \| (~person(mary))) <=> ((~room(mary)) \| (~room(paul)) \| (~((X!3 = \|'paul'\|) \| (X!3 = \|'mary'\|) \| (~room(X!3)))) \| like(mary, fred) \| (~happy(mary)) \| (~creative(mary)) \| (~person(mary)))), inference(monotonicity,[status(thm)],[40])). tff(42,plain, (((~room(mary)) \| (~room(paul)) \| (~((X!3 = \|'paul'\|) \| (X!3 = \|'mary'\|) \| (~room(X!3)))) \| like(mary, fred) \| (~happy(mary)) \| (~creative(mary)) \| (~person(mary))) <=> (like(mary, fred) \| (~room(mary)) \| (~room(paul)) \| (~((X!3 = \|'paul'\|) \| (X!3 = \|'mary'\|) \| (~room(X!3)))) \| (~happy(mary)) \| (~creative(mary)) \| (~person(mary)))), inference(transitivity,[status(thm)],[41, 39])). tff(43,plain, ((room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~like(mary, fred)) & happy(mary) & creative(mary) & person(mary)) <=> (room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~like(mary, fred)) & happy(mary) & creative(mary) & person(mary))), inference(rewrite,[status(thm)],[])). tff(44,plain, ((~(room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~like(mary, fred)) & happy(mary) & creative(mary) & person(mary))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~like(mary, fred)) & happy(mary) & creative(mary) & person(mary)))), inference(monotonicity,[status(thm)],[43])). tff(45,plain, ((~(room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~like(mary, fred)) & happy(mary) & creative(mary) & person(mary))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~like(mary, fred)) & happy(mary) & creative(mary) & person(mary)))), inference(rewrite,[status(thm)],[])). tff(46,plain, (~(room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~like(mary, fred)) & happy(mary) & creative(mary) & person(mary))), inference(or_elim,[status(thm)],[4])). tff(47,plain, (~(room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~like(mary, fred)) & happy(mary) & creative(mary) & person(mary))), inference(modus_ponens,[status(thm)],[46, 44])). tff(48,plain, (~(room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~like(mary, fred)) & happy(mary) & creative(mary) & person(mary))), inference(modus_ponens,[status(thm)],[47, 45])). tff(49,plain, (~(room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~like(mary, fred)) & happy(mary) & creative(mary) & person(mary))), inference(modus_ponens,[status(thm)],[48, 44])). unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary))))) (a!2 (refl (~ (not (room paul)) (not (room paul))))) (a!3 (forall ((X $i)) (or (= X \|'paul'\|) (= X \|'mary'\|) (not (room X))))) (a!4 (not (or (= X!3 \|'paul'\|) (= X!3 \|'mary'\|) (not (room X!3))))) (a!5 (refl (~ (not (happy mary)) (not (happy mary))))) (a!6 (refl (~ (not (creative mary)) (not (creative mary))))) (a!7 (refl (~ (not (person mary)) (not (person mary)))))) (let ((a!8 (not (and (room mary) (room paul) a!3 (not (like mary fred)) (happy mary) (creative mary) (person mary))))) (let ((a!9 (~ a!8 (or (not (room mary)) (not (room paul)) a!4 (like mary fred) (not (happy mary)) (not (creative mary)) (not (person mary)))))) (nnf-neg a!1 a!2 (sk (~ (not a!3) a!4)) (refl (~ (like mary fred) (like mary fred))) a!5 a!6 a!7 a!9))))	room(raymond)&room(jack)&(![X]:(room(X)=>(X='raymond'\|X='jack')))& ((((((hate(margaret,raymond))\|(~like(raymond,melissa)))&(~((hate(margaret,raymond))\|(~like(raymond,melissa))))))<=>((like(melissa,raymond))&(~(happy(raymond)&creative(raymond)&person(raymond)))))& (((?[X,Y]:(~room(X)&~room(Y)&(like(melissa,X)&like(melissa,Y))&(X!=Y))))<=>(![X]:(taller(raymond,X))))& (~like(margaret,raymond))& ((like(melissa,raymond) & like(raymond,melissa)))& (~((enjoys_bird_watching(raymond))\|(like(raymond,margaret))))& (taller(raymond,margaret))& (~((rich(raymond)&creative(raymond)&person(raymond))\|(quiet(raymond)&person(raymond)))))	room(raymond)&room(jack)&(![X]:(room(X)=>(X='raymond'\|X='jack')))& ((~like(raymond,margaret))&(happy(raymond)&creative(raymond)&person(raymond)))	contradiction	contradiction	contradiction
Diana, Jennifer, Christine, Richard are the only persons in the room. 'Diana and Jennifer are respectively brave and tall' if 'Jennifer neither hates James nor is taller than James'. 'Richard practices graffiti art' unless 'Christine is liked by James'. Richard is hated by James. Richard is the least quiet in the room. More than one person outside the room is a brave tourist. Richard is not tall, not brave, not creative and does not like James. Jennifer who does not hate James, is not creative, not quiet, not tall. More than one person outside the room is not hated by James.	Someone who is not a quiet person is quieter than someone who is not creative, not brave, not quiet, not tall.	entailment	% SZS status Unsatisfiable % SZS output start Proof tff(quieter_type, type, ( quieter: ( $i * $i ) > $o)). tff(alice_type, type, ( alice: $i)). tff(quiet_type, type, ( quiet: $i > $o)). tff(paul_type, type, ( paul: $i)). tff(hate_type, type, ( hate: ( $i * $i ) > $o)). tff(lucy_type, type, ( lucy: $i)). tff(room_type, type, ( room: $i > $o)). tff(tall_type, type, ( tall: $i > $o)). tff(creative_type, type, ( creative: $i > $o)). tff(like_type, type, ( like: ( $i * $i ) > $o)). tff(brave_type, type, ( brave: $i > $o)). tff(tourist_type, type, ( tourist: $i > $o)). tff(predb_type, type, ( predb: $i > $o)). tff(fred_type, type, ( fred: $i)). tff(mary_type, type, ( mary: $i)). tff(taller_type, type, ( taller: ( $i * $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(person_type, type, ( person: $i > $o)). tff(susan_type, type, ( susan: $i)). tff(john_type, type, ( john: $i)). tff(tptp_fun_X_4_type, type, ( tptp_fun_X_4: $i)). tff(1,assumption,(~quieter(alice, paul)), introduced(assumption)). tff(2,plain, (^[X: $i] : refl(quieter(alice, X) <=> quieter(alice, X))), inference(bind,[status(th)],[])). tff(3,plain, (![X: $i] : quieter(alice, X) <=> ![X: $i] : quieter(alice, X)), inference(quant_intro,[status(thm)],[2])). tff(4,plain, (![X: $i] : quieter(alice, X) <=> ![X: $i] : quieter(alice, X)), 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'\|)))) & (((((((((~(hate(lucy, paul) \| taller(lucy, paul))) => (brave(mary) & tall(paul))) & ((~like(fred, lucy)) => predb(alice))) & hate(alice, lucy)) & ![X: $i] : quieter(alice, X)) & ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & (((brave(X) & tourist(X)) & brave(Y)) & tourist(Y))) & (~(X = Y)))) & ((((~tall(alice)) & (~brave(alice))) & (~creative(alice))) & (~like(lucy, alice)))) & ((~hate(lucy, paul)) & (((~creative(paul)) & (~quiet(paul))) & (~tall(paul))))) & ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & ((~hate(X, lucy)) & (~hate(Y, lucy)))) & (~(X = Y))))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)) \| (X = \|'alice'\|)))) & ?[X: $i, Y: $i] : (((~(quiet(X) & person(X))) & ((((~creative(Y)) & (~brave(Y))) & (~quiet(Y))) & (~tall(Y)))) & quieter(X, Y))))) <=> (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (hate(lucy, paul) \| taller(lucy, paul) \| (brave(mary) & tall(paul))) & (like(fred, lucy) \| predb(alice)) & hate(alice, lucy) & ![X: $i] : quieter(alice, X) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & brave(X) & tourist(X) & brave(Y) & tourist(Y) & (~(X = Y))) & (~tall(alice)) & (~brave(alice)) & (~creative(alice)) & (~like(lucy, alice)) & (~hate(lucy, paul)) & (~creative(paul)) & (~quiet(paul)) & (~tall(paul)) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~hate(X, lucy)) & (~hate(Y, lucy)) & (~(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] : ((~(quiet(X) & person(X))) & (~creative(Y)) & (~brave(Y)) & (~quiet(Y)) & (~tall(Y)) & quieter(X, Y)))))), 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'\|)))) & (((((((((~(hate(lucy, paul) \| taller(lucy, paul))) => (brave(mary) & tall(paul))) & ((~like(fred, lucy)) => predb(alice))) & hate(alice, lucy)) & ![X: $i] : quieter(alice, X)) & ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & (((brave(X) & tourist(X)) & brave(Y)) & tourist(Y))) & (~(X = Y)))) & ((((~tall(alice)) & (~brave(alice))) & (~creative(alice))) & (~like(lucy, alice)))) & ((~hate(lucy, paul)) & (((~creative(paul)) & (~quiet(paul))) & (~tall(paul))))) & ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & ((~hate(X, lucy)) & (~hate(Y, lucy)))) & (~(X = Y))))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)) \| (X = \|'alice'\|)))) & ?[X: $i, Y: $i] : (((~(quiet(X) & person(X))) & ((((~creative(Y)) & (~brave(Y))) & (~quiet(Y))) & (~tall(Y)))) & quieter(X, Y))))), file('/mnt/tmpfs//67981917167664533096556.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))) & (hate(lucy, paul) \| taller(lucy, paul) \| (brave(mary) & tall(paul))) & (like(fred, lucy) \| predb(alice)) & hate(alice, lucy) & ![X: $i] : quieter(alice, X) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & brave(X) & tourist(X) & brave(Y) & tourist(Y) & (~(X = Y))) & (~tall(alice)) & (~brave(alice)) & (~creative(alice)) & (~like(lucy, alice)) & (~hate(lucy, paul)) & (~creative(paul)) & (~quiet(paul)) & (~tall(paul)) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~hate(X, lucy)) & (~hate(Y, lucy)) & (~(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] : ((~(quiet(X) & person(X))) & (~creative(Y)) & (~brave(Y)) & (~quiet(Y)) & (~tall(Y)) & quieter(X, Y))))), 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))) & (hate(lucy, paul) \| taller(lucy, paul) \| (brave(mary) & tall(paul))) & (like(fred, lucy) \| predb(alice)) & hate(alice, lucy) & ![X: $i] : quieter(alice, X) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & brave(X) & tourist(X) & brave(Y) & tourist(Y) & (~(X = Y))) & (~tall(alice)) & (~brave(alice)) & (~creative(alice)) & (~like(lucy, alice)) & (~hate(lucy, paul)) & (~creative(paul)) & (~quiet(paul)) & (~tall(paul)) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~hate(X, lucy)) & (~hate(Y, lucy)) & (~(X = Y)))), inference(or_elim,[status(thm)],[7])). tff(9,plain, (![X: $i] : quieter(alice, X)), inference(and_elim,[status(thm)],[8])). tff(10,plain, (![X: $i] : quieter(alice, X)), inference(modus_ponens,[status(thm)],[9, 4])). tff(11,plain,( ![X: $i] : quieter(alice, X)), inference(skolemize,[status(sab)],[10])). tff(12,plain, (![X: $i] : quieter(alice, X)), inference(modus_ponens,[status(thm)],[11, 3])). tff(13,plain, ((~![X: $i] : quieter(alice, X)) \| quieter(alice, paul)), inference(quant_inst,[status(thm)],[])). tff(14,plain, ($false), inference(unit_resolution,[status(thm)],[13, 12, 1])). tff(15,plain,(quieter(alice, paul)), inference(lemma,lemma(discharge,[]))). tff(16,plain, ((~quiet(paul)) <=> (~quiet(paul))), inference(rewrite,[status(thm)],[])). tff(17,plain, (~quiet(paul)), inference(and_elim,[status(thm)],[8])). tff(18,plain, (~quiet(paul)), inference(modus_ponens,[status(thm)],[17, 16])). tff(19,plain, ((~(alice = paul)) <=> (~(alice = 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//67981917167664533096556.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, (~(alice = paul)), inference(and_elim,[status(thm)],[42])). tff(44,plain, (~(alice = paul)), inference(modus_ponens,[status(thm)],[43, 19])). tff(45,plain, (^[X: $i, Y: $i] : refl(((X = Y) \| quiet(Y) \| (~quieter(X, Y)) \| (~quiet(X))) <=> ((X = Y) \| quiet(Y) \| (~quieter(X, Y)) \| (~quiet(X))))), inference(bind,[status(th)],[])). tff(46,plain, (![X: $i, Y: $i] : ((X = Y) \| quiet(Y) \| (~quieter(X, Y)) \| (~quiet(X))) <=> ![X: $i, Y: $i] : ((X = Y) \| quiet(Y) \| (~quieter(X, Y)) \| (~quiet(X)))), inference(quant_intro,[status(thm)],[45])). tff(47,plain, (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((quieter(X, Y) & quiet(X)) <=> (~((~quieter(X, Y)) \| (~quiet(X))))), ((~(quieter(X, Y) & quiet(X))) <=> (~(~((~quieter(X, Y)) \| (~quiet(X))))))), rewrite((~(~((~quieter(X, Y)) \| (~quiet(X))))) <=> ((~quieter(X, Y)) \| (~quiet(X)))), ((~(quieter(X, Y) & quiet(X))) <=> ((~quieter(X, Y)) \| (~quiet(X))))), (((X = Y) \| quiet(Y) \| (~(quieter(X, Y) & quiet(X)))) <=> ((X = Y) \| quiet(Y) \| ((~quieter(X, Y)) \| (~quiet(X)))))), rewrite(((X = Y) \| quiet(Y) \| ((~quieter(X, Y)) \| (~quiet(X)))) <=> ((X = Y) \| quiet(Y) \| (~quieter(X, Y)) \| (~quiet(X)))), (((X = Y) \| quiet(Y) \| (~(quieter(X, Y) & quiet(X)))) <=> ((X = Y) \| quiet(Y) \| (~quieter(X, Y)) \| (~quiet(X)))))), inference(bind,[status(th)],[])). tff(48,plain, (![X: $i, Y: $i] : ((X = Y) \| quiet(Y) \| (~(quieter(X, Y) & quiet(X)))) <=> ![X: $i, Y: $i] : ((X = Y) \| quiet(Y) \| (~quieter(X, Y)) \| (~quiet(X)))), inference(quant_intro,[status(thm)],[47])). tff(49,plain, (![X: $i, Y: $i] : ((X = Y) \| quiet(Y) \| (~(quieter(X, Y) & quiet(X)))) <=> ![X: $i, Y: $i] : ((X = Y) \| quiet(Y) \| (~(quieter(X, Y) & quiet(X))))), inference(rewrite,[status(thm)],[])). tff(50,plain, (^[X: $i, Y: $i] : trans(monotonicity(rewrite(((quieter(X, Y) & quiet(X)) => quiet(Y)) <=> (quiet(Y) \| (~(quieter(X, Y) & quiet(X))))), (((~(X = Y)) => ((quieter(X, Y) & quiet(X)) => quiet(Y))) <=> ((~(X = Y)) => (quiet(Y) \| (~(quieter(X, Y) & quiet(X))))))), rewrite(((~(X = Y)) => (quiet(Y) \| (~(quieter(X, Y) & quiet(X))))) <=> ((X = Y) \| quiet(Y) \| (~(quieter(X, Y) & quiet(X))))), (((~(X = Y)) => ((quieter(X, Y) & quiet(X)) => quiet(Y))) <=> ((X = Y) \| quiet(Y) \| (~(quieter(X, Y) & quiet(X))))))), inference(bind,[status(th)],[])). tff(51,plain, (![X: $i, Y: $i] : ((~(X = Y)) => ((quieter(X, Y) & quiet(X)) => quiet(Y))) <=> ![X: $i, Y: $i] : ((X = Y) \| quiet(Y) \| (~(quieter(X, Y) & quiet(X))))), inference(quant_intro,[status(thm)],[50])). tff(52,axiom,(![X: $i, Y: $i] : ((~(X = Y)) => ((quieter(X, Y) & quiet(X)) => quiet(Y)))), file('/mnt/tmpfs//67981917167664533096556.p','b12')). tff(53,plain, (![X: $i, Y: $i] : ((X = Y) \| quiet(Y) \| (~(quieter(X, Y) & quiet(X))))), inference(modus_ponens,[status(thm)],[52, 51])). tff(54,plain, (![X: $i, Y: $i] : ((X = Y) \| quiet(Y) \| (~(quieter(X, Y) & quiet(X))))), inference(modus_ponens,[status(thm)],[53, 49])). tff(55,plain,( ![X: $i, Y: $i] : ((X = Y) \| quiet(Y) \| (~(quieter(X, Y) & quiet(X))))), inference(skolemize,[status(sab)],[54])). tff(56,plain, (![X: $i, Y: $i] : ((X = Y) \| quiet(Y) \| (~quieter(X, Y)) \| (~quiet(X)))), inference(modus_ponens,[status(thm)],[55, 48])). tff(57,plain, (![X: $i, Y: $i] : ((X = Y) \| quiet(Y) \| (~quieter(X, Y)) \| (~quiet(X)))), inference(modus_ponens,[status(thm)],[56, 46])). tff(58,plain, (((~![X: $i, Y: $i] : ((X = Y) \| quiet(Y) \| (~quieter(X, Y)) \| (~quiet(X)))) \| ((alice = paul) \| quiet(paul) \| (~quiet(alice)) \| (~quieter(alice, paul)))) <=> ((~![X: $i, Y: $i] : ((X = Y) \| quiet(Y) \| (~quieter(X, Y)) \| (~quiet(X)))) \| (alice = paul) \| quiet(paul) \| (~quiet(alice)) \| (~quieter(alice, paul)))), inference(rewrite,[status(thm)],[])). tff(59,plain, (((alice = paul) \| quiet(paul) \| (~quieter(alice, paul)) \| (~quiet(alice))) <=> ((alice = paul) \| quiet(paul) \| (~quiet(alice)) \| (~quieter(alice, paul)))), inference(rewrite,[status(thm)],[])). tff(60,plain, (((~![X: $i, Y: $i] : ((X = Y) \| quiet(Y) \| (~quieter(X, Y)) \| (~quiet(X)))) \| ((alice = paul) \| quiet(paul) \| (~quieter(alice, paul)) \| (~quiet(alice)))) <=> ((~![X: $i, Y: $i] : ((X = Y) \| quiet(Y) \| (~quieter(X, Y)) \| (~quiet(X)))) \| ((alice = paul) \| quiet(paul) \| (~quiet(alice)) \| (~quieter(alice, paul))))), inference(monotonicity,[status(thm)],[59])). tff(61,plain, (((~![X: $i, Y: $i] : ((X = Y) \| quiet(Y) \| (~quieter(X, Y)) \| (~quiet(X)))) \| ((alice = paul) \| quiet(paul) \| (~quieter(alice, paul)) \| (~quiet(alice)))) <=> ((~![X: $i, Y: $i] : ((X = Y) \| quiet(Y) \| (~quieter(X, Y)) \| (~quiet(X)))) \| (alice = paul) \| quiet(paul) \| (~quiet(alice)) \| (~quieter(alice, paul)))), inference(transitivity,[status(thm)],[60, 58])). tff(62,plain, ((~![X: $i, Y: $i] : ((X = Y) \| quiet(Y) \| (~quieter(X, Y)) \| (~quiet(X)))) \| ((alice = paul) \| quiet(paul) \| (~quieter(alice, paul)) \| (~quiet(alice)))), inference(quant_inst,[status(thm)],[])). tff(63,plain, ((~![X: $i, Y: $i] : ((X = Y) \| quiet(Y) \| (~quieter(X, Y)) \| (~quiet(X)))) \| (alice = paul) \| quiet(paul) \| (~quiet(alice)) \| (~quieter(alice, paul))), inference(modus_ponens,[status(thm)],[62, 61])). tff(64,plain, ((~quiet(alice)) \| (~quieter(alice, paul))), inference(unit_resolution,[status(thm)],[63, 57, 44, 18])). tff(65,plain, (~quiet(alice)), inference(unit_resolution,[status(thm)],[64, 15])). tff(66,plain, (((~person(alice)) \| (~quiet(alice))) \| quiet(alice)), inference(tautology,[status(thm)],[])). tff(67,plain, ((~person(alice)) \| (~quiet(alice))), inference(unit_resolution,[status(thm)],[66, 65])). tff(68,assumption,(~((X!4 = \|'alice'\|) \| (X!4 = \|'fred'\|) \| (X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|) \| (~room(X!4)))), introduced(assumption)). tff(69,plain, (((X!4 = \|'alice'\|) \| (X!4 = \|'fred'\|) \| (X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|) \| (~room(X!4))) \| room(X!4)), inference(tautology,[status(thm)],[])). tff(70,plain, (room(X!4)), inference(unit_resolution,[status(thm)],[69, 68])). tff(71,plain, (((X!4 = \|'alice'\|) \| (X!4 = \|'fred'\|) \| (X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|) \| (~room(X!4))) \| (~(X!4 = \|'mary'\|))), inference(tautology,[status(thm)],[])). tff(72,plain, (~(X!4 = \|'mary'\|)), inference(unit_resolution,[status(thm)],[71, 68])). tff(73,plain, (((X!4 = \|'alice'\|) \| (X!4 = \|'fred'\|) \| (X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|) \| (~room(X!4))) \| (~(X!4 = \|'paul'\|))), inference(tautology,[status(thm)],[])). tff(74,plain, (~(X!4 = \|'paul'\|)), inference(unit_resolution,[status(thm)],[73, 68])). tff(75,plain, (((X!4 = \|'alice'\|) \| (X!4 = \|'fred'\|) \| (X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|) \| (~room(X!4))) \| (~(X!4 = \|'fred'\|))), inference(tautology,[status(thm)],[])). tff(76,plain, (~(X!4 = \|'fred'\|)), inference(unit_resolution,[status(thm)],[75, 68])). tff(77,plain, (((X!4 = \|'alice'\|) \| (X!4 = \|'fred'\|) \| (X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|) \| (~room(X!4))) \| (~(X!4 = \|'alice'\|))), inference(tautology,[status(thm)],[])). tff(78,plain, (~(X!4 = \|'alice'\|)), inference(unit_resolution,[status(thm)],[77, 68])). tff(79,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(80,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)],[79])). tff(81,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(82,plain, (![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))), inference(and_elim,[status(thm)],[8])). tff(83,plain, (![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))), inference(modus_ponens,[status(thm)],[82, 81])). tff(84,plain,( ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))), inference(skolemize,[status(sab)],[83])). tff(85,plain, (![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))), inference(modus_ponens,[status(thm)],[84, 80])). tff(86,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(87,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(88,plain, ((~![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| (X!4 = \|'alice'\|) \| (X!4 = \|'fred'\|) \| (X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|) \| (~room(X!4))), inference(modus_ponens,[status(thm)],[87, 86])). tff(89,plain, ($false), inference(unit_resolution,[status(thm)],[88, 85, 78, 76, 74, 72, 70])). tff(90,plain,((X!4 = \|'alice'\|) \| (X!4 = \|'fred'\|) \| (X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|) \| (~room(X!4))), inference(lemma,lemma(discharge,[]))). tff(91,plain, (room(alice) <=> room(alice)), inference(rewrite,[status(thm)],[])). tff(92,plain, (room(alice)), inference(and_elim,[status(thm)],[8])). tff(93,plain, (room(alice)), inference(modus_ponens,[status(thm)],[92, 91])). tff(94,plain, (room(fred) <=> room(fred)), inference(rewrite,[status(thm)],[])). tff(95,plain, (room(fred)), inference(and_elim,[status(thm)],[8])). tff(96,plain, (room(fred)), inference(modus_ponens,[status(thm)],[95, 94])). tff(97,plain, (room(paul) <=> room(paul)), inference(rewrite,[status(thm)],[])). tff(98,plain, (room(paul)), inference(and_elim,[status(thm)],[8])). tff(99,plain, (room(paul)), inference(modus_ponens,[status(thm)],[98, 97])). tff(100,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(101,plain, (room(mary)), inference(and_elim,[status(thm)],[8])). tff(102,plain, (room(mary)), inference(modus_ponens,[status(thm)],[101, 100])). tff(103,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] : (tall(Y) \| quiet(Y) \| brave(Y) \| creative(Y) \| (~quieter(X, Y)) \| (~((~quiet(X)) \| (~person(X)))))) <=> ((~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] : (tall(Y) \| quiet(Y) \| brave(Y) \| creative(Y) \| (~quieter(X, Y)) \| (~((~quiet(X)) \| (~person(X))))))), inference(rewrite,[status(thm)],[])). tff(104,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] : (tall(Y) \| quiet(Y) \| brave(Y) \| creative(Y) \| (~quieter(X, Y)) \| (~((~quiet(X)) \| (~person(X)))))) <=> ((~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] : (tall(Y) \| quiet(Y) \| brave(Y) \| creative(Y) \| (~quieter(X, Y)) \| (~((~quiet(X)) \| (~person(X))))))), inference(rewrite,[status(thm)],[])). tff(105,plain, (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((quiet(X) & person(X)) <=> (~((~quiet(X)) \| (~person(X))))), ((~(quiet(X) & person(X))) <=> (~(~((~quiet(X)) \| (~person(X))))))), rewrite((~(~((~quiet(X)) \| (~person(X))))) <=> ((~quiet(X)) \| (~person(X)))), ((~(quiet(X) & person(X))) <=> ((~quiet(X)) \| (~person(X))))), (((~(quiet(X) & person(X))) & (~creative(Y)) & (~brave(Y)) & (~quiet(Y)) & (~tall(Y)) & quieter(X, Y)) <=> (((~quiet(X)) \| (~person(X))) & (~creative(Y)) & (~brave(Y)) & (~quiet(Y)) & (~tall(Y)) & quieter(X, Y)))), rewrite((((~quiet(X)) \| (~person(X))) & (~creative(Y)) & (~brave(Y)) & (~quiet(Y)) & (~tall(Y)) & quieter(X, Y)) <=> (~(tall(Y) \| quiet(Y) \| brave(Y) \| creative(Y) \| (~quieter(X, Y)) \| (~((~quiet(X)) \| (~person(X))))))), (((~(quiet(X) & person(X))) & (~creative(Y)) & (~brave(Y)) & (~quiet(Y)) & (~tall(Y)) & quieter(X, Y)) <=> (~(tall(Y) \| quiet(Y) \| brave(Y) \| creative(Y) \| (~quieter(X, Y)) \| (~((~quiet(X)) \| (~person(X)))))))), ((~((~(quiet(X) & person(X))) & (~creative(Y)) & (~brave(Y)) & (~quiet(Y)) & (~tall(Y)) & quieter(X, Y))) <=> (~(~(tall(Y) \| quiet(Y) \| brave(Y) \| creative(Y) \| (~quieter(X, Y)) \| (~((~quiet(X)) \| (~person(X))))))))), rewrite((~(~(tall(Y) \| quiet(Y) \| brave(Y) \| creative(Y) \| (~quieter(X, Y)) \| (~((~quiet(X)) \| (~person(X))))))) <=> (tall(Y) \| quiet(Y) \| brave(Y) \| creative(Y) \| (~quieter(X, Y)) \| (~((~quiet(X)) \| (~person(X)))))), ((~((~(quiet(X) & person(X))) & (~creative(Y)) & (~brave(Y)) & (~quiet(Y)) & (~tall(Y)) & quieter(X, Y))) <=> (tall(Y) \| quiet(Y) \| brave(Y) \| creative(Y) \| (~quieter(X, Y)) \| (~((~quiet(X)) \| (~person(X)))))))), inference(bind,[status(th)],[])). tff(106,plain, (![X: $i, Y: $i] : (~((~(quiet(X) & person(X))) & (~creative(Y)) & (~brave(Y)) & (~quiet(Y)) & (~tall(Y)) & quieter(X, Y))) <=> ![X: $i, Y: $i] : (tall(Y) \| quiet(Y) \| brave(Y) \| creative(Y) \| (~quieter(X, Y)) \| (~((~quiet(X)) \| (~person(X)))))), inference(quant_intro,[status(thm)],[105])). tff(107,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(108,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] : (~((~(quiet(X) & person(X))) & (~creative(Y)) & (~brave(Y)) & (~quiet(Y)) & (~tall(Y)) & quieter(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] : (tall(Y) \| quiet(Y) \| brave(Y) \| creative(Y) \| (~quieter(X, Y)) \| (~((~quiet(X)) \| (~person(X))))))), inference(monotonicity,[status(thm)],[107, 106])). tff(109,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] : (~((~(quiet(X) & person(X))) & (~creative(Y)) & (~brave(Y)) & (~quiet(Y)) & (~tall(Y)) & quieter(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] : (tall(Y) \| quiet(Y) \| brave(Y) \| creative(Y) \| (~quieter(X, Y)) \| (~((~quiet(X)) \| (~person(X))))))), inference(transitivity,[status(thm)],[108, 104])). tff(110,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] : (~((~(quiet(X) & person(X))) & (~creative(Y)) & (~brave(Y)) & (~quiet(Y)) & (~tall(Y)) & quieter(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] : (~((~(quiet(X) & person(X))) & (~creative(Y)) & (~brave(Y)) & (~quiet(Y)) & (~tall(Y)) & quieter(X, Y))))), inference(rewrite,[status(thm)],[])). tff(111,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] : (~((~(quiet(X) & person(X))) & (~creative(Y)) & (~brave(Y)) & (~quiet(Y)) & (~tall(Y)) & quieter(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] : (~((~(quiet(X) & person(X))) & (~creative(Y)) & (~brave(Y)) & (~quiet(Y)) & (~tall(Y)) & quieter(X, Y))))), inference(monotonicity,[status(thm)],[107])). tff(112,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] : (~((~(quiet(X) & person(X))) & (~creative(Y)) & (~brave(Y)) & (~quiet(Y)) & (~tall(Y)) & quieter(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] : (~((~(quiet(X) & person(X))) & (~creative(Y)) & (~brave(Y)) & (~quiet(Y)) & (~tall(Y)) & quieter(X, Y))))), inference(transitivity,[status(thm)],[111, 110])). tff(113,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] : ((~(quiet(X) & person(X))) & (~creative(Y)) & (~brave(Y)) & (~quiet(Y)) & (~tall(Y)) & quieter(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] : ((~(quiet(X) & person(X))) & (~creative(Y)) & (~brave(Y)) & (~quiet(Y)) & (~tall(Y)) & quieter(X, Y)))), inference(rewrite,[status(thm)],[])). tff(114,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] : ((~(quiet(X) & person(X))) & (~creative(Y)) & (~brave(Y)) & (~quiet(Y)) & (~tall(Y)) & quieter(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] : ((~(quiet(X) & person(X))) & (~creative(Y)) & (~brave(Y)) & (~quiet(Y)) & (~tall(Y)) & quieter(X, Y))))), inference(monotonicity,[status(thm)],[113])). tff(115,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] : ((~(quiet(X) & person(X))) & (~creative(Y)) & (~brave(Y)) & (~quiet(Y)) & (~tall(Y)) & quieter(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] : ((~(quiet(X) & person(X))) & (~creative(Y)) & (~brave(Y)) & (~quiet(Y)) & (~tall(Y)) & quieter(X, Y))))), inference(rewrite,[status(thm)],[])). tff(116,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] : ((~(quiet(X) & person(X))) & (~creative(Y)) & (~brave(Y)) & (~quiet(Y)) & (~tall(Y)) & quieter(X, Y)))), inference(or_elim,[status(thm)],[7])). tff(117,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] : ((~(quiet(X) & person(X))) & (~creative(Y)) & (~brave(Y)) & (~quiet(Y)) & (~tall(Y)) & quieter(X, Y)))), inference(modus_ponens,[status(thm)],[116, 114])). tff(118,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] : ((~(quiet(X) & person(X))) & (~creative(Y)) & (~brave(Y)) & (~quiet(Y)) & (~tall(Y)) & quieter(X, Y)))), inference(modus_ponens,[status(thm)],[117, 115])). tff(119,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] : ((~(quiet(X) & person(X))) & (~creative(Y)) & (~brave(Y)) & (~quiet(Y)) & (~tall(Y)) & quieter(X, Y)))), inference(modus_ponens,[status(thm)],[118, 114])). 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 (not (and (quiet X) (person X))) (not (creative Y)) (not (brave Y)) (not (quiet Y)) (not (tall Y)) (quieter X Y)))) (refl (~ (not a!1) (not a!1)))))) (a!8 (exists ((X $i) (Y $i)) (and (not (and (quiet X) (person X))) (not (creative Y)) (not (brave Y)) (not (quiet Y)) (not (tall Y)) (quieter X Y)))) (a!9 (forall ((X $i) (Y $i)) (let ((a!1 (and (not (and (quiet X) (person X))) (not (creative Y)) (not (brave Y)) (not (quiet Y)) (not (tall Y)) (quieter 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(diana)&room(jennifer)&room(christine)&room(richard)&(![X]:(room(X)=>(X='diana'\|X='jennifer'\|X='christine'\|X='richard')))& (((~((hate(james,jennifer))\|(taller(james,jennifer))))=>((brave(diana))&(tall(jennifer))))& (~(like(christine,james))=>(practices_graffiti_art(richard)))& (hate(richard,james))& (![X]:(quieter(richard,X)))& ((?[X,Y]:(~room(X)&~room(Y)&(brave(X)&tourist(X)&brave(Y)&tourist(Y))&(X!=Y))))& ((~tall(richard)&~brave(richard)&~creative(richard))&(~like(james,richard)))& ((~hate(james,jennifer))&(~creative(jennifer)&~quiet(jennifer)&~tall(jennifer)))& ((?[X,Y]:(~room(X)&~room(Y)&(~hate(X,james)&~hate(Y,james))&(X!=Y)))))	room(diana)&room(jennifer)&room(christine)&room(richard)&(![X]:(room(X)=>(X='diana'\|X='jennifer'\|X='christine'\|X='richard')))& (?[X,Y]:((~(quiet(X)&person(X)))&(~creative(Y)&~brave(Y)&~quiet(Y)&~tall(Y))&(quieter(X,Y))))	entailment	neutral	contradiction
Michael, Carmen, Richard, Tamara are the only persons in the room. 'Only one person in the room does not hate Valentin' unless 'Carmen is taller than Valentin'. Michael who is not Carmen, does not hate Valentin. Carmen is taller than Valentin.	Tamara neither is hated by Valentin nor hates Valentin.	neutral	% SZS status Satisfiable	room(michael)&room(carmen)&room(richard)&room(tamara)&(![X]:(room(X)=>(X='michael'\|X='carmen'\|X='richard'\|X='tamara')))& ((~(taller(valentin,carmen))=>(((?[X]:(room(X)&~hate(valentin,X)))&(![X,Y]:((~hate(valentin,X)&~hate(valentin,Y))=>(X=Y))))))& ((michael!=carmen)&(~hate(valentin,michael)))& (taller(valentin,carmen)))	room(michael)&room(carmen)&room(richard)&room(tamara)&(![X]:(room(X)=>(X='michael'\|X='carmen'\|X='richard'\|X='tamara')))& (~((hate(tamara,valentin))\|(hate(valentin,tamara))))	entailment	contradiction	contradiction
Yolanda, Otis, Robert are the only persons in the room. Otis and Robert are respectively brave and happy unless someone who does not collect rare minerals is richer than someone who sketches as a hobby. Yolanda and Robert are not a rich person. Robert is the least rich in the room. Someone who likes Cary like someone who is not a rich person. Robert neither sketches as a hobby nor is not rich. More than one person outside the room does not hate Cary.	Someone who is not a happy rich creative european is richer than someone who is not a tall person.	entailment	% SZS status Unsatisfiable % SZS output start Proof tff(rich_type, type, ( rich: $i > $o)). tff(fred_type, type, ( fred: $i)). tff(tptp_fun_Y_2_type, type, ( tptp_fun_Y_2: $i)). tff(person_type, type, ( person: $i > $o)). tff(tall_type, type, ( tall: $i > $o)). tff(creative_type, type, ( creative: $i > $o)). tff(european_type, type, ( european: $i > $o)). tff(happy_type, type, ( happy: $i > $o)). tff(predc_type, type, ( predc: $i > $o)). tff(hate_type, type, ( hate: ( $i * $i ) > $o)). tff(lucy_type, type, ( lucy: $i)). tff(room_type, type, ( room: $i > $o)). tff(like_type, type, ( like: ( $i * $i ) > $o)). tff(richer_type, type, ( richer: ( $i * $i ) > $o)). tff(mary_type, type, ( mary: $i)). tff(preda_type, type, ( preda: $i > $o)). tff(brave_type, type, ( brave: $i > $o)). tff(paul_type, type, ( paul: $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_X_6_type, type, ( tptp_fun_X_6: $i)). tff(tptp_fun_X_3_type, type, ( tptp_fun_X_3: $i)). tff(1,plain, (rich(fred) <=> rich(fred)), inference(rewrite,[status(thm)],[])). tff(2,plain, ((~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)))) & (((((((~?[X: $i, Y: $i] : (((~preda(X)) & predc(Y)) & richer(X, Y))) => (brave(paul) & happy(fred))) & ((~(rich(mary) & person(mary))) & (~(rich(fred) & person(fred))))) & ![X: $i] : richer(fred, X)) & ?[X: $i, Y: $i] : ((like(lucy, X) & (~(rich(Y) & person(Y)))) & like(X, Y))) & (~(predc(fred) \| (~rich(fred))))) & ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & ((~hate(lucy, X)) & (~hate(lucy, Y)))) & (~(X = Y))))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)))) & ?[X: $i, Y: $i] : (((~(((happy(X) & rich(X)) & creative(X)) & european(X))) & (~(tall(Y) & person(Y)))) & richer(X, Y))))) <=> (~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((brave(paul) & happy(fred)) \| ?[X: $i, Y: $i] : ((~preda(X)) & predc(Y) & richer(X, Y))) & (~(rich(mary) & person(mary))) & (~(rich(fred) & person(fred))) & ![X: $i] : richer(fred, X) & ?[X: $i, Y: $i] : (like(lucy, X) & (~(rich(Y) & person(Y))) & like(X, Y)) & (~(predc(fred) \| (~rich(fred)))) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~hate(lucy, X)) & (~hate(lucy, Y)) & (~(X = Y))))) \| (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ?[X: $i, Y: $i] : ((~(happy(X) & rich(X) & creative(X) & european(X))) & (~(tall(Y) & person(Y))) & richer(X, Y)))))), inference(rewrite,[status(thm)],[])). tff(3,axiom,(~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)))) & (((((((~?[X: $i, Y: $i] : (((~preda(X)) & predc(Y)) & richer(X, Y))) => (brave(paul) & happy(fred))) & ((~(rich(mary) & person(mary))) & (~(rich(fred) & person(fred))))) & ![X: $i] : richer(fred, X)) & ?[X: $i, Y: $i] : ((like(lucy, X) & (~(rich(Y) & person(Y)))) & like(X, Y))) & (~(predc(fred) \| (~rich(fred))))) & ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & ((~hate(lucy, X)) & (~hate(lucy, Y)))) & (~(X = Y))))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)))) & ?[X: $i, Y: $i] : (((~(((happy(X) & rich(X)) & creative(X)) & european(X))) & (~(tall(Y) & person(Y)))) & richer(X, Y))))), file('/mnt/tmpfs//6065207960950291322599000.p','negated')). tff(4,plain, (~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((brave(paul) & happy(fred)) \| ?[X: $i, Y: $i] : ((~preda(X)) & predc(Y) & richer(X, Y))) & (~(rich(mary) & person(mary))) & (~(rich(fred) & person(fred))) & ![X: $i] : richer(fred, X) & ?[X: $i, Y: $i] : (like(lucy, X) & (~(rich(Y) & person(Y))) & like(X, Y)) & (~(predc(fred) \| (~rich(fred)))) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~hate(lucy, X)) & (~hate(lucy, Y)) & (~(X = Y))))) \| (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ?[X: $i, Y: $i] : ((~(happy(X) & rich(X) & creative(X) & european(X))) & (~(tall(Y) & person(Y))) & richer(X, Y))))), 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))) & ((brave(paul) & happy(fred)) \| ?[X: $i, Y: $i] : ((~preda(X)) & predc(Y) & richer(X, Y))) & (~(rich(mary) & person(mary))) & (~(rich(fred) & person(fred))) & ![X: $i] : richer(fred, X) & ?[X: $i, Y: $i] : (like(lucy, X) & (~(rich(Y) & person(Y))) & like(X, Y)) & (~(predc(fred) \| (~rich(fred)))) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~hate(lucy, X)) & (~hate(lucy, Y)) & (~(X = Y)))), inference(or_elim,[status(thm)],[4])). tff(6,plain, (~(predc(fred) \| (~rich(fred)))), inference(and_elim,[status(thm)],[5])). tff(7,plain, (rich(fred)), inference(or_elim,[status(thm)],[6])). tff(8,plain, (rich(fred)), inference(modus_ponens,[status(thm)],[7, 1])). tff(9,plain, ((~(~((~rich(fred)) \| (~person(fred))))) <=> ((~rich(fred)) \| (~person(fred)))), inference(rewrite,[status(thm)],[])). tff(10,plain, ((rich(fred) & person(fred)) <=> (~((~rich(fred)) \| (~person(fred))))), inference(rewrite,[status(thm)],[])). tff(11,plain, ((~(rich(fred) & person(fred))) <=> (~(~((~rich(fred)) \| (~person(fred)))))), inference(monotonicity,[status(thm)],[10])). tff(12,plain, ((~(rich(fred) & person(fred))) <=> ((~rich(fred)) \| (~person(fred)))), inference(transitivity,[status(thm)],[11, 9])). tff(13,plain, ((~(rich(fred) & person(fred))) <=> (~(rich(fred) & person(fred)))), inference(rewrite,[status(thm)],[])). tff(14,plain, (~(rich(fred) & person(fred))), inference(and_elim,[status(thm)],[5])). tff(15,plain, (~(rich(fred) & person(fred))), inference(modus_ponens,[status(thm)],[14, 13])). tff(16,plain, ((~rich(fred)) \| (~person(fred))), inference(modus_ponens,[status(thm)],[15, 12])). tff(17,plain, (~person(fred)), inference(unit_resolution,[status(thm)],[16, 8])). tff(18,plain, (^[X: $i] : refl((person(X) \| (~european(X))) <=> (person(X) \| (~european(X))))), inference(bind,[status(th)],[])). tff(19,plain, (![X: $i] : (person(X) \| (~european(X))) <=> ![X: $i] : (person(X) \| (~european(X)))), inference(quant_intro,[status(thm)],[18])). tff(20,plain, (![X: $i] : (person(X) \| (~european(X))) <=> ![X: $i] : (person(X) \| (~european(X)))), inference(rewrite,[status(thm)],[])). tff(21,plain, (^[X: $i] : rewrite((european(X) => person(X)) <=> (person(X) \| (~european(X))))), inference(bind,[status(th)],[])). tff(22,plain, (![X: $i] : (european(X) => person(X)) <=> ![X: $i] : (person(X) \| (~european(X)))), inference(quant_intro,[status(thm)],[21])). tff(23,axiom,(![X: $i] : (european(X) => person(X))), file('/mnt/tmpfs//6065207960950291322599000.p','b2')). tff(24,plain, (![X: $i] : (person(X) \| (~european(X)))), inference(modus_ponens,[status(thm)],[23, 22])). tff(25,plain, (![X: $i] : (person(X) \| (~european(X)))), inference(modus_ponens,[status(thm)],[24, 20])). tff(26,plain,( ![X: $i] : (person(X) \| (~european(X)))), inference(skolemize,[status(sab)],[25])). tff(27,plain, (![X: $i] : (person(X) \| (~european(X)))), inference(modus_ponens,[status(thm)],[26, 19])). tff(28,plain, (((~![X: $i] : (person(X) \| (~european(X)))) \| (person(fred) \| (~european(fred)))) <=> ((~![X: $i] : (person(X) \| (~european(X)))) \| person(fred) \| (~european(fred)))), inference(rewrite,[status(thm)],[])). tff(29,plain, ((~![X: $i] : (person(X) \| (~european(X)))) \| (person(fred) \| (~european(fred)))), inference(quant_inst,[status(thm)],[])). tff(30,plain, ((~![X: $i] : (person(X) \| (~european(X)))) \| person(fred) \| (~european(fred))), inference(modus_ponens,[status(thm)],[29, 28])). tff(31,plain, (~european(fred)), inference(unit_resolution,[status(thm)],[30, 27, 17])). tff(32,plain, (((~rich(fred)) \| (~happy(fred)) \| (~european(fred)) \| (~creative(fred))) \| european(fred)), inference(tautology,[status(thm)],[])). tff(33,plain, ((~rich(fred)) \| (~happy(fred)) \| (~european(fred)) \| (~creative(fred))), inference(unit_resolution,[status(thm)],[32, 31])). tff(34,plain, (^[X: $i] : refl(richer(fred, X) <=> richer(fred, X))), inference(bind,[status(th)],[])). tff(35,plain, (![X: $i] : richer(fred, X) <=> ![X: $i] : richer(fred, X)), inference(quant_intro,[status(thm)],[34])). tff(36,plain, (![X: $i] : richer(fred, X) <=> ![X: $i] : richer(fred, X)), inference(rewrite,[status(thm)],[])). tff(37,plain, (![X: $i] : richer(fred, X)), inference(and_elim,[status(thm)],[5])). tff(38,plain, (![X: $i] : richer(fred, X)), inference(modus_ponens,[status(thm)],[37, 36])). tff(39,plain,( ![X: $i] : richer(fred, X)), inference(skolemize,[status(sab)],[38])). tff(40,plain, (![X: $i] : richer(fred, X)), inference(modus_ponens,[status(thm)],[39, 35])). tff(41,plain, ((~![X: $i] : richer(fred, X)) \| richer(fred, Y!2)), inference(quant_inst,[status(thm)],[])). tff(42,plain, (richer(fred, Y!2)), inference(unit_resolution,[status(thm)],[41, 40])). tff(43,assumption,(~((X!6 = \|'fred'\|) \| (X!6 = \|'paul'\|) \| (X!6 = \|'mary'\|) \| (~room(X!6)))), introduced(assumption)). tff(44,plain, (((X!6 = \|'fred'\|) \| (X!6 = \|'paul'\|) \| (X!6 = \|'mary'\|) \| (~room(X!6))) \| room(X!6)), inference(tautology,[status(thm)],[])). tff(45,plain, (room(X!6)), inference(unit_resolution,[status(thm)],[44, 43])). tff(46,plain, (((X!6 = \|'fred'\|) \| (X!6 = \|'paul'\|) \| (X!6 = \|'mary'\|) \| (~room(X!6))) \| (~(X!6 = \|'mary'\|))), inference(tautology,[status(thm)],[])). tff(47,plain, (~(X!6 = \|'mary'\|)), inference(unit_resolution,[status(thm)],[46, 43])). tff(48,plain, (((X!6 = \|'fred'\|) \| (X!6 = \|'paul'\|) \| (X!6 = \|'mary'\|) \| (~room(X!6))) \| (~(X!6 = \|'paul'\|))), inference(tautology,[status(thm)],[])). tff(49,plain, (~(X!6 = \|'paul'\|)), inference(unit_resolution,[status(thm)],[48, 43])). tff(50,plain, (((X!6 = \|'fred'\|) \| (X!6 = \|'paul'\|) \| (X!6 = \|'mary'\|) \| (~room(X!6))) \| (~(X!6 = \|'fred'\|))), inference(tautology,[status(thm)],[])). tff(51,plain, (~(X!6 = \|'fred'\|)), inference(unit_resolution,[status(thm)],[50, 43])). tff(52,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(53,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)],[52])). tff(54,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(55,plain, (![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))), inference(and_elim,[status(thm)],[5])). tff(56,plain, (![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))), inference(modus_ponens,[status(thm)],[55, 54])). tff(57,plain,( ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))), inference(skolemize,[status(sab)],[56])). tff(58,plain, (![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))), inference(modus_ponens,[status(thm)],[57, 53])). tff(59,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(60,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(61,plain, ((~![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| (X!6 = \|'fred'\|) \| (X!6 = \|'paul'\|) \| (X!6 = \|'mary'\|) \| (~room(X!6))), inference(modus_ponens,[status(thm)],[60, 59])). tff(62,plain, ($false), inference(unit_resolution,[status(thm)],[61, 58, 51, 49, 47, 45])). tff(63,plain,((X!6 = \|'fred'\|) \| (X!6 = \|'paul'\|) \| (X!6 = \|'mary'\|) \| (~room(X!6))), inference(lemma,lemma(discharge,[]))). tff(64,plain, (room(fred) <=> room(fred)), inference(rewrite,[status(thm)],[])). tff(65,plain, (room(fred)), inference(and_elim,[status(thm)],[5])). tff(66,plain, (room(fred)), inference(modus_ponens,[status(thm)],[65, 64])). tff(67,plain, (room(paul) <=> room(paul)), inference(rewrite,[status(thm)],[])). tff(68,plain, (room(paul)), inference(and_elim,[status(thm)],[5])). tff(69,plain, (room(paul)), 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)],[5])). tff(72,plain, (room(mary)), inference(modus_ponens,[status(thm)],[71, 70])). tff(73,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!6 = \|'fred'\|) \| (X!6 = \|'paul'\|) \| (X!6 = \|'mary'\|) \| (~room(X!6)))) \| ![X: $i, Y: $i] : ((~richer(X, Y)) \| (~((~rich(X)) \| (~happy(X)) \| (~creative(X)) \| (~european(X)))) \| (~((~tall(Y)) \| (~person(Y)))))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!6 = \|'fred'\|) \| (X!6 = \|'paul'\|) \| (X!6 = \|'mary'\|) \| (~room(X!6)))) \| ![X: $i, Y: $i] : ((~richer(X, Y)) \| (~((~rich(X)) \| (~happy(X)) \| (~creative(X)) \| (~european(X)))) \| (~((~tall(Y)) \| (~person(Y))))))), inference(rewrite,[status(thm)],[])). tff(74,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!6 = \|'fred'\|) \| (X!6 = \|'paul'\|) \| (X!6 = \|'mary'\|) \| (~room(X!6)))) \| ![X: $i, Y: $i] : ((~richer(X, Y)) \| (~((~rich(X)) \| (~happy(X)) \| (~creative(X)) \| (~european(X)))) \| (~((~tall(Y)) \| (~person(Y)))))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!6 = \|'fred'\|) \| (X!6 = \|'paul'\|) \| (X!6 = \|'mary'\|) \| (~room(X!6)))) \| ![X: $i, Y: $i] : ((~richer(X, Y)) \| (~((~rich(X)) \| (~happy(X)) \| (~creative(X)) \| (~european(X)))) \| (~((~tall(Y)) \| (~person(Y))))))), inference(rewrite,[status(thm)],[])). tff(75,plain, (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((happy(X) & rich(X) & creative(X) & european(X)) <=> (~((~rich(X)) \| (~happy(X)) \| (~creative(X)) \| (~european(X))))), ((~(happy(X) & rich(X) & creative(X) & european(X))) <=> (~(~((~rich(X)) \| (~happy(X)) \| (~creative(X)) \| (~european(X))))))), rewrite((~(~((~rich(X)) \| (~happy(X)) \| (~creative(X)) \| (~european(X))))) <=> ((~rich(X)) \| (~happy(X)) \| (~creative(X)) \| (~european(X)))), ((~(happy(X) & rich(X) & creative(X) & european(X))) <=> ((~rich(X)) \| (~happy(X)) \| (~creative(X)) \| (~european(X))))), trans(monotonicity(rewrite((tall(Y) & person(Y)) <=> (~((~tall(Y)) \| (~person(Y))))), ((~(tall(Y) & person(Y))) <=> (~(~((~tall(Y)) \| (~person(Y))))))), rewrite((~(~((~tall(Y)) \| (~person(Y))))) <=> ((~tall(Y)) \| (~person(Y)))), ((~(tall(Y) & person(Y))) <=> ((~tall(Y)) \| (~person(Y))))), (((~(happy(X) & rich(X) & creative(X) & european(X))) & (~(tall(Y) & person(Y))) & richer(X, Y)) <=> (((~rich(X)) \| (~happy(X)) \| (~creative(X)) \| (~european(X))) & ((~tall(Y)) \| (~person(Y))) & richer(X, Y)))), rewrite((((~rich(X)) \| (~happy(X)) \| (~creative(X)) \| (~european(X))) & ((~tall(Y)) \| (~person(Y))) & richer(X, Y)) <=> (~((~richer(X, Y)) \| (~((~rich(X)) \| (~happy(X)) \| (~creative(X)) \| (~european(X)))) \| (~((~tall(Y)) \| (~person(Y))))))), (((~(happy(X) & rich(X) & creative(X) & european(X))) & (~(tall(Y) & person(Y))) & richer(X, Y)) <=> (~((~richer(X, Y)) \| (~((~rich(X)) \| (~happy(X)) \| (~creative(X)) \| (~european(X)))) \| (~((~tall(Y)) \| (~person(Y)))))))), ((~((~(happy(X) & rich(X) & creative(X) & european(X))) & (~(tall(Y) & person(Y))) & richer(X, Y))) <=> (~(~((~richer(X, Y)) \| (~((~rich(X)) \| (~happy(X)) \| (~creative(X)) \| (~european(X)))) \| (~((~tall(Y)) \| (~person(Y))))))))), rewrite((~(~((~richer(X, Y)) \| (~((~rich(X)) \| (~happy(X)) \| (~creative(X)) \| (~european(X)))) \| (~((~tall(Y)) \| (~person(Y))))))) <=> ((~richer(X, Y)) \| (~((~rich(X)) \| (~happy(X)) \| (~creative(X)) \| (~european(X)))) \| (~((~tall(Y)) \| (~person(Y)))))), ((~((~(happy(X) & rich(X) & creative(X) & european(X))) & (~(tall(Y) & person(Y))) & richer(X, Y))) <=> ((~richer(X, Y)) \| (~((~rich(X)) \| (~happy(X)) \| (~creative(X)) \| (~european(X)))) \| (~((~tall(Y)) \| (~person(Y)))))))), inference(bind,[status(th)],[])). tff(76,plain, (![X: $i, Y: $i] : (~((~(happy(X) & rich(X) & creative(X) & european(X))) & (~(tall(Y) & person(Y))) & richer(X, Y))) <=> ![X: $i, Y: $i] : ((~richer(X, Y)) \| (~((~rich(X)) \| (~happy(X)) \| (~creative(X)) \| (~european(X)))) \| (~((~tall(Y)) \| (~person(Y)))))), inference(quant_intro,[status(thm)],[75])). tff(77,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(78,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!6 = \|'fred'\|) \| (X!6 = \|'paul'\|) \| (X!6 = \|'mary'\|) \| (~room(X!6)))) \| ![X: $i, Y: $i] : (~((~(happy(X) & rich(X) & creative(X) & european(X))) & (~(tall(Y) & person(Y))) & richer(X, Y)))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!6 = \|'fred'\|) \| (X!6 = \|'paul'\|) \| (X!6 = \|'mary'\|) \| (~room(X!6)))) \| ![X: $i, Y: $i] : ((~richer(X, Y)) \| (~((~rich(X)) \| (~happy(X)) \| (~creative(X)) \| (~european(X)))) \| (~((~tall(Y)) \| (~person(Y))))))), inference(monotonicity,[status(thm)],[77, 76])). tff(79,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!6 = \|'fred'\|) \| (X!6 = \|'paul'\|) \| (X!6 = \|'mary'\|) \| (~room(X!6)))) \| ![X: $i, Y: $i] : (~((~(happy(X) & rich(X) & creative(X) & european(X))) & (~(tall(Y) & person(Y))) & richer(X, Y)))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!6 = \|'fred'\|) \| (X!6 = \|'paul'\|) \| (X!6 = \|'mary'\|) \| (~room(X!6)))) \| ![X: $i, Y: $i] : ((~richer(X, Y)) \| (~((~rich(X)) \| (~happy(X)) \| (~creative(X)) \| (~european(X)))) \| (~((~tall(Y)) \| (~person(Y))))))), inference(transitivity,[status(thm)],[78, 74])). tff(80,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!6 = \|'fred'\|) \| (X!6 = \|'paul'\|) \| (X!6 = \|'mary'\|) \| (~room(X!6)))) \| ![X: $i, Y: $i] : (~((~(happy(X) & rich(X) & creative(X) & european(X))) & (~(tall(Y) & person(Y))) & richer(X, Y)))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!6 = \|'fred'\|) \| (X!6 = \|'paul'\|) \| (X!6 = \|'mary'\|) \| (~room(X!6)))) \| ![X: $i, Y: $i] : (~((~(happy(X) & rich(X) & creative(X) & european(X))) & (~(tall(Y) & person(Y))) & richer(X, Y))))), inference(rewrite,[status(thm)],[])). tff(81,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!6 = \|'fred'\|) \| (X!6 = \|'paul'\|) \| (X!6 = \|'mary'\|) \| (~room(X!6)))) \| ![X: $i, Y: $i] : (~((~(happy(X) & rich(X) & creative(X) & european(X))) & (~(tall(Y) & person(Y))) & richer(X, Y)))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!6 = \|'fred'\|) \| (X!6 = \|'paul'\|) \| (X!6 = \|'mary'\|) \| (~room(X!6)))) \| ![X: $i, Y: $i] : (~((~(happy(X) & rich(X) & creative(X) & european(X))) & (~(tall(Y) & person(Y))) & richer(X, Y))))), inference(monotonicity,[status(thm)],[77])). tff(82,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!6 = \|'fred'\|) \| (X!6 = \|'paul'\|) \| (X!6 = \|'mary'\|) \| (~room(X!6)))) \| ![X: $i, Y: $i] : (~((~(happy(X) & rich(X) & creative(X) & european(X))) & (~(tall(Y) & person(Y))) & richer(X, Y)))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!6 = \|'fred'\|) \| (X!6 = \|'paul'\|) \| (X!6 = \|'mary'\|) \| (~room(X!6)))) \| ![X: $i, Y: $i] : (~((~(happy(X) & rich(X) & creative(X) & european(X))) & (~(tall(Y) & person(Y))) & richer(X, Y))))), inference(transitivity,[status(thm)],[81, 80])). tff(83,plain, ((room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ?[X: $i, Y: $i] : ((~(happy(X) & rich(X) & creative(X) & european(X))) & (~(tall(Y) & person(Y))) & richer(X, Y))) <=> (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ?[X: $i, Y: $i] : ((~(happy(X) & rich(X) & creative(X) & european(X))) & (~(tall(Y) & person(Y))) & richer(X, Y)))), inference(rewrite,[status(thm)],[])). tff(84,plain, ((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ?[X: $i, Y: $i] : ((~(happy(X) & rich(X) & creative(X) & european(X))) & (~(tall(Y) & person(Y))) & richer(X, Y)))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ?[X: $i, Y: $i] : ((~(happy(X) & rich(X) & creative(X) & european(X))) & (~(tall(Y) & person(Y))) & richer(X, Y))))), inference(monotonicity,[status(thm)],[83])). tff(85,plain, ((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ?[X: $i, Y: $i] : ((~(happy(X) & rich(X) & creative(X) & european(X))) & (~(tall(Y) & person(Y))) & richer(X, Y)))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ?[X: $i, Y: $i] : ((~(happy(X) & rich(X) & creative(X) & european(X))) & (~(tall(Y) & person(Y))) & richer(X, Y))))), inference(rewrite,[status(thm)],[])). tff(86,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ?[X: $i, Y: $i] : ((~(happy(X) & rich(X) & creative(X) & european(X))) & (~(tall(Y) & person(Y))) & richer(X, Y)))), inference(or_elim,[status(thm)],[4])). tff(87,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ?[X: $i, Y: $i] : ((~(happy(X) & rich(X) & creative(X) & european(X))) & (~(tall(Y) & person(Y))) & richer(X, Y)))), inference(modus_ponens,[status(thm)],[86, 84])). tff(88,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ?[X: $i, Y: $i] : ((~(happy(X) & rich(X) & creative(X) & european(X))) & (~(tall(Y) & person(Y))) & richer(X, Y)))), inference(modus_ponens,[status(thm)],[87, 85])). tff(89,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ?[X: $i, Y: $i] : ((~(happy(X) & rich(X) & creative(X) & european(X))) & (~(tall(Y) & person(Y))) & richer(X, Y)))), inference(modus_ponens,[status(thm)],[88, 84])). 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 (and (happy X) (rich X) (creative X) (european X))) (not (and (tall Y) (person Y))) (richer X Y)))) (refl (~ (not a!1) (not a!1)))))) (a!7 (exists ((X $i) (Y $i)) (and (not (and (happy X) (rich X) (creative X) (european X))) (not (and (tall Y) (person Y))) (richer X Y)))) (a!8 (forall ((X $i) (Y $i)) (let ((a!1 (and (not (and (happy X) (rich X) (creative X) (european X))) (not (and (tall Y) (person Y))) (richer X Y)))) (not a!1))))) (let ((a!9 (~ (not (and (room mary) (room paul) (room fred) a!4 a!7)) (or (not (room mary)) (not (room paul)) (not (room fred)) a!5 a!8)))) (nnf-neg a!1 a!2 a!3 (sk (~ (not a!4) a!5)) (nnf-neg (proof-bind a!6) (~ (not a!7) a!8)) a!9)))	room(yolanda)&room(otis)&room(robert)&(![X]:(room(X)=>(X='yolanda'\|X='otis'\|X='robert')))& ((~(?[X,Y]:((does_not_collect_rare_minerals(X))&(sketches_as_a_hobby(Y))&(richer(X,Y))))=>((brave(otis))&(happy(robert))))& (~(rich(yolanda)&person(yolanda))&~(rich(robert)&person(robert)))& (![X]:(richer(robert,X)))& (?[X,Y]:((like(cary,X))&(~(rich(Y)&person(Y)))&(like(X,Y))))& (~((sketches_as_a_hobby(robert))\|(~rich(robert))))& ((?[X,Y]:(~room(X)&~room(Y)&(~hate(cary,X)&~hate(cary,Y))&(X!=Y)))))	room(yolanda)&room(otis)&room(robert)&(![X]:(room(X)=>(X='yolanda'\|X='otis'\|X='robert')))& (?[X,Y]:((~(happy(X)&rich(X)&creative(X)&european(X)))&(~(tall(Y)&person(Y)))&(richer(X,Y))))	neutral	neutral	neutral
Leslie does not enjoy bird watching and is not happy, not quiet, not creative, not brave.	Leslie neither is not creative, not quiet, not tall, not brave nor plays the violin.	neutral	% SZS status Satisfiable	room(leslie)&room(henry)&(![X]:(room(X)=>(X='leslie'\|X='henry')))& ((does_not_enjoy_bird_watching(leslie))&(~happy(leslie)&~quiet(leslie)&~creative(leslie)&~brave(leslie)))	room(leslie)&room(henry)&(![X]:(room(X)=>(X='leslie'\|X='henry')))& (~((~creative(leslie)&~quiet(leslie)&~tall(leslie)&~brave(leslie))\|(plays_the_violin(leslie))))	neutral	contradiction	contradiction
Elizebeth, Angela, Justin, Michele are the only persons in the room. "Someone who is not tall, not creative, not rich like someone who is not Elizebeth" only if "Elizebeth is the least tall in the room". "Michele does not play the violin" if "everyone outside the room who is a creative tourist collects vintage vinyl records" and vice versa. Justin who is not a rich person, is not a rich tall person. Justin is the least rich in the room. Someone who is not a creative person like someone who is not Justin. Justin is the tallest in the room. Elizebeth is liked by Linnea. Someone outside the room who plays the violin is a tall person.	Someone who is not a rich creative person is richer than someone who is not a rich creative tourist.	entailment	% SZS status Unsatisfiable % SZS output start Proof tff(tourist_type, type, ( tourist: $i > $o)). tff(fred_type, type, ( fred: $i)). tff(creative_type, type, ( creative: $i > $o)). tff(rich_type, type, ( rich: $i > $o)). tff(person_type, type, ( person: $i > $o)). tff(richer_type, type, ( richer: ( $i * $i ) > $o)). tff(predb_type, type, ( predb: $i > $o)). tff(tall_type, type, ( tall: $i > $o)). tff(room_type, type, ( room: $i > $o)). tff(like_type, type, ( like: ( $i * $i ) > $o)). tff(john_type, type, ( john: $i)). tff(mary_type, type, ( mary: $i)). tff(taller_type, type, ( taller: ( $i * $i ) > $o)). tff(predc_type, type, ( predc: $i > $o)). tff(alice_type, type, ( alice: $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(paul_type, type, ( paul: $i)). tff(tptp_fun_X_4_type, type, ( tptp_fun_X_4: $i)). tff(1,assumption,(~rich(fred)), introduced(assumption)). tff(2,plain, (((~rich(fred)) \| (~person(fred)) \| (~creative(fred))) \| rich(fred)), inference(tautology,[status(thm)],[])). tff(3,plain, ((~rich(fred)) \| (~person(fred)) \| (~creative(fred))), inference(unit_resolution,[status(thm)],[2, 1])). tff(4,plain, (((~rich(fred)) \| (~tourist(fred)) \| (~creative(fred))) \| rich(fred)), inference(tautology,[status(thm)],[])). tff(5,plain, ((~rich(fred)) \| (~tourist(fred)) \| (~creative(fred))), inference(unit_resolution,[status(thm)],[4, 1])). tff(6,plain, (^[X: $i] : refl(richer(fred, X) <=> richer(fred, X))), inference(bind,[status(th)],[])). tff(7,plain, (![X: $i] : richer(fred, X) <=> ![X: $i] : richer(fred, X)), inference(quant_intro,[status(thm)],[6])). tff(8,plain, (![X: $i] : richer(fred, X) <=> ![X: $i] : richer(fred, X)), inference(rewrite,[status(thm)],[])). tff(9,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] : (((((~tall(X)) & (~creative(X))) & (~rich(X))) & (~(Y = mary))) & like(X, Y)) => ![X: $i] : taller(mary, X)) & (![X: $i] : ((~room(X)) => ((creative(X) & tourist(X)) => predc(X))) <=> (~predb(alice)))) & ((~(rich(fred) & person(fred))) & (~((rich(fred) & tall(fred)) & person(fred))))) & ![X: $i] : richer(fred, X)) & ?[X: $i, Y: $i] : (((~(creative(X) & person(X))) & (~(Y = fred))) & like(X, Y))) & ![X: $i] : taller(X, fred)) & like(mary, john)) & ?[X: $i] : ((~room(X)) => (predb(X) => (tall(X) & person(X)))))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)) \| (X = \|'alice'\|)))) & ?[X: $i, Y: $i] : (((~((rich(X) & creative(X)) & person(X))) & (~((rich(Y) & creative(Y)) & tourist(Y)))) & richer(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] : ((~tall(X)) & (~creative(X)) & (~rich(X)) & (~(Y = mary)) & like(X, Y))) \| ![X: $i] : taller(mary, X)) & (~(predb(alice) <=> ![X: $i] : (room(X) \| predc(X) \| (~(creative(X) & tourist(X)))))) & (~(rich(fred) & person(fred))) & (~(rich(fred) & tall(fred) & person(fred))) & ![X: $i] : richer(fred, X) & ?[X: $i, Y: $i] : ((~(creative(X) & person(X))) & (~(Y = fred)) & like(X, Y)) & ![X: $i] : taller(X, fred) & like(mary, john) & ?[X: $i] : (room(X) \| (tall(X) & person(X)) \| (~predb(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] : ((~(rich(X) & creative(X) & person(X))) & (~(rich(Y) & creative(Y) & tourist(Y))) & richer(X, Y)))))), inference(rewrite,[status(thm)],[])). tff(10,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] : (((((~tall(X)) & (~creative(X))) & (~rich(X))) & (~(Y = mary))) & like(X, Y)) => ![X: $i] : taller(mary, X)) & (![X: $i] : ((~room(X)) => ((creative(X) & tourist(X)) => predc(X))) <=> (~predb(alice)))) & ((~(rich(fred) & person(fred))) & (~((rich(fred) & tall(fred)) & person(fred))))) & ![X: $i] : richer(fred, X)) & ?[X: $i, Y: $i] : (((~(creative(X) & person(X))) & (~(Y = fred))) & like(X, Y))) & ![X: $i] : taller(X, fred)) & like(mary, john)) & ?[X: $i] : ((~room(X)) => (predb(X) => (tall(X) & person(X)))))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)) \| (X = \|'alice'\|)))) & ?[X: $i, Y: $i] : (((~((rich(X) & creative(X)) & person(X))) & (~((rich(Y) & creative(Y)) & tourist(Y)))) & richer(X, Y))))), file('/mnt/tmpfs//8993286162577085995613303.p','negated')). tff(11,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] : ((~tall(X)) & (~creative(X)) & (~rich(X)) & (~(Y = mary)) & like(X, Y))) \| ![X: $i] : taller(mary, X)) & (~(predb(alice) <=> ![X: $i] : (room(X) \| predc(X) \| (~(creative(X) & tourist(X)))))) & (~(rich(fred) & person(fred))) & (~(rich(fred) & tall(fred) & person(fred))) & ![X: $i] : richer(fred, X) & ?[X: $i, Y: $i] : ((~(creative(X) & person(X))) & (~(Y = fred)) & like(X, Y)) & ![X: $i] : taller(X, fred) & like(mary, john) & ?[X: $i] : (room(X) \| (tall(X) & person(X)) \| (~predb(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] : ((~(rich(X) & creative(X) & person(X))) & (~(rich(Y) & creative(Y) & tourist(Y))) & richer(X, Y))))), inference(modus_ponens,[status(thm)],[10, 9])). tff(12,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] : ((~tall(X)) & (~creative(X)) & (~rich(X)) & (~(Y = mary)) & like(X, Y))) \| ![X: $i] : taller(mary, X)) & (~(predb(alice) <=> ![X: $i] : (room(X) \| predc(X) \| (~(creative(X) & tourist(X)))))) & (~(rich(fred) & person(fred))) & (~(rich(fred) & tall(fred) & person(fred))) & ![X: $i] : richer(fred, X) & ?[X: $i, Y: $i] : ((~(creative(X) & person(X))) & (~(Y = fred)) & like(X, Y)) & ![X: $i] : taller(X, fred) & like(mary, john) & ?[X: $i] : (room(X) \| (tall(X) & person(X)) \| (~predb(X)))), inference(or_elim,[status(thm)],[11])). tff(13,plain, (![X: $i] : richer(fred, X)), inference(and_elim,[status(thm)],[12])). tff(14,plain, (![X: $i] : richer(fred, X)), inference(modus_ponens,[status(thm)],[13, 8])). tff(15,plain,( ![X: $i] : richer(fred, X)), inference(skolemize,[status(sab)],[14])). tff(16,plain, (![X: $i] : richer(fred, X)), inference(modus_ponens,[status(thm)],[15, 7])). tff(17,plain, ((~![X: $i] : richer(fred, X)) \| richer(fred, fred)), inference(quant_inst,[status(thm)],[])). tff(18,plain, (richer(fred, fred)), inference(unit_resolution,[status(thm)],[17, 16])). tff(19,assumption,(~((X!4 = \|'alice'\|) \| (X!4 = \|'fred'\|) \| (X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|) \| (~room(X!4)))), introduced(assumption)). tff(20,plain, (((X!4 = \|'alice'\|) \| (X!4 = \|'fred'\|) \| (X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|) \| (~room(X!4))) \| room(X!4)), inference(tautology,[status(thm)],[])). tff(21,plain, (room(X!4)), inference(unit_resolution,[status(thm)],[20, 19])). tff(22,plain, (((X!4 = \|'alice'\|) \| (X!4 = \|'fred'\|) \| (X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|) \| (~room(X!4))) \| (~(X!4 = \|'mary'\|))), inference(tautology,[status(thm)],[])). tff(23,plain, (~(X!4 = \|'mary'\|)), inference(unit_resolution,[status(thm)],[22, 19])). tff(24,plain, (((X!4 = \|'alice'\|) \| (X!4 = \|'fred'\|) \| (X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|) \| (~room(X!4))) \| (~(X!4 = \|'paul'\|))), inference(tautology,[status(thm)],[])). tff(25,plain, (~(X!4 = \|'paul'\|)), inference(unit_resolution,[status(thm)],[24, 19])). tff(26,plain, (((X!4 = \|'alice'\|) \| (X!4 = \|'fred'\|) \| (X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|) \| (~room(X!4))) \| (~(X!4 = \|'fred'\|))), inference(tautology,[status(thm)],[])). tff(27,plain, (~(X!4 = \|'fred'\|)), inference(unit_resolution,[status(thm)],[26, 19])). tff(28,plain, (((X!4 = \|'alice'\|) \| (X!4 = \|'fred'\|) \| (X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|) \| (~room(X!4))) \| (~(X!4 = \|'alice'\|))), inference(tautology,[status(thm)],[])). tff(29,plain, (~(X!4 = \|'alice'\|)), inference(unit_resolution,[status(thm)],[28, 19])). tff(30,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(31,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)],[30])). 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(rewrite,[status(thm)],[])). tff(33,plain, (![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))), inference(and_elim,[status(thm)],[12])). tff(34,plain, (![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))), inference(modus_ponens,[status(thm)],[33, 32])). tff(35,plain,( ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))), inference(skolemize,[status(sab)],[34])). tff(36,plain, (![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))), inference(modus_ponens,[status(thm)],[35, 31])). 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)))) <=> ((~![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(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)))), inference(quant_inst,[status(thm)],[])). tff(39,plain, ((~![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| (X!4 = \|'alice'\|) \| (X!4 = \|'fred'\|) \| (X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|) \| (~room(X!4))), inference(modus_ponens,[status(thm)],[38, 37])). tff(40,plain, ($false), inference(unit_resolution,[status(thm)],[39, 36, 29, 27, 25, 23, 21])). tff(41,plain,((X!4 = \|'alice'\|) \| (X!4 = \|'fred'\|) \| (X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|) \| (~room(X!4))), inference(lemma,lemma(discharge,[]))). tff(42,plain, (room(alice) <=> room(alice)), inference(rewrite,[status(thm)],[])). tff(43,plain, (room(alice)), inference(and_elim,[status(thm)],[12])). 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)],[12])). 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)],[12])). tff(50,plain, (room(paul)), inference(modus_ponens,[status(thm)],[49, 48])). tff(51,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(52,plain, (room(mary)), inference(and_elim,[status(thm)],[12])). tff(53,plain, (room(mary)), inference(modus_ponens,[status(thm)],[52, 51])). tff(54,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] : ((~richer(X, Y)) \| (~((~rich(X)) \| (~creative(X)) \| (~person(X)))) \| (~((~tourist(Y)) \| (~creative(Y)) \| (~rich(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] : ((~richer(X, Y)) \| (~((~rich(X)) \| (~creative(X)) \| (~person(X)))) \| (~((~tourist(Y)) \| (~creative(Y)) \| (~rich(Y))))))), inference(rewrite,[status(thm)],[])). tff(55,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] : ((~richer(X, Y)) \| (~((~rich(X)) \| (~creative(X)) \| (~person(X)))) \| (~((~tourist(Y)) \| (~creative(Y)) \| (~rich(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] : ((~richer(X, Y)) \| (~((~rich(X)) \| (~creative(X)) \| (~person(X)))) \| (~((~tourist(Y)) \| (~creative(Y)) \| (~rich(Y))))))), inference(rewrite,[status(thm)],[])). tff(56,plain, (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((rich(X) & creative(X) & person(X)) <=> (~((~rich(X)) \| (~creative(X)) \| (~person(X))))), ((~(rich(X) & creative(X) & person(X))) <=> (~(~((~rich(X)) \| (~creative(X)) \| (~person(X))))))), rewrite((~(~((~rich(X)) \| (~creative(X)) \| (~person(X))))) <=> ((~rich(X)) \| (~creative(X)) \| (~person(X)))), ((~(rich(X) & creative(X) & person(X))) <=> ((~rich(X)) \| (~creative(X)) \| (~person(X))))), trans(monotonicity(rewrite((rich(Y) & creative(Y) & tourist(Y)) <=> (~((~tourist(Y)) \| (~creative(Y)) \| (~rich(Y))))), ((~(rich(Y) & creative(Y) & tourist(Y))) <=> (~(~((~tourist(Y)) \| (~creative(Y)) \| (~rich(Y))))))), rewrite((~(~((~tourist(Y)) \| (~creative(Y)) \| (~rich(Y))))) <=> ((~tourist(Y)) \| (~creative(Y)) \| (~rich(Y)))), ((~(rich(Y) & creative(Y) & tourist(Y))) <=> ((~tourist(Y)) \| (~creative(Y)) \| (~rich(Y))))), (((~(rich(X) & creative(X) & person(X))) & (~(rich(Y) & creative(Y) & tourist(Y))) & richer(X, Y)) <=> (((~rich(X)) \| (~creative(X)) \| (~person(X))) & ((~tourist(Y)) \| (~creative(Y)) \| (~rich(Y))) & richer(X, Y)))), rewrite((((~rich(X)) \| (~creative(X)) \| (~person(X))) & ((~tourist(Y)) \| (~creative(Y)) \| (~rich(Y))) & richer(X, Y)) <=> (~((~richer(X, Y)) \| (~((~rich(X)) \| (~creative(X)) \| (~person(X)))) \| (~((~tourist(Y)) \| (~creative(Y)) \| (~rich(Y))))))), (((~(rich(X) & creative(X) & person(X))) & (~(rich(Y) & creative(Y) & tourist(Y))) & richer(X, Y)) <=> (~((~richer(X, Y)) \| (~((~rich(X)) \| (~creative(X)) \| (~person(X)))) \| (~((~tourist(Y)) \| (~creative(Y)) \| (~rich(Y)))))))), ((~((~(rich(X) & creative(X) & person(X))) & (~(rich(Y) & creative(Y) & tourist(Y))) & richer(X, Y))) <=> (~(~((~richer(X, Y)) \| (~((~rich(X)) \| (~creative(X)) \| (~person(X)))) \| (~((~tourist(Y)) \| (~creative(Y)) \| (~rich(Y))))))))), rewrite((~(~((~richer(X, Y)) \| (~((~rich(X)) \| (~creative(X)) \| (~person(X)))) \| (~((~tourist(Y)) \| (~creative(Y)) \| (~rich(Y))))))) <=> ((~richer(X, Y)) \| (~((~rich(X)) \| (~creative(X)) \| (~person(X)))) \| (~((~tourist(Y)) \| (~creative(Y)) \| (~rich(Y)))))), ((~((~(rich(X) & creative(X) & person(X))) & (~(rich(Y) & creative(Y) & tourist(Y))) & richer(X, Y))) <=> ((~richer(X, Y)) \| (~((~rich(X)) \| (~creative(X)) \| (~person(X)))) \| (~((~tourist(Y)) \| (~creative(Y)) \| (~rich(Y)))))))), inference(bind,[status(th)],[])). tff(57,plain, (![X: $i, Y: $i] : (~((~(rich(X) & creative(X) & person(X))) & (~(rich(Y) & creative(Y) & tourist(Y))) & richer(X, Y))) <=> ![X: $i, Y: $i] : ((~richer(X, Y)) \| (~((~rich(X)) \| (~creative(X)) \| (~person(X)))) \| (~((~tourist(Y)) \| (~creative(Y)) \| (~rich(Y)))))), inference(quant_intro,[status(thm)],[56])). tff(58,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(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] : (~((~(rich(X) & creative(X) & person(X))) & (~(rich(Y) & creative(Y) & tourist(Y))) & richer(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] : ((~richer(X, Y)) \| (~((~rich(X)) \| (~creative(X)) \| (~person(X)))) \| (~((~tourist(Y)) \| (~creative(Y)) \| (~rich(Y))))))), inference(monotonicity,[status(thm)],[58, 57])). 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] : (~((~(rich(X) & creative(X) & person(X))) & (~(rich(Y) & creative(Y) & tourist(Y))) & richer(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] : ((~richer(X, Y)) \| (~((~rich(X)) \| (~creative(X)) \| (~person(X)))) \| (~((~tourist(Y)) \| (~creative(Y)) \| (~rich(Y))))))), inference(transitivity,[status(thm)],[59, 55])). 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] : (~((~(rich(X) & creative(X) & person(X))) & (~(rich(Y) & creative(Y) & tourist(Y))) & richer(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] : (~((~(rich(X) & creative(X) & person(X))) & (~(rich(Y) & creative(Y) & tourist(Y))) & richer(X, Y))))), inference(rewrite,[status(thm)],[])). tff(62,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] : (~((~(rich(X) & creative(X) & person(X))) & (~(rich(Y) & creative(Y) & tourist(Y))) & richer(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] : (~((~(rich(X) & creative(X) & person(X))) & (~(rich(Y) & creative(Y) & tourist(Y))) & richer(X, Y))))), inference(monotonicity,[status(thm)],[58])). tff(63,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] : (~((~(rich(X) & creative(X) & person(X))) & (~(rich(Y) & creative(Y) & tourist(Y))) & richer(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] : (~((~(rich(X) & creative(X) & person(X))) & (~(rich(Y) & creative(Y) & tourist(Y))) & richer(X, Y))))), inference(transitivity,[status(thm)],[62, 61])). 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] : ((~(rich(X) & creative(X) & person(X))) & (~(rich(Y) & creative(Y) & tourist(Y))) & richer(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] : ((~(rich(X) & creative(X) & person(X))) & (~(rich(Y) & creative(Y) & tourist(Y))) & richer(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] : ((~(rich(X) & creative(X) & person(X))) & (~(rich(Y) & creative(Y) & tourist(Y))) & richer(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] : ((~(rich(X) & creative(X) & person(X))) & (~(rich(Y) & creative(Y) & tourist(Y))) & richer(X, Y))))), inference(monotonicity,[status(thm)],[64])). 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] : ((~(rich(X) & creative(X) & person(X))) & (~(rich(Y) & creative(Y) & tourist(Y))) & richer(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] : ((~(rich(X) & creative(X) & person(X))) & (~(rich(Y) & creative(Y) & tourist(Y))) & richer(X, Y))))), 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))) & ?[X: $i, Y: $i] : ((~(rich(X) & creative(X) & person(X))) & (~(rich(Y) & creative(Y) & tourist(Y))) & richer(X, Y)))), inference(or_elim,[status(thm)],[11])). 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] : ((~(rich(X) & creative(X) & person(X))) & (~(rich(Y) & creative(Y) & tourist(Y))) & richer(X, Y)))), inference(modus_ponens,[status(thm)],[67, 65])). tff(69,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] : ((~(rich(X) & creative(X) & person(X))) & (~(rich(Y) & creative(Y) & tourist(Y))) & richer(X, Y)))), inference(modus_ponens,[status(thm)],[68, 66])). tff(70,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] : ((~(rich(X) & creative(X) & person(X))) & (~(rich(Y) & creative(Y) & tourist(Y))) & richer(X, Y)))), inference(modus_ponens,[status(thm)],[69, 65])). 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 (not (and (rich X) (creative X) (person X))) (not (and (rich Y) (creative Y) (tourist Y))) (richer X Y)))) (refl (~ (not a!1) (not a!1)))))) (a!8 (exists ((X $i) (Y $i)) (and (not (and (rich X) (creative X) (person X))) (not (and (rich Y) (creative Y) (tourist Y))) (richer X Y)))) (a!9 (forall ((X $i) (Y $i)) (let ((a!1 (and (not (and (rich X) (creative X) (person X))) (not (and (rich Y) (creative Y) (tourist Y))) (richer 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(elizebeth)&room(angela)&room(justin)&room(michele)&(![X]:(room(X)=>(X='elizebeth'\|X='angela'\|X='justin'\|X='michele')))& (((?[X,Y]:((~tall(X)&~creative(X)&~rich(X))&(Y!=elizebeth)&(like(X,Y))))=>(![X]:(taller(elizebeth,X))))& ((![X]:(~room(X)=>(((creative(X)&tourist(X))=>(collects_vintage_vinyl_records(X))))))<=>(does_not_play_the_violin(michele)))& ((~(rich(justin)&person(justin)))&(~(rich(justin)&tall(justin)&person(justin))))& (![X]:(richer(justin,X)))& (?[X,Y]:((~(creative(X)&person(X)))&(Y!=justin)&(like(X,Y))))& (![X]:(taller(X,justin)))& (like(elizebeth,linnea))& (?[X]:(~room(X)=>(((plays_the_violin(X))=>(tall(X)&person(X)))))))	room(elizebeth)&room(angela)&room(justin)&room(michele)&(![X]:(room(X)=>(X='elizebeth'\|X='angela'\|X='justin'\|X='michele')))& (?[X,Y]:((~(rich(X)&creative(X)&person(X)))&(~(rich(Y)&creative(Y)&tourist(Y)))&(richer(X,Y))))	neutral	neutral	neutral
Claudia likes Ashley or can play the piano or both.	Claudia likes Ashley or is liked by Ashley or both.	neutral	% SZS status Satisfiable	room(lora)&room(reba)&room(claudia)&(![X]:(room(X)=>(X='lora'\|X='reba'\|X='claudia')))& (((like(ashley,claudia))\|(can_play_the_piano(claudia))))	room(lora)&room(reba)&room(claudia)&(![X]:(room(X)=>(X='lora'\|X='reba'\|X='claudia')))& (((like(ashley,claudia))\|(like(claudia,ashley))))	neutral	entailment	entailment
Forrest, Ronnie, Kathleen, Jessie are the only persons in the room. At most one of the following is true:. -Only one person outside the room is not Jessie. -Someone outside the room does not have a tattoo.	It is not the case that 'Forrest who has a tattoo, is not Ronnie'.	neutral	% SZS status Satisfiable	room(forrest)&room(ronnie)&room(kathleen)&room(jessie)&(![X]:(room(X)=>(X='forrest'\|X='ronnie'\|X='kathleen'\|X='jessie')))& (~(((?[X]:(~room(X)&X!=jessie))&(![X,Y]:((X!=jessie&Y!=jessie)=>(X=Y))))&?[X]:(~room(X)=>(does_not_have_a_tattoo(X)))))	room(forrest)&room(ronnie)&room(kathleen)&room(jessie)&(![X]:(room(X)=>(X='forrest'\|X='ronnie'\|X='kathleen'\|X='jessie')))& (~((has_a_tattoo(forrest))&(forrest!=ronnie)))	entailment	entailment	entailment
Stephanie, Bonita are the only persons in the room. If Stephanie neither is a rich european nor does not drive a hybrid car then only one person outside the room does not hate Richard otherwise only one person outside the room is not hated by Esther. More than one person in the room is hated by Esther unless Stephanie is not hated by Richard or is a rich quiet european or both. Only one person in the room is hated by Richard. Stephanie hates Richard. Someone who is not hated by Cora is quieter than someone who does not own a smart tv. Richard is richer than Stephanie. Esther is a sibling of Stephanie.	Stephanie is not liked by Richard or is not a happy quiet creative rich person or both.	neutral	% SZS status Satisfiable	room(stephanie)&room(bonita)&(![X]:(room(X)=>(X='stephanie'\|X='bonita')))& ((((~((rich(stephanie)&european(stephanie))\|(does_not_drive_a_hybrid_car(stephanie))))=>(((?[X]:(~room(X)&~hate(richard,X)))&(![X,Y]:((~hate(richard,X)&~hate(richard,Y))=>(X=Y))))))\|((~(~((rich(stephanie)&european(stephanie))\|(does_not_drive_a_hybrid_car(stephanie)))))=>(((?[X]:(~room(X)&~hate(X,esther)))&(![X,Y]:((~hate(X,esther)&~hate(Y,esther))=>(X=Y)))))))& (~(((~hate(stephanie,richard))\|(rich(stephanie)&quiet(stephanie)&european(stephanie))))=>((?[X,Y]:(room(X)&room(Y)&(hate(X,esther)&hate(Y,esther))&(X!=Y)))))& (((?[X]:(room(X)&hate(X,richard)))&(![X,Y]:((hate(X,richard)&hate(Y,richard))=>(X=Y)))))& (hate(richard,stephanie))& (?[X,Y]:((~hate(X,cora))&(does_not_own_a_smart_tv(Y))&(quieter(X,Y))))& (richer(stephanie,richard))& (sibling(stephanie,esther)))	room(stephanie)&room(bonita)&(![X]:(room(X)=>(X='stephanie'\|X='bonita')))& (((~like(stephanie,richard))\|(~(happy(stephanie)&quiet(stephanie)&creative(stephanie)&rich(stephanie)&person(stephanie)))))	neutral	entailment	entailment
Stephen is the only person in the room. "Stephen is the richest in the room" unless "Stephen is the tallest in the room". Stephen is not liked by Peggy and is not creative, not rich, not tall. Stephen who is not creative, not tall, not rich, is not creative, not tall. Stephen neither is not liked by Lydia nor is a sibling of Peggy. Stephen is the tallest in the room. Stephen is the richest in the room.	Someone who is a rich creative tourist like someone who is not liked by Lydia.	contradiction	-	room(stephen)&(![X]:(room(X)=>(X='stephen')))& ((~(![X]:(taller(X,stephen)))=>(![X]:(richer(X,stephen))))& ((~like(stephen,peggy))&(~creative(stephen)&~rich(stephen)&~tall(stephen)))& ((~creative(stephen)&~tall(stephen)&~rich(stephen))&(~creative(stephen)&~tall(stephen)))& (~((~like(stephen,lydia))\|(sibling(peggy,stephen))))& (![X]:(taller(X,stephen)))& (![X]:(richer(X,stephen))))	room(stephen)&(![X]:(room(X)=>(X='stephen')))& (?[X,Y]:((rich(X)&creative(X)&tourist(X))&(~like(Y,lydia))&(like(X,Y))))	contradiction	neutral	contradiction
Jennifer, Robert, Carla are the only persons in the room. Carla is a quiet tall brave person and is not Robert. Everyone outside the room is not a tall quiet tourist. Only one person outside the room is not a quiet person. Carla is the least tall in the room. Someone who is a brave tourist is taller than someone who hates Clinton.	Robert is a tall quiet person or is a creative quiet person or both.	entailment	% SZS status Unsatisfiable % SZS output start Proof tff(quiet_type, type, ( quiet: $i > $o)). tff(paul_type, type, ( paul: $i)). tff(person_type, type, ( person: $i > $o)). tff(tptp_fun_X_0_type, type, ( tptp_fun_X_0: $i)). tff(room_type, type, ( room: $i > $o)). tff(taller_type, type, ( taller: ( $i * $i ) > $o)). tff(hate_type, type, ( hate: ( $i * $i ) > $o)). tff(lucy_type, type, ( lucy: $i)). tff(tourist_type, type, ( tourist: $i > $o)). tff(brave_type, type, ( brave: $i > $o)). tff(fred_type, type, ( fred: $i)). tff(tall_type, type, ( tall: $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(mary_type, type, ( mary: $i)). tff(creative_type, type, ( creative: $i > $o)). tff(susan_type, type, ( susan: $i)). tff(john_type, type, ( john: $i)). tff(alice_type, type, ( alice: $i)). tff(tptp_fun_X_3_type, type, ( tptp_fun_X_3: $i)). tff(1,assumption,(X!0 = paul), introduced(assumption)). tff(2,plain, (room(X!0) <=> room(paul)), inference(monotonicity,[status(thm)],[1])). tff(3,plain, (room(paul) <=> room(X!0)), inference(symmetry,[status(thm)],[2])). tff(4,plain, (room(paul) <=> room(paul)), inference(rewrite,[status(thm)],[])). tff(5,plain, ((~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)))) & ((((((((quiet(fred) & tall(fred)) & brave(fred)) & person(fred)) & (~(fred = paul))) & ![X: $i] : ((~room(X)) => (~((tall(X) & quiet(X)) & tourist(X))))) & (?[X: $i] : ((~room(X)) & (~(quiet(X) & person(X)))) & ![X: $i, Y: $i] : (((~(quiet(X) & person(X))) & (~(quiet(Y) & person(Y)))) => (X = Y)))) & ![X: $i] : taller(fred, X)) & ?[X: $i, Y: $i] : (((brave(X) & tourist(X)) & hate(lucy, Y)) & taller(X, Y)))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)))) & (((tall(paul) & quiet(paul)) & person(paul)) \| ((creative(paul) & quiet(paul)) & person(paul)))))) <=> (~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & quiet(fred) & tall(fred) & brave(fred) & person(fred) & (~(fred = paul)) & ![X: $i] : (room(X) \| (~(tall(X) & quiet(X) & tourist(X)))) & ?[X: $i] : ((~room(X)) & (~(quiet(X) & person(X)))) & ![X: $i, Y: $i] : ((~((~(quiet(X) & person(X))) & (~(quiet(Y) & person(Y))))) \| (X = Y)) & ![X: $i] : taller(fred, X) & ?[X: $i, Y: $i] : (brave(X) & tourist(X) & hate(lucy, Y) & taller(X, Y)))) \| (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((tall(paul) & quiet(paul) & person(paul)) \| (creative(paul) & quiet(paul) & person(paul))))))), inference(rewrite,[status(thm)],[])). tff(6,axiom,(~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)))) & ((((((((quiet(fred) & tall(fred)) & brave(fred)) & person(fred)) & (~(fred = paul))) & ![X: $i] : ((~room(X)) => (~((tall(X) & quiet(X)) & tourist(X))))) & (?[X: $i] : ((~room(X)) & (~(quiet(X) & person(X)))) & ![X: $i, Y: $i] : (((~(quiet(X) & person(X))) & (~(quiet(Y) & person(Y)))) => (X = Y)))) & ![X: $i] : taller(fred, X)) & ?[X: $i, Y: $i] : (((brave(X) & tourist(X)) & hate(lucy, Y)) & taller(X, Y)))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)))) & (((tall(paul) & quiet(paul)) & person(paul)) \| ((creative(paul) & quiet(paul)) & person(paul)))))), file('/mnt/tmpfs//6910178833852785322319524.p','negated')). tff(7,plain, (~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & quiet(fred) & tall(fred) & brave(fred) & person(fred) & (~(fred = paul)) & ![X: $i] : (room(X) \| (~(tall(X) & quiet(X) & tourist(X)))) & ?[X: $i] : ((~room(X)) & (~(quiet(X) & person(X)))) & ![X: $i, Y: $i] : ((~((~(quiet(X) & person(X))) & (~(quiet(Y) & person(Y))))) \| (X = Y)) & ![X: $i] : taller(fred, X) & ?[X: $i, Y: $i] : (brave(X) & tourist(X) & hate(lucy, Y) & taller(X, Y)))) \| (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((tall(paul) & quiet(paul) & person(paul)) \| (creative(paul) & quiet(paul) & person(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))) & quiet(fred) & tall(fred) & brave(fred) & person(fred) & (~(fred = paul)) & ![X: $i] : (room(X) \| (~(tall(X) & quiet(X) & tourist(X)))) & ?[X: $i] : ((~room(X)) & (~(quiet(X) & person(X)))) & ![X: $i, Y: $i] : ((~((~(quiet(X) & person(X))) & (~(quiet(Y) & person(Y))))) \| (X = Y)) & ![X: $i] : taller(fred, X) & ?[X: $i, Y: $i] : (brave(X) & tourist(X) & hate(lucy, Y) & taller(X, Y))), inference(or_elim,[status(thm)],[7])). tff(9,plain, (room(paul)), inference(and_elim,[status(thm)],[8])). tff(10,plain, (room(paul)), 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)) & (~(quiet(X) & person(X)))) <=> ?[X: $i] : ((~room(X)) & (~(quiet(X) & person(X))))), inference(rewrite,[status(thm)],[])). tff(13,plain, (?[X: $i] : ((~room(X)) & (~(quiet(X) & person(X))))), inference(and_elim,[status(thm)],[8])). tff(14,plain, (?[X: $i] : ((~room(X)) & (~(quiet(X) & person(X))))), inference(modus_ponens,[status(thm)],[13, 12])). tff(15,plain,( (~room(X!0)) & (~(quiet(X!0) & person(X!0)))), inference(skolemize,[status(sab)],[14])). tff(16,plain, (~room(X!0)), inference(and_elim,[status(thm)],[15])). tff(17,plain, ($false), inference(unit_resolution,[status(thm)],[16, 11])). tff(18,plain,(~(X!0 = paul)), inference(lemma,lemma(discharge,[]))). tff(19,assumption,(~((~quiet(X!0)) \| (~person(X!0)))), introduced(assumption)). tff(20,plain, (((~quiet(X!0)) \| (~person(X!0))) \| quiet(X!0)), inference(tautology,[status(thm)],[])). tff(21,plain, (quiet(X!0)), inference(unit_resolution,[status(thm)],[20, 19])). tff(22,plain, (((~quiet(X!0)) \| (~person(X!0))) \| person(X!0)), inference(tautology,[status(thm)],[])). tff(23,plain, (person(X!0)), inference(unit_resolution,[status(thm)],[22, 19])). tff(24,plain, ((~(~((~quiet(X!0)) \| (~person(X!0))))) <=> ((~quiet(X!0)) \| (~person(X!0)))), inference(rewrite,[status(thm)],[])). tff(25,plain, ((quiet(X!0) & person(X!0)) <=> (~((~quiet(X!0)) \| (~person(X!0))))), inference(rewrite,[status(thm)],[])). tff(26,plain, ((~(quiet(X!0) & person(X!0))) <=> (~(~((~quiet(X!0)) \| (~person(X!0)))))), inference(monotonicity,[status(thm)],[25])). tff(27,plain, ((~(quiet(X!0) & person(X!0))) <=> ((~quiet(X!0)) \| (~person(X!0)))), inference(transitivity,[status(thm)],[26, 24])). tff(28,plain, (~(quiet(X!0) & person(X!0))), inference(and_elim,[status(thm)],[15])). tff(29,plain, ((~quiet(X!0)) \| (~person(X!0))), inference(modus_ponens,[status(thm)],[28, 27])). tff(30,plain, ($false), inference(unit_resolution,[status(thm)],[29, 23, 21])). tff(31,plain,((~quiet(X!0)) \| (~person(X!0))), inference(lemma,lemma(discharge,[]))). tff(32,plain, (^[X: $i, Y: $i] : refl(((X = Y) \| (~((~quiet(X)) \| (~person(X)))) \| (~((~quiet(Y)) \| (~person(Y))))) <=> ((X = Y) \| (~((~quiet(X)) \| (~person(X)))) \| (~((~quiet(Y)) \| (~person(Y))))))), inference(bind,[status(th)],[])). tff(33,plain, (![X: $i, Y: $i] : ((X = Y) \| (~((~quiet(X)) \| (~person(X)))) \| (~((~quiet(Y)) \| (~person(Y))))) <=> ![X: $i, Y: $i] : ((X = Y) \| (~((~quiet(X)) \| (~person(X)))) \| (~((~quiet(Y)) \| (~person(Y)))))), inference(quant_intro,[status(thm)],[32])). tff(34,plain, (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((quiet(X) & person(X)) <=> (~((~quiet(X)) \| (~person(X))))), ((~(quiet(X) & person(X))) <=> (~(~((~quiet(X)) \| (~person(X))))))), rewrite((~(~((~quiet(X)) \| (~person(X))))) <=> ((~quiet(X)) \| (~person(X)))), ((~(quiet(X) & person(X))) <=> ((~quiet(X)) \| (~person(X))))), trans(monotonicity(rewrite((quiet(Y) & person(Y)) <=> (~((~quiet(Y)) \| (~person(Y))))), ((~(quiet(Y) & person(Y))) <=> (~(~((~quiet(Y)) \| (~person(Y))))))), rewrite((~(~((~quiet(Y)) \| (~person(Y))))) <=> ((~quiet(Y)) \| (~person(Y)))), ((~(quiet(Y) & person(Y))) <=> ((~quiet(Y)) \| (~person(Y))))), (((~(quiet(X) & person(X))) & (~(quiet(Y) & person(Y)))) <=> (((~quiet(X)) \| (~person(X))) & ((~quiet(Y)) \| (~person(Y)))))), rewrite((((~quiet(X)) \| (~person(X))) & ((~quiet(Y)) \| (~person(Y)))) <=> (~((~((~quiet(X)) \| (~person(X)))) \| (~((~quiet(Y)) \| (~person(Y))))))), (((~(quiet(X) & person(X))) & (~(quiet(Y) & person(Y)))) <=> (~((~((~quiet(X)) \| (~person(X)))) \| (~((~quiet(Y)) \| (~person(Y)))))))), ((~((~(quiet(X) & person(X))) & (~(quiet(Y) & person(Y))))) <=> (~(~((~((~quiet(X)) \| (~person(X)))) \| (~((~quiet(Y)) \| (~person(Y))))))))), rewrite((~(~((~((~quiet(X)) \| (~person(X)))) \| (~((~quiet(Y)) \| (~person(Y))))))) <=> ((~((~quiet(X)) \| (~person(X)))) \| (~((~quiet(Y)) \| (~person(Y)))))), ((~((~(quiet(X) & person(X))) & (~(quiet(Y) & person(Y))))) <=> ((~((~quiet(X)) \| (~person(X)))) \| (~((~quiet(Y)) \| (~person(Y))))))), (((~((~(quiet(X) & person(X))) & (~(quiet(Y) & person(Y))))) \| (X = Y)) <=> (((~((~quiet(X)) \| (~person(X)))) \| (~((~quiet(Y)) \| (~person(Y))))) \| (X = Y)))), rewrite((((~((~quiet(X)) \| (~person(X)))) \| (~((~quiet(Y)) \| (~person(Y))))) \| (X = Y)) <=> ((X = Y) \| (~((~quiet(X)) \| (~person(X)))) \| (~((~quiet(Y)) \| (~person(Y)))))), (((~((~(quiet(X) & person(X))) & (~(quiet(Y) & person(Y))))) \| (X = Y)) <=> ((X = Y) \| (~((~quiet(X)) \| (~person(X)))) \| (~((~quiet(Y)) \| (~person(Y)))))))), inference(bind,[status(th)],[])). tff(35,plain, (![X: $i, Y: $i] : ((~((~(quiet(X) & person(X))) & (~(quiet(Y) & person(Y))))) \| (X = Y)) <=> ![X: $i, Y: $i] : ((X = Y) \| (~((~quiet(X)) \| (~person(X)))) \| (~((~quiet(Y)) \| (~person(Y)))))), inference(quant_intro,[status(thm)],[34])). tff(36,plain, (![X: $i, Y: $i] : ((~((~(quiet(X) & person(X))) & (~(quiet(Y) & person(Y))))) \| (X = Y)) <=> ![X: $i, Y: $i] : ((~((~(quiet(X) & person(X))) & (~(quiet(Y) & person(Y))))) \| (X = Y))), inference(rewrite,[status(thm)],[])). tff(37,plain, (![X: $i, Y: $i] : ((~((~(quiet(X) & person(X))) & (~(quiet(Y) & person(Y))))) \| (X = Y))), inference(and_elim,[status(thm)],[8])). tff(38,plain, (![X: $i, Y: $i] : ((~((~(quiet(X) & person(X))) & (~(quiet(Y) & person(Y))))) \| (X = Y))), inference(modus_ponens,[status(thm)],[37, 36])). tff(39,plain,( ![X: $i, Y: $i] : ((~((~(quiet(X) & person(X))) & (~(quiet(Y) & person(Y))))) \| (X = Y))), inference(skolemize,[status(sab)],[38])). tff(40,plain, (![X: $i, Y: $i] : ((X = Y) \| (~((~quiet(X)) \| (~person(X)))) \| (~((~quiet(Y)) \| (~person(Y)))))), inference(modus_ponens,[status(thm)],[39, 35])). tff(41,plain, (![X: $i, Y: $i] : ((X = Y) \| (~((~quiet(X)) \| (~person(X)))) \| (~((~quiet(Y)) \| (~person(Y)))))), inference(modus_ponens,[status(thm)],[40, 33])). tff(42,plain, (((~![X: $i, Y: $i] : ((X = Y) \| (~((~quiet(X)) \| (~person(X)))) \| (~((~quiet(Y)) \| (~person(Y)))))) \| ((~((~quiet(X!0)) \| (~person(X!0)))) \| (X!0 = paul) \| (~((~quiet(paul)) \| (~person(paul)))))) <=> ((~![X: $i, Y: $i] : ((X = Y) \| (~((~quiet(X)) \| (~person(X)))) \| (~((~quiet(Y)) \| (~person(Y)))))) \| (~((~quiet(X!0)) \| (~person(X!0)))) \| (X!0 = paul) \| (~((~quiet(paul)) \| (~person(paul)))))), inference(rewrite,[status(thm)],[])). tff(43,plain, (((X!0 = paul) \| (~((~quiet(X!0)) \| (~person(X!0)))) \| (~((~quiet(paul)) \| (~person(paul))))) <=> ((~((~quiet(X!0)) \| (~person(X!0)))) \| (X!0 = paul) \| (~((~quiet(paul)) \| (~person(paul)))))), inference(rewrite,[status(thm)],[])). tff(44,plain, ((~((~quiet(paul)) \| (~person(paul)))) <=> (~((~quiet(paul)) \| (~person(paul))))), inference(rewrite,[status(thm)],[])). tff(45,plain, ((~((~quiet(X!0)) \| (~person(X!0)))) <=> (~((~quiet(X!0)) \| (~person(X!0))))), inference(rewrite,[status(thm)],[])). tff(46,plain, (((X!0 = paul) \| (~((~quiet(X!0)) \| (~person(X!0)))) \| (~((~quiet(paul)) \| (~person(paul))))) <=> ((X!0 = paul) \| (~((~quiet(X!0)) \| (~person(X!0)))) \| (~((~quiet(paul)) \| (~person(paul)))))), inference(monotonicity,[status(thm)],[45, 44])). tff(47,plain, (((X!0 = paul) \| (~((~quiet(X!0)) \| (~person(X!0)))) \| (~((~quiet(paul)) \| (~person(paul))))) <=> ((~((~quiet(X!0)) \| (~person(X!0)))) \| (X!0 = paul) \| (~((~quiet(paul)) \| (~person(paul)))))), inference(transitivity,[status(thm)],[46, 43])). tff(48,plain, (((~![X: $i, Y: $i] : ((X = Y) \| (~((~quiet(X)) \| (~person(X)))) \| (~((~quiet(Y)) \| (~person(Y)))))) \| ((X!0 = paul) \| (~((~quiet(X!0)) \| (~person(X!0)))) \| (~((~quiet(paul)) \| (~person(paul)))))) <=> ((~![X: $i, Y: $i] : ((X = Y) \| (~((~quiet(X)) \| (~person(X)))) \| (~((~quiet(Y)) \| (~person(Y)))))) \| ((~((~quiet(X!0)) \| (~person(X!0)))) \| (X!0 = paul) \| (~((~quiet(paul)) \| (~person(paul))))))), inference(monotonicity,[status(thm)],[47])). tff(49,plain, (((~![X: $i, Y: $i] : ((X = Y) \| (~((~quiet(X)) \| (~person(X)))) \| (~((~quiet(Y)) \| (~person(Y)))))) \| ((X!0 = paul) \| (~((~quiet(X!0)) \| (~person(X!0)))) \| (~((~quiet(paul)) \| (~person(paul)))))) <=> ((~![X: $i, Y: $i] : ((X = Y) \| (~((~quiet(X)) \| (~person(X)))) \| (~((~quiet(Y)) \| (~person(Y)))))) \| (~((~quiet(X!0)) \| (~person(X!0)))) \| (X!0 = paul) \| (~((~quiet(paul)) \| (~person(paul)))))), inference(transitivity,[status(thm)],[48, 42])). tff(50,plain, ((~![X: $i, Y: $i] : ((X = Y) \| (~((~quiet(X)) \| (~person(X)))) \| (~((~quiet(Y)) \| (~person(Y)))))) \| ((X!0 = paul) \| (~((~quiet(X!0)) \| (~person(X!0)))) \| (~((~quiet(paul)) \| (~person(paul)))))), inference(quant_inst,[status(thm)],[])). tff(51,plain, ((~![X: $i, Y: $i] : ((X = Y) \| (~((~quiet(X)) \| (~person(X)))) \| (~((~quiet(Y)) \| (~person(Y)))))) \| (~((~quiet(X!0)) \| (~person(X!0)))) \| (X!0 = paul) \| (~((~quiet(paul)) \| (~person(paul))))), inference(modus_ponens,[status(thm)],[50, 49])). tff(52,plain, ((~((~quiet(X!0)) \| (~person(X!0)))) \| (X!0 = paul) \| (~((~quiet(paul)) \| (~person(paul))))), inference(unit_resolution,[status(thm)],[51, 41])). tff(53,plain, (~((~quiet(paul)) \| (~person(paul)))), inference(unit_resolution,[status(thm)],[52, 31, 18])). tff(54,plain, (((~quiet(paul)) \| (~person(paul))) \| quiet(paul)), inference(tautology,[status(thm)],[])). tff(55,plain, (quiet(paul)), inference(unit_resolution,[status(thm)],[54, 53])). tff(56,plain, (((~quiet(paul)) \| (~person(paul))) \| person(paul)), inference(tautology,[status(thm)],[])). tff(57,plain, (person(paul)), inference(unit_resolution,[status(thm)],[56, 53])). tff(58,plain, (^[X: $i] : refl(taller(fred, X) <=> taller(fred, X))), inference(bind,[status(th)],[])). tff(59,plain, (![X: $i] : taller(fred, X) <=> ![X: $i] : taller(fred, X)), inference(quant_intro,[status(thm)],[58])). tff(60,plain, (![X: $i] : taller(fred, X) <=> ![X: $i] : taller(fred, X)), inference(rewrite,[status(thm)],[])). tff(61,plain, (![X: $i] : taller(fred, X)), inference(and_elim,[status(thm)],[8])). tff(62,plain, (![X: $i] : taller(fred, X)), inference(modus_ponens,[status(thm)],[61, 60])). tff(63,plain,( ![X: $i] : taller(fred, X)), inference(skolemize,[status(sab)],[62])). tff(64,plain, (![X: $i] : taller(fred, X)), inference(modus_ponens,[status(thm)],[63, 59])). tff(65,plain, ((~![X: $i] : taller(fred, X)) \| taller(fred, paul)), inference(quant_inst,[status(thm)],[])). tff(66,plain, (taller(fred, paul)), inference(unit_resolution,[status(thm)],[65, 64])). tff(67,plain, (tall(fred) <=> tall(fred)), inference(rewrite,[status(thm)],[])). tff(68,plain, (tall(fred)), inference(and_elim,[status(thm)],[8])). tff(69,plain, (tall(fred)), inference(modus_ponens,[status(thm)],[68, 67])). tff(70,plain, ((~(fred = paul)) <=> (~(fred = paul))), inference(rewrite,[status(thm)],[])). tff(71,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//6910178833852785322319524.p','b14')). tff(72,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)],[71])). tff(73,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)],[72])). tff(74,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)],[73])). tff(75,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)],[74])). tff(76,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)],[75])). tff(77,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)],[76])). tff(78,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)],[77])). tff(79,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)],[78])). tff(80,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)],[79])). tff(81,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)],[80])). tff(82,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)],[81])). tff(83,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)],[82])). tff(84,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)],[83])). tff(85,plain, ((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = 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(~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))), inference(and_elim,[status(thm)],[85])). tff(87,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)],[86])). tff(88,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)],[87])). tff(89,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)],[88])). tff(90,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)],[89])). tff(91,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)],[90])). tff(92,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)],[91])). tff(93,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)],[92])). tff(94,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)],[93])). tff(95,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)],[94])). tff(96,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)],[95])). tff(97,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)],[96])). tff(98,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)],[97])). tff(99,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)],[98])). tff(100,plain, (~(fred = paul)), inference(and_elim,[status(thm)],[99])). tff(101,plain, (~(fred = paul)), inference(modus_ponens,[status(thm)],[100, 70])). tff(102,plain, (^[X: $i, Y: $i] : refl(((X = Y) \| tall(Y) \| (~taller(X, Y)) \| (~tall(X))) <=> ((X = Y) \| tall(Y) \| (~taller(X, Y)) \| (~tall(X))))), inference(bind,[status(th)],[])). tff(103,plain, (![X: $i, Y: $i] : ((X = Y) \| tall(Y) \| (~taller(X, Y)) \| (~tall(X))) <=> ![X: $i, Y: $i] : ((X = Y) \| tall(Y) \| (~taller(X, Y)) \| (~tall(X)))), inference(quant_intro,[status(thm)],[102])). tff(104,plain, (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((taller(X, Y) & tall(X)) <=> (~((~taller(X, Y)) \| (~tall(X))))), ((~(taller(X, Y) & tall(X))) <=> (~(~((~taller(X, Y)) \| (~tall(X))))))), rewrite((~(~((~taller(X, Y)) \| (~tall(X))))) <=> ((~taller(X, Y)) \| (~tall(X)))), ((~(taller(X, Y) & tall(X))) <=> ((~taller(X, Y)) \| (~tall(X))))), (((X = Y) \| tall(Y) \| (~(taller(X, Y) & tall(X)))) <=> ((X = Y) \| tall(Y) \| ((~taller(X, Y)) \| (~tall(X)))))), rewrite(((X = Y) \| tall(Y) \| ((~taller(X, Y)) \| (~tall(X)))) <=> ((X = Y) \| tall(Y) \| (~taller(X, Y)) \| (~tall(X)))), (((X = Y) \| tall(Y) \| (~(taller(X, Y) & tall(X)))) <=> ((X = Y) \| tall(Y) \| (~taller(X, Y)) \| (~tall(X)))))), inference(bind,[status(th)],[])). tff(105,plain, (![X: $i, Y: $i] : ((X = Y) \| tall(Y) \| (~(taller(X, Y) & tall(X)))) <=> ![X: $i, Y: $i] : ((X = Y) \| tall(Y) \| (~taller(X, Y)) \| (~tall(X)))), inference(quant_intro,[status(thm)],[104])). tff(106,plain, (![X: $i, Y: $i] : ((X = Y) \| tall(Y) \| (~(taller(X, Y) & tall(X)))) <=> ![X: $i, Y: $i] : ((X = Y) \| tall(Y) \| (~(taller(X, Y) & tall(X))))), inference(rewrite,[status(thm)],[])). tff(107,plain, (^[X: $i, Y: $i] : trans(monotonicity(rewrite(((taller(X, Y) & tall(X)) => tall(Y)) <=> (tall(Y) \| (~(taller(X, Y) & tall(X))))), (((~(X = Y)) => ((taller(X, Y) & tall(X)) => tall(Y))) <=> ((~(X = Y)) => (tall(Y) \| (~(taller(X, Y) & tall(X))))))), rewrite(((~(X = Y)) => (tall(Y) \| (~(taller(X, Y) & tall(X))))) <=> ((X = Y) \| tall(Y) \| (~(taller(X, Y) & tall(X))))), (((~(X = Y)) => ((taller(X, Y) & tall(X)) => tall(Y))) <=> ((X = Y) \| tall(Y) \| (~(taller(X, Y) & tall(X))))))), inference(bind,[status(th)],[])). tff(108,plain, (![X: $i, Y: $i] : ((~(X = Y)) => ((taller(X, Y) & tall(X)) => tall(Y))) <=> ![X: $i, Y: $i] : ((X = Y) \| tall(Y) \| (~(taller(X, Y) & tall(X))))), inference(quant_intro,[status(thm)],[107])). tff(109,axiom,(![X: $i, Y: $i] : ((~(X = Y)) => ((taller(X, Y) & tall(X)) => tall(Y)))), file('/mnt/tmpfs//6910178833852785322319524.p','b9')). tff(110,plain, (![X: $i, Y: $i] : ((X = Y) \| tall(Y) \| (~(taller(X, Y) & tall(X))))), inference(modus_ponens,[status(thm)],[109, 108])). tff(111,plain, (![X: $i, Y: $i] : ((X = Y) \| tall(Y) \| (~(taller(X, Y) & tall(X))))), inference(modus_ponens,[status(thm)],[110, 106])). tff(112,plain,( ![X: $i, Y: $i] : ((X = Y) \| tall(Y) \| (~(taller(X, Y) & tall(X))))), inference(skolemize,[status(sab)],[111])). tff(113,plain, (![X: $i, Y: $i] : ((X = Y) \| tall(Y) \| (~taller(X, Y)) \| (~tall(X)))), inference(modus_ponens,[status(thm)],[112, 105])). tff(114,plain, (![X: $i, Y: $i] : ((X = Y) \| tall(Y) \| (~taller(X, Y)) \| (~tall(X)))), inference(modus_ponens,[status(thm)],[113, 103])). tff(115,plain, (((~![X: $i, Y: $i] : ((X = Y) \| tall(Y) \| (~taller(X, Y)) \| (~tall(X)))) \| ((fred = paul) \| tall(paul) \| (~tall(fred)) \| (~taller(fred, paul)))) <=> ((~![X: $i, Y: $i] : ((X = Y) \| tall(Y) \| (~taller(X, Y)) \| (~tall(X)))) \| (fred = paul) \| tall(paul) \| (~tall(fred)) \| (~taller(fred, paul)))), inference(rewrite,[status(thm)],[])). tff(116,plain, (((fred = paul) \| tall(paul) \| (~taller(fred, paul)) \| (~tall(fred))) <=> ((fred = paul) \| tall(paul) \| (~tall(fred)) \| (~taller(fred, paul)))), inference(rewrite,[status(thm)],[])). tff(117,plain, (((~![X: $i, Y: $i] : ((X = Y) \| tall(Y) \| (~taller(X, Y)) \| (~tall(X)))) \| ((fred = paul) \| tall(paul) \| (~taller(fred, paul)) \| (~tall(fred)))) <=> ((~![X: $i, Y: $i] : ((X = Y) \| tall(Y) \| (~taller(X, Y)) \| (~tall(X)))) \| ((fred = paul) \| tall(paul) \| (~tall(fred)) \| (~taller(fred, paul))))), inference(monotonicity,[status(thm)],[116])). tff(118,plain, (((~![X: $i, Y: $i] : ((X = Y) \| tall(Y) \| (~taller(X, Y)) \| (~tall(X)))) \| ((fred = paul) \| tall(paul) \| (~taller(fred, paul)) \| (~tall(fred)))) <=> ((~![X: $i, Y: $i] : ((X = Y) \| tall(Y) \| (~taller(X, Y)) \| (~tall(X)))) \| (fred = paul) \| tall(paul) \| (~tall(fred)) \| (~taller(fred, paul)))), inference(transitivity,[status(thm)],[117, 115])). tff(119,plain, ((~![X: $i, Y: $i] : ((X = Y) \| tall(Y) \| (~taller(X, Y)) \| (~tall(X)))) \| ((fred = paul) \| tall(paul) \| (~taller(fred, paul)) \| (~tall(fred)))), inference(quant_inst,[status(thm)],[])). tff(120,plain, ((~![X: $i, Y: $i] : ((X = Y) \| tall(Y) \| (~taller(X, Y)) \| (~tall(X)))) \| (fred = paul) \| tall(paul) \| (~tall(fred)) \| (~taller(fred, paul))), inference(modus_ponens,[status(thm)],[119, 118])). tff(121,plain, (tall(paul)), inference(unit_resolution,[status(thm)],[120, 114, 101, 69, 66])). tff(122,assumption,(~((X!3 = \|'fred'\|) \| (X!3 = \|'paul'\|) \| (X!3 = \|'mary'\|) \| (~room(X!3)))), introduced(assumption)). tff(123,plain, (((X!3 = \|'fred'\|) \| (X!3 = \|'paul'\|) \| (X!3 = \|'mary'\|) \| (~room(X!3))) \| room(X!3)), inference(tautology,[status(thm)],[])). tff(124,plain, (room(X!3)), inference(unit_resolution,[status(thm)],[123, 122])). tff(125,plain, (((X!3 = \|'fred'\|) \| (X!3 = \|'paul'\|) \| (X!3 = \|'mary'\|) \| (~room(X!3))) \| (~(X!3 = \|'mary'\|))), inference(tautology,[status(thm)],[])). tff(126,plain, (~(X!3 = \|'mary'\|)), inference(unit_resolution,[status(thm)],[125, 122])). tff(127,plain, (((X!3 = \|'fred'\|) \| (X!3 = \|'paul'\|) \| (X!3 = \|'mary'\|) \| (~room(X!3))) \| (~(X!3 = \|'paul'\|))), inference(tautology,[status(thm)],[])). tff(128,plain, (~(X!3 = \|'paul'\|)), inference(unit_resolution,[status(thm)],[127, 122])). tff(129,plain, (((X!3 = \|'fred'\|) \| (X!3 = \|'paul'\|) \| (X!3 = \|'mary'\|) \| (~room(X!3))) \| (~(X!3 = \|'fred'\|))), inference(tautology,[status(thm)],[])). tff(130,plain, (~(X!3 = \|'fred'\|)), inference(unit_resolution,[status(thm)],[129, 122])). tff(131,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(132,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)],[131])). tff(133,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(134,plain, (![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))), inference(and_elim,[status(thm)],[8])). tff(135,plain, (![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))), inference(modus_ponens,[status(thm)],[134, 133])). tff(136,plain,( ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))), inference(skolemize,[status(sab)],[135])). tff(137,plain, (![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))), inference(modus_ponens,[status(thm)],[136, 132])). tff(138,plain, (((~![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| ((X!3 = \|'fred'\|) \| (X!3 = \|'paul'\|) \| (X!3 = \|'mary'\|) \| (~room(X!3)))) <=> ((~![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| (X!3 = \|'fred'\|) \| (X!3 = \|'paul'\|) \| (X!3 = \|'mary'\|) \| (~room(X!3)))), inference(rewrite,[status(thm)],[])). tff(139,plain, ((~![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| ((X!3 = \|'fred'\|) \| (X!3 = \|'paul'\|) \| (X!3 = \|'mary'\|) \| (~room(X!3)))), inference(quant_inst,[status(thm)],[])). tff(140,plain, ((~![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| (X!3 = \|'fred'\|) \| (X!3 = \|'paul'\|) \| (X!3 = \|'mary'\|) \| (~room(X!3))), inference(modus_ponens,[status(thm)],[139, 138])). tff(141,plain, ($false), inference(unit_resolution,[status(thm)],[140, 137, 130, 128, 126, 124])). tff(142,plain,((X!3 = \|'fred'\|) \| (X!3 = \|'paul'\|) \| (X!3 = \|'mary'\|) \| (~room(X!3))), inference(lemma,lemma(discharge,[]))). tff(143,plain, (room(fred) <=> room(fred)), inference(rewrite,[status(thm)],[])). tff(144,plain, (room(fred)), inference(and_elim,[status(thm)],[8])). tff(145,plain, (room(fred)), inference(modus_ponens,[status(thm)],[144, 143])). tff(146,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(147,plain, (room(mary)), inference(and_elim,[status(thm)],[8])). tff(148,plain, (room(mary)), inference(modus_ponens,[status(thm)],[147, 146])). tff(149,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!3 = \|'fred'\|) \| (X!3 = \|'paul'\|) \| (X!3 = \|'mary'\|) \| (~room(X!3)))) \| (~((~((~tall(paul)) \| (~quiet(paul)) \| (~person(paul)))) \| (~((~quiet(paul)) \| (~person(paul)) \| (~creative(paul))))))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!3 = \|'fred'\|) \| (X!3 = \|'paul'\|) \| (X!3 = \|'mary'\|) \| (~room(X!3)))) \| (~((~((~tall(paul)) \| (~quiet(paul)) \| (~person(paul)))) \| (~((~quiet(paul)) \| (~person(paul)) \| (~creative(paul)))))))), inference(rewrite,[status(thm)],[])). tff(150,plain, ((~((tall(paul) & quiet(paul) & person(paul)) \| (creative(paul) & quiet(paul) & person(paul)))) <=> (~((~((~tall(paul)) \| (~quiet(paul)) \| (~person(paul)))) \| (~((~quiet(paul)) \| (~person(paul)) \| (~creative(paul))))))), inference(rewrite,[status(thm)],[])). tff(151,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(152,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!3 = \|'fred'\|) \| (X!3 = \|'paul'\|) \| (X!3 = \|'mary'\|) \| (~room(X!3)))) \| (~((tall(paul) & quiet(paul) & person(paul)) \| (creative(paul) & quiet(paul) & person(paul))))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!3 = \|'fred'\|) \| (X!3 = \|'paul'\|) \| (X!3 = \|'mary'\|) \| (~room(X!3)))) \| (~((~((~tall(paul)) \| (~quiet(paul)) \| (~person(paul)))) \| (~((~quiet(paul)) \| (~person(paul)) \| (~creative(paul)))))))), inference(monotonicity,[status(thm)],[151, 150])). tff(153,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!3 = \|'fred'\|) \| (X!3 = \|'paul'\|) \| (X!3 = \|'mary'\|) \| (~room(X!3)))) \| (~((tall(paul) & quiet(paul) & person(paul)) \| (creative(paul) & quiet(paul) & person(paul))))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!3 = \|'fred'\|) \| (X!3 = \|'paul'\|) \| (X!3 = \|'mary'\|) \| (~room(X!3)))) \| (~((~((~tall(paul)) \| (~quiet(paul)) \| (~person(paul)))) \| (~((~quiet(paul)) \| (~person(paul)) \| (~creative(paul)))))))), inference(transitivity,[status(thm)],[152, 149])). tff(154,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!3 = \|'fred'\|) \| (X!3 = \|'paul'\|) \| (X!3 = \|'mary'\|) \| (~room(X!3)))) \| (~((tall(paul) & quiet(paul) & person(paul)) \| (creative(paul) & quiet(paul) & person(paul))))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!3 = \|'fred'\|) \| (X!3 = \|'paul'\|) \| (X!3 = \|'mary'\|) \| (~room(X!3)))) \| (~((tall(paul) & quiet(paul) & person(paul)) \| (creative(paul) & quiet(paul) & person(paul)))))), inference(rewrite,[status(thm)],[])). tff(155,plain, ((~((tall(paul) & quiet(paul) & person(paul)) \| (creative(paul) & quiet(paul) & person(paul)))) <=> (~((tall(paul) & quiet(paul) & person(paul)) \| (creative(paul) & quiet(paul) & person(paul))))), inference(rewrite,[status(thm)],[])). tff(156,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!3 = \|'fred'\|) \| (X!3 = \|'paul'\|) \| (X!3 = \|'mary'\|) \| (~room(X!3)))) \| (~((tall(paul) & quiet(paul) & person(paul)) \| (creative(paul) & quiet(paul) & person(paul))))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!3 = \|'fred'\|) \| (X!3 = \|'paul'\|) \| (X!3 = \|'mary'\|) \| (~room(X!3)))) \| (~((tall(paul) & quiet(paul) & person(paul)) \| (creative(paul) & quiet(paul) & person(paul)))))), inference(monotonicity,[status(thm)],[151, 155])). tff(157,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!3 = \|'fred'\|) \| (X!3 = \|'paul'\|) \| (X!3 = \|'mary'\|) \| (~room(X!3)))) \| (~((tall(paul) & quiet(paul) & person(paul)) \| (creative(paul) & quiet(paul) & person(paul))))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!3 = \|'fred'\|) \| (X!3 = \|'paul'\|) \| (X!3 = \|'mary'\|) \| (~room(X!3)))) \| (~((tall(paul) & quiet(paul) & person(paul)) \| (creative(paul) & quiet(paul) & person(paul)))))), inference(transitivity,[status(thm)],[156, 154])). tff(158,plain, ((room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((tall(paul) & quiet(paul) & person(paul)) \| (creative(paul) & quiet(paul) & person(paul)))) <=> (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((tall(paul) & quiet(paul) & person(paul)) \| (creative(paul) & quiet(paul) & person(paul))))), inference(rewrite,[status(thm)],[])). tff(159,plain, ((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((tall(paul) & quiet(paul) & person(paul)) \| (creative(paul) & quiet(paul) & person(paul))))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((tall(paul) & quiet(paul) & person(paul)) \| (creative(paul) & quiet(paul) & person(paul)))))), inference(monotonicity,[status(thm)],[158])). tff(160,plain, ((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((tall(paul) & quiet(paul) & person(paul)) \| (creative(paul) & quiet(paul) & person(paul))))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((tall(paul) & quiet(paul) & person(paul)) \| (creative(paul) & quiet(paul) & person(paul)))))), inference(rewrite,[status(thm)],[])). tff(161,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((tall(paul) & quiet(paul) & person(paul)) \| (creative(paul) & quiet(paul) & person(paul))))), inference(or_elim,[status(thm)],[7])). tff(162,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((tall(paul) & quiet(paul) & person(paul)) \| (creative(paul) & quiet(paul) & person(paul))))), inference(modus_ponens,[status(thm)],[161, 159])). tff(163,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((tall(paul) & quiet(paul) & person(paul)) \| (creative(paul) & quiet(paul) & person(paul))))), inference(modus_ponens,[status(thm)],[162, 160])). tff(164,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((tall(paul) & quiet(paul) & person(paul)) \| (creative(paul) & quiet(paul) & person(paul))))), inference(modus_ponens,[status(thm)],[163, 159])). 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 (or (and (tall paul) (quiet paul) (person paul)) (and (creative paul) (quiet paul) (person paul))))) (let ((a!7 (~ (not (and (room mary) (room paul) (room fred) a!4 a!6)) (or (not (room mary)) (not (room paul)) (not (room fred)) a!5 (not a!6))))) (nnf-neg a!1 a!2 a!3 (sk (~ (not a!4) a!5)) (refl (~ (not a!6) (not a!6))) a!7)))	room(jennifer)&room(robert)&room(carla)&(![X]:(room(X)=>(X='jennifer'\|X='robert'\|X='carla')))& (((quiet(carla)&tall(carla)&brave(carla)&person(carla))&(carla!=robert))& (![X]:(~room(X)=>(~(tall(X)&quiet(X)&tourist(X)))))& (((?[X]:(~room(X)&~(quiet(X)&person(X))))&(![X,Y]:((~(quiet(X)&person(X))&~(quiet(Y)&person(Y)))=>(X=Y)))))& (![X]:(taller(carla,X)))& (?[X,Y]:((brave(X)&tourist(X))&(hate(clinton,Y))&(taller(X,Y)))))	room(jennifer)&room(robert)&room(carla)&(![X]:(room(X)=>(X='jennifer'\|X='robert'\|X='carla')))& (((tall(robert)&quiet(robert)&person(robert))\|(creative(robert)&quiet(robert)&person(robert))))	neutral	neutral	entailment
Janet, Walter, Leon are the only persons in the room. 'Someone who does not like Howard is a client of someone who is not happy' unless 'Janet is the least quiet in the room'. Someone who does not like Howard is a client of someone who is not happy. Janet is not brave, not quiet, not happy or is not a brave person or both. More than one person outside the room is not liked by Howard.	Janet is quieter than Reinaldo or does not like Howard or both.	neutral	% SZS status Satisfiable	room(janet)&room(walter)&room(leon)&(![X]:(room(X)=>(X='janet'\|X='walter'\|X='leon')))& ((~(![X]:(quieter(janet,X)))=>(?[X,Y]:((~like(howard,X))&(~happy(Y))&(client(X,Y)))))& (?[X,Y]:((~like(howard,X))&(~happy(Y))&(client(X,Y))))& (((~brave(janet)&~quiet(janet)&~happy(janet))\|(~(brave(janet)&person(janet)))))& ((?[X,Y]:(~room(X)&~room(Y)&(~like(X,howard)&~like(Y,howard))&(X!=Y)))))	room(janet)&room(walter)&room(leon)&(![X]:(room(X)=>(X='janet'\|X='walter'\|X='leon')))& (((quieter(reinaldo,janet))\|(~like(howard,janet))))	contradiction	entailment	entailment
Benjamin, Donnie, Derrick are the only persons in the room. Donnie is the least quiet in the room. Donnie who does not like Sara, likes Gwendolyn. More than one person outside the room is not Donnie. Everyone in the room who is not a tall person is not liked by Gwendolyn.	Derrick does not like Sara or is not hated by Gwendolyn or both.	neutral	% SZS status Satisfiable	room(benjamin)&room(donnie)&room(derrick)&(![X]:(room(X)=>(X='benjamin'\|X='donnie'\|X='derrick')))& ((![X]:(quieter(donnie,X)))& ((~like(sara,donnie))&(like(gwendolyn,donnie)))& ((?[X,Y]:(~room(X)&~room(Y)&(X!=donnie&Y!=donnie)&(X!=Y))))& (![X]:(room(X)=>(((~(tall(X)&person(X)))=>(~like(X,gwendolyn)))))))	room(benjamin)&room(donnie)&room(derrick)&(![X]:(room(X)=>(X='benjamin'\|X='donnie'\|X='derrick')))& (((~like(sara,derrick))\|(~hate(derrick,gwendolyn))))	neutral	entailment	entailment
Donna, Daniel are the only persons in the room. If Donna is the least tall in the room then Donna is the least rich in the room otherwise Donna neither is a rich european nor does not hate Mechelle. If someone who is not liked by Mechelle like someone who likes Mechelle then Donna is the least rich in the room otherwise someone who does not like John hate someone who is not liked by Cecil. More than one person in the room owns a microscope. Someone in the room is not a creative rich european. Donna neither is a rich european nor does not hate Mechelle. More than one person in the room is not rich.	Daniel is richer than Mechelle or is not a rich creative european or both.	entailment	% SZS status Unsatisfiable % SZS output start Proof tff(room_type, type, ( room: $i > $o)). tff(tptp_fun_X_5_type, type, ( tptp_fun_X_5: $i)). tff(tptp_fun__mary__type, type, ( tptp_fun__mary_: $i)). tff(tptp_fun__paul__type, type, ( tptp_fun__paul_: $i)). tff(european_type, type, ( european: $i > $o)). tff(paul_type, type, ( paul: $i)). tff(creative_type, type, ( creative: $i > $o)). tff(rich_type, type, ( rich: $i > $o)). tff(richer_type, type, ( richer: ( $i * $i ) > $o)). tff(susan_type, type, ( susan: $i)). tff(tptp_fun_X_4_type, type, ( tptp_fun_X_4: $i)). tff(tptp_fun_Y_3_type, type, ( tptp_fun_Y_3: $i)). tff(hate_type, type, ( hate: ( $i * $i ) > $o)). tff(mary_type, type, ( mary: $i)). tff(preda_type, type, ( preda: $i > $o)). tff(like_type, type, ( like: ( $i * $i ) > $o)). tff(alice_type, type, ( alice: $i)). tff(lucy_type, type, ( lucy: $i)). tff(taller_type, type, ( taller: ( $i * $i ) > $o)). tff(1,assumption,(rich(paul)), introduced(assumption)). tff(2,assumption,(Y!3 = \|'mary'\|), introduced(assumption)). tff(3,plain, ((X!4 = Y!3) <=> (X!4 = \|'mary'\|)), inference(monotonicity,[status(thm)],[2])). tff(4,plain, ((~(X!4 = Y!3)) <=> (~(X!4 = \|'mary'\|))), inference(monotonicity,[status(thm)],[3])). tff(5,plain, (?[X: $i, Y: $i] : (room(X) & room(Y) & (~rich(X)) & (~rich(Y)) & (~(X = Y))) <=> ?[X: $i, Y: $i] : (room(X) & room(Y) & (~rich(X)) & (~rich(Y)) & (~(X = Y)))), inference(rewrite,[status(thm)],[])). tff(6,plain, ((~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = \|'mary'\|) \| (X = \|'paul'\|)))) & (((((((![X: $i] : taller(mary, X) => ![X: $i] : richer(mary, X)) \| ((~![X: $i] : taller(mary, X)) => (~((rich(mary) & european(mary)) \| (~hate(susan, mary)))))) & ((?[X: $i, Y: $i] : (((~like(X, susan)) & like(susan, Y)) & like(X, Y)) => ![X: $i] : richer(mary, X)) \| ((~?[X: $i, Y: $i] : (((~like(X, susan)) & like(susan, Y)) & like(X, Y))) => ?[X: $i, Y: $i] : (((~like(lucy, X)) & (~like(Y, alice))) & hate(X, Y))))) & ?[X: $i, Y: $i] : (((room(X) & room(Y)) & (preda(X) & preda(Y))) & (~(X = Y)))) & ?[X: $i] : (room(X) => (~((creative(X) & rich(X)) & european(X))))) & (~((rich(mary) & european(mary)) \| (~hate(susan, mary))))) & ?[X: $i, Y: $i] : (((room(X) & room(Y)) & ((~rich(X)) & (~rich(Y)))) & (~(X = Y))))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = \|'mary'\|) \| (X = \|'paul'\|)))) & (richer(susan, paul) \| (~((rich(paul) & creative(paul)) & european(paul))))))) <=> (~((~(room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ?[X: $i, Y: $i] : (room(X) & room(Y) & preda(X) & preda(Y) & (~(X = Y))) & ?[X: $i] : ((~room(X)) \| (~(creative(X) & rich(X) & european(X)))) & (~((rich(mary) & european(mary)) \| (~hate(susan, mary)))) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~rich(X)) & (~rich(Y)) & (~(X = Y))))) \| (room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (richer(susan, paul) \| (~(rich(paul) & creative(paul) & european(paul)))))))), inference(rewrite,[status(thm)],[])). tff(7,axiom,(~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = \|'mary'\|) \| (X = \|'paul'\|)))) & (((((((![X: $i] : taller(mary, X) => ![X: $i] : richer(mary, X)) \| ((~![X: $i] : taller(mary, X)) => (~((rich(mary) & european(mary)) \| (~hate(susan, mary)))))) & ((?[X: $i, Y: $i] : (((~like(X, susan)) & like(susan, Y)) & like(X, Y)) => ![X: $i] : richer(mary, X)) \| ((~?[X: $i, Y: $i] : (((~like(X, susan)) & like(susan, Y)) & like(X, Y))) => ?[X: $i, Y: $i] : (((~like(lucy, X)) & (~like(Y, alice))) & hate(X, Y))))) & ?[X: $i, Y: $i] : (((room(X) & room(Y)) & (preda(X) & preda(Y))) & (~(X = Y)))) & ?[X: $i] : (room(X) => (~((creative(X) & rich(X)) & european(X))))) & (~((rich(mary) & european(mary)) \| (~hate(susan, mary))))) & ?[X: $i, Y: $i] : (((room(X) & room(Y)) & ((~rich(X)) & (~rich(Y)))) & (~(X = Y))))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = \|'mary'\|) \| (X = \|'paul'\|)))) & (richer(susan, paul) \| (~((rich(paul) & creative(paul)) & european(paul))))))), file('/mnt/tmpfs//5230515318099239241160777.p','negated')). tff(8,plain, (~((~(room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ?[X: $i, Y: $i] : (room(X) & room(Y) & preda(X) & preda(Y) & (~(X = Y))) & ?[X: $i] : ((~room(X)) \| (~(creative(X) & rich(X) & european(X)))) & (~((rich(mary) & european(mary)) \| (~hate(susan, mary)))) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~rich(X)) & (~rich(Y)) & (~(X = Y))))) \| (room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (richer(susan, paul) \| (~(rich(paul) & creative(paul) & european(paul))))))), inference(modus_ponens,[status(thm)],[7, 6])). tff(9,plain, (room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ?[X: $i, Y: $i] : (room(X) & room(Y) & preda(X) & preda(Y) & (~(X = Y))) & ?[X: $i] : ((~room(X)) \| (~(creative(X) & rich(X) & european(X)))) & (~((rich(mary) & european(mary)) \| (~hate(susan, mary)))) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~rich(X)) & (~rich(Y)) & (~(X = Y)))), inference(or_elim,[status(thm)],[8])). tff(10,plain, (?[X: $i, Y: $i] : (room(X) & room(Y) & (~rich(X)) & (~rich(Y)) & (~(X = Y)))), inference(and_elim,[status(thm)],[9])). tff(11,plain, (?[X: $i, Y: $i] : (room(X) & room(Y) & (~rich(X)) & (~rich(Y)) & (~(X = Y)))), inference(modus_ponens,[status(thm)],[10, 5])). tff(12,plain,( room(X!4) & room(Y!3) & (~rich(X!4)) & (~rich(Y!3)) & (~(X!4 = Y!3))), inference(skolemize,[status(sab)],[11])). tff(13,plain, (~(X!4 = Y!3)), inference(and_elim,[status(thm)],[12])). tff(14,plain, (~(X!4 = \|'mary'\|)), inference(modus_ponens,[status(thm)],[13, 4])). tff(15,plain, (room(X!4)), inference(and_elim,[status(thm)],[12])). tff(16,plain, (^[X: $i] : refl(((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) <=> ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))))), inference(bind,[status(th)],[])). tff(17,plain, (![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) <=> ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))), inference(quant_intro,[status(thm)],[16])). tff(18,plain, (![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) <=> ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))), inference(rewrite,[status(thm)],[])). tff(19,plain, (![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))), inference(and_elim,[status(thm)],[9])). tff(20,plain, (![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))), inference(modus_ponens,[status(thm)],[19, 18])). tff(21,plain,( ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))), inference(skolemize,[status(sab)],[20])). tff(22,plain, (![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))), inference(modus_ponens,[status(thm)],[21, 17])). tff(23,plain, (((~![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| ((X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|) \| (~room(X!4)))) <=> ((~![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| (X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|) \| (~room(X!4)))), inference(rewrite,[status(thm)],[])). tff(24,plain, ((~![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| ((X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|) \| (~room(X!4)))), inference(quant_inst,[status(thm)],[])). tff(25,plain, ((~![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| (X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|) \| (~room(X!4))), inference(modus_ponens,[status(thm)],[24, 23])). tff(26,plain, ((X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|)), inference(unit_resolution,[status(thm)],[25, 22, 15])). tff(27,plain, (X!4 = \|'paul'\|), inference(unit_resolution,[status(thm)],[26, 14])). tff(28,plain, (\|'paul'\| = X!4), inference(symmetry,[status(thm)],[27])). tff(29,plain, (\|'mary'\| = Y!3), inference(symmetry,[status(thm)],[2])). tff(30,assumption,(paul = \|'mary'\|), introduced(assumption)). tff(31,plain, (paul = Y!3), inference(transitivity,[status(thm)],[30, 29])). tff(32,plain, (rich(paul) <=> rich(Y!3)), inference(monotonicity,[status(thm)],[31])). tff(33,plain, (rich(Y!3) <=> rich(paul)), inference(symmetry,[status(thm)],[32])). tff(34,plain, ((~rich(Y!3)) <=> (~rich(paul))), inference(monotonicity,[status(thm)],[33])). tff(35,plain, (~rich(Y!3)), inference(and_elim,[status(thm)],[12])). tff(36,plain, (~rich(paul)), inference(modus_ponens,[status(thm)],[35, 34])). tff(37,plain, ($false), inference(unit_resolution,[status(thm)],[1, 36])). tff(38,plain,((~(paul = \|'mary'\|)) \| (~rich(paul)) \| (~(Y!3 = \|'mary'\|))), inference(lemma,lemma(discharge,[]))). tff(39,plain, (~(paul = \|'mary'\|)), inference(unit_resolution,[status(thm)],[38, 2, 1])). tff(40,plain, (room(paul) <=> room(paul)), inference(rewrite,[status(thm)],[])). tff(41,plain, (room(paul)), inference(and_elim,[status(thm)],[9])). tff(42,plain, (room(paul)), inference(modus_ponens,[status(thm)],[41, 40])). tff(43,plain, (((~![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| ((~room(paul)) \| (paul = \|'paul'\|) \| (paul = \|'mary'\|))) <=> ((~![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| (~room(paul)) \| (paul = \|'paul'\|) \| (paul = \|'mary'\|))), inference(rewrite,[status(thm)],[])). tff(44,plain, (((paul = \|'paul'\|) \| (paul = \|'mary'\|) \| (~room(paul))) <=> ((~room(paul)) \| (paul = \|'paul'\|) \| (paul = \|'mary'\|))), inference(rewrite,[status(thm)],[])). tff(45,plain, (((~![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| ((paul = \|'paul'\|) \| (paul = \|'mary'\|) \| (~room(paul)))) <=> ((~![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| ((~room(paul)) \| (paul = \|'paul'\|) \| (paul = \|'mary'\|)))), inference(monotonicity,[status(thm)],[44])). tff(46,plain, (((~![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| ((paul = \|'paul'\|) \| (paul = \|'mary'\|) \| (~room(paul)))) <=> ((~![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| (~room(paul)) \| (paul = \|'paul'\|) \| (paul = \|'mary'\|))), inference(transitivity,[status(thm)],[45, 43])). tff(47,plain, ((~![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| ((paul = \|'paul'\|) \| (paul = \|'mary'\|) \| (~room(paul)))), inference(quant_inst,[status(thm)],[])). tff(48,plain, ((~![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| (~room(paul)) \| (paul = \|'paul'\|) \| (paul = \|'mary'\|)), inference(modus_ponens,[status(thm)],[47, 46])). tff(49,plain, ((paul = \|'paul'\|) \| (paul = \|'mary'\|)), inference(unit_resolution,[status(thm)],[48, 42, 22])). tff(50,plain, (paul = \|'paul'\|), inference(unit_resolution,[status(thm)],[49, 39])). tff(51,plain, (paul = X!4), inference(transitivity,[status(thm)],[50, 28])). tff(52,plain, (rich(paul) <=> rich(X!4)), inference(monotonicity,[status(thm)],[51])). tff(53,plain, (rich(X!4) <=> rich(paul)), inference(symmetry,[status(thm)],[52])). tff(54,plain, ((~rich(X!4)) <=> (~rich(paul))), inference(monotonicity,[status(thm)],[53])). tff(55,plain, (~rich(X!4)), inference(and_elim,[status(thm)],[12])). tff(56,plain, (~rich(paul)), inference(modus_ponens,[status(thm)],[55, 54])). tff(57,plain, ($false), inference(unit_resolution,[status(thm)],[1, 56])). tff(58,plain,((~(Y!3 = \|'mary'\|)) \| (~rich(paul))), inference(lemma,lemma(discharge,[]))). tff(59,plain, (~(Y!3 = \|'mary'\|)), inference(unit_resolution,[status(thm)],[58, 1])). tff(60,plain, (room(Y!3)), inference(and_elim,[status(thm)],[12])). tff(61,plain, (((~![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| ((Y!3 = \|'paul'\|) \| (Y!3 = \|'mary'\|) \| (~room(Y!3)))) <=> ((~![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| (Y!3 = \|'paul'\|) \| (Y!3 = \|'mary'\|) \| (~room(Y!3)))), inference(rewrite,[status(thm)],[])). tff(62,plain, ((~![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| ((Y!3 = \|'paul'\|) \| (Y!3 = \|'mary'\|) \| (~room(Y!3)))), inference(quant_inst,[status(thm)],[])). tff(63,plain, ((~![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| (Y!3 = \|'paul'\|) \| (Y!3 = \|'mary'\|) \| (~room(Y!3))), inference(modus_ponens,[status(thm)],[62, 61])). tff(64,plain, ((Y!3 = \|'paul'\|) \| (Y!3 = \|'mary'\|)), inference(unit_resolution,[status(thm)],[63, 22, 60])). tff(65,plain, (Y!3 = \|'paul'\|), inference(unit_resolution,[status(thm)],[64, 59])). tff(66,plain, ((X!4 = Y!3) <=> (X!4 = \|'paul'\|)), inference(monotonicity,[status(thm)],[65])). tff(67,plain, ((~(X!4 = Y!3)) <=> (~(X!4 = \|'paul'\|))), inference(monotonicity,[status(thm)],[66])). tff(68,plain, (~(X!4 = \|'paul'\|)), inference(modus_ponens,[status(thm)],[13, 67])). tff(69,plain, (X!4 = \|'mary'\|), inference(unit_resolution,[status(thm)],[26, 68])). tff(70,plain, (\|'mary'\| = X!4), inference(symmetry,[status(thm)],[69])). tff(71,plain, (\|'paul'\| = Y!3), inference(symmetry,[status(thm)],[65])). tff(72,assumption,(paul = \|'paul'\|), introduced(assumption)). tff(73,plain, (paul = Y!3), inference(transitivity,[status(thm)],[72, 71])). tff(74,plain, (rich(paul) <=> rich(Y!3)), inference(monotonicity,[status(thm)],[73])). tff(75,plain, (rich(Y!3) <=> rich(paul)), inference(symmetry,[status(thm)],[74])). tff(76,plain, ((~rich(Y!3)) <=> (~rich(paul))), inference(monotonicity,[status(thm)],[75])). tff(77,plain, (~rich(paul)), inference(modus_ponens,[status(thm)],[35, 76])). tff(78,plain, ($false), inference(unit_resolution,[status(thm)],[1, 77])). tff(79,plain,((~(paul = \|'paul'\|)) \| (~rich(paul))), inference(lemma,lemma(discharge,[]))). tff(80,plain, (~(paul = \|'paul'\|)), inference(unit_resolution,[status(thm)],[79, 1])). tff(81,plain, (paul = \|'mary'\|), inference(unit_resolution,[status(thm)],[49, 80])). tff(82,plain, (paul = X!4), inference(transitivity,[status(thm)],[81, 70])). tff(83,plain, (rich(paul) <=> rich(X!4)), inference(monotonicity,[status(thm)],[82])). tff(84,plain, (rich(X!4) <=> rich(paul)), inference(symmetry,[status(thm)],[83])). tff(85,plain, ((~rich(X!4)) <=> (~rich(paul))), inference(monotonicity,[status(thm)],[84])). tff(86,plain, (~rich(paul)), inference(modus_ponens,[status(thm)],[55, 85])). tff(87,plain, ($false), inference(unit_resolution,[status(thm)],[1, 86])). tff(88,plain,(~rich(paul)), inference(lemma,lemma(discharge,[]))). tff(89,plain, ((richer(susan, paul) \| (~rich(paul)) \| (~creative(paul)) \| (~european(paul))) \| rich(paul)), inference(tautology,[status(thm)],[])). tff(90,plain, (richer(susan, paul) \| (~rich(paul)) \| (~creative(paul)) \| (~european(paul))), inference(unit_resolution,[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)],[9])). tff(93,plain, (room(mary)), inference(modus_ponens,[status(thm)],[92, 91])). tff(94,plain, (((~room(mary)) \| (~room(paul)) \| (~((X!5 = \|'paul'\|) \| (X!5 = \|'mary'\|) \| (~room(X!5)))) \| (~(richer(susan, paul) \| (~(rich(paul) & creative(paul) & european(paul)))))) <=> ((~room(mary)) \| (~room(paul)) \| (~((X!5 = \|'paul'\|) \| (X!5 = \|'mary'\|) \| (~room(X!5)))) \| (~(richer(susan, paul) \| (~rich(paul)) \| (~creative(paul)) \| (~european(paul)))))), inference(rewrite,[status(thm)],[])). tff(95,plain, ((~(richer(susan, paul) \| (~(rich(paul) & creative(paul) & european(paul))))) <=> (~(richer(susan, paul) \| (~(rich(paul) & creative(paul) & european(paul)))))), inference(rewrite,[status(thm)],[])). tff(96,plain, ((~((X!5 = \|'paul'\|) \| (X!5 = \|'mary'\|) \| (~room(X!5)))) <=> (~((X!5 = \|'paul'\|) \| (X!5 = \|'mary'\|) \| (~room(X!5))))), inference(rewrite,[status(thm)],[])). tff(97,plain, (((~room(mary)) \| (~room(paul)) \| (~((X!5 = \|'paul'\|) \| (X!5 = \|'mary'\|) \| (~room(X!5)))) \| (~(richer(susan, paul) \| (~(rich(paul) & creative(paul) & european(paul)))))) <=> ((~room(mary)) \| (~room(paul)) \| (~((X!5 = \|'paul'\|) \| (X!5 = \|'mary'\|) \| (~room(X!5)))) \| (~(richer(susan, paul) \| (~(rich(paul) & creative(paul) & european(paul))))))), inference(monotonicity,[status(thm)],[96, 95])). tff(98,plain, ((room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (richer(susan, paul) \| (~(rich(paul) & creative(paul) & european(paul))))) <=> (room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (richer(susan, paul) \| (~(rich(paul) & creative(paul) & european(paul)))))), inference(rewrite,[status(thm)],[])). tff(99,plain, ((~(room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (richer(susan, paul) \| (~(rich(paul) & creative(paul) & european(paul)))))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (richer(susan, paul) \| (~(rich(paul) & creative(paul) & european(paul))))))), inference(monotonicity,[status(thm)],[98])). tff(100,plain, ((~(room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (richer(susan, paul) \| (~(rich(paul) & creative(paul) & european(paul)))))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (richer(susan, paul) \| (~(rich(paul) & creative(paul) & european(paul))))))), inference(rewrite,[status(thm)],[])). tff(101,plain, (~(room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (richer(susan, paul) \| (~(rich(paul) & creative(paul) & european(paul)))))), inference(or_elim,[status(thm)],[8])). tff(102,plain, (~(room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (richer(susan, paul) \| (~(rich(paul) & creative(paul) & european(paul)))))), inference(modus_ponens,[status(thm)],[101, 99])). tff(103,plain, (~(room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (richer(susan, paul) \| (~(rich(paul) & creative(paul) & european(paul)))))), inference(modus_ponens,[status(thm)],[102, 100])). tff(104,plain, (~(room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (richer(susan, paul) \| (~(rich(paul) & creative(paul) & european(paul)))))), inference(modus_ponens,[status(thm)],[103, 99])). 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!5 \|'paul'\|) (= X!5 \|'mary'\|) (not (room X!5))))) (a!5 (or (richer susan paul) (not (and (rich paul) (creative paul) (european 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(donna)&room(daniel)&(![X]:(room(X)=>(X='donna'\|X='daniel')))& ((((![X]:(taller(donna,X)))=>(![X]:(richer(donna,X))))\|((~(![X]:(taller(donna,X))))=>(~((rich(donna)&european(donna))\|(~hate(mechelle,donna))))))& (((?[X,Y]:((~like(X,mechelle))&(like(mechelle,Y))&(like(X,Y))))=>(![X]:(richer(donna,X))))\|((~(?[X,Y]:((~like(X,mechelle))&(like(mechelle,Y))&(like(X,Y)))))=>(?[X,Y]:((~like(john,X))&(~like(Y,cecil))&(hate(X,Y))))))& ((?[X,Y]:(room(X)&room(Y)&(owns_a_microscope(X)&owns_a_microscope(Y))&(X!=Y))))& (?[X]:(room(X)=>(~(creative(X)&rich(X)&european(X)))))& (~((rich(donna)&european(donna))\|(~hate(mechelle,donna))))& ((?[X,Y]:(room(X)&room(Y)&(~rich(X)&~rich(Y))&(X!=Y)))))	room(donna)&room(daniel)&(![X]:(room(X)=>(X='donna'\|X='daniel')))& (((richer(mechelle,daniel))\|(~(rich(daniel)&creative(daniel)&european(daniel)))))	neutral	neutral	entailment
Helen, Christine, Robert are the only persons in the room. Someone who is a creative tourist like someone who is not Robert if more than one person in the room likes Edward and vice versa. Christine either does not like Brad or is not a scotch connoisseur if Christine and Helen like each other and vice versa. If Robert and Helen are respectively tall and rich then more than one person outside the room is liked by Brad otherwise Helen and Robert like each other. If Robert and Helen are not liked by Edward then Christine and Helen are not creative. Brad is a sibling of Robert unless Christine neither likes Edward nor does not collect rare sneakers. If Robert either is not liked by Brad or likes Edward then Robert neither does not like Brad nor is richer than Edward otherwise someone in the room is not liked by Edward. More than one person outside the room is liked by Brad. Only one person outside the room is a scotch connoisseur. More than one person outside the room is liked by Brad. Edward and Christine like each other. Someone who is not creative is taller than someone who is not Robert.	Christine who does not like Edward, is a rich tourist.	contradiction	-	room(helen)&room(christine)&room(robert)&(![X]:(room(X)=>(X='helen'\|X='christine'\|X='robert')))& ((((?[X,Y]:(room(X)&room(Y)&(like(edward,X)&like(edward,Y))&(X!=Y))))<=>(?[X,Y]:((creative(X)&tourist(X))&(Y!=robert)&(like(X,Y)))))& (((like(christine,helen) & like(helen,christine)))<=>((((~like(brad,christine))\|(is_not_a_scotch_connoisseur(christine)))&(~((~like(brad,christine))\|(is_not_a_scotch_connoisseur(christine)))))))& ((((tall(robert))&(rich(helen)))=>((?[X,Y]:(~room(X)&~room(Y)&(like(X,brad)&like(Y,brad))&(X!=Y)))))\|((~((tall(robert))&(rich(helen))))=>((like(helen,robert) & like(robert,helen)))))& ((~like(robert,edward)&~like(helen,edward))=>(~creative(christine)&~creative(helen)))& (~(~((like(edward,christine))\|(does_not_collect_rare_sneakers(christine))))=>(sibling(robert,brad)))& ((((((~like(robert,brad))\|(like(edward,robert)))&(~((~like(robert,brad))\|(like(edward,robert))))))=>(~((~like(brad,robert))\|(richer(edward,robert)))))\|((~((((~like(robert,brad))\|(like(edward,robert)))&(~((~like(robert,brad))\|(like(edward,robert)))))))=>(?[X]:(room(X)=>(~like(X,edward))))))& ((?[X,Y]:(~room(X)&~room(Y)&(like(X,brad)&like(Y,brad))&(X!=Y))))& (((?[X]:(~room(X)&is_a_scotch_connoisseur(X)))&(![X,Y]:((is_a_scotch_connoisseur(X)&is_a_scotch_connoisseur(Y))=>(X=Y)))))& ((?[X,Y]:(~room(X)&~room(Y)&(like(X,brad)&like(Y,brad))&(X!=Y))))& ((like(edward,christine) & like(christine,edward)))& (?[X,Y]:((~creative(X))&(Y!=robert)&(taller(X,Y)))))	room(helen)&room(christine)&room(robert)&(![X]:(room(X)=>(X='helen'\|X='christine'\|X='robert')))& ((~like(edward,christine))&(rich(christine)&tourist(christine)))	contradiction	neutral	contradiction
Martha is the only person in the room. "Someone who is not Martha like someone who is a client of Bernard" if "Martha neither is a rich tourist nor does not hate Bernard" and vice versa. Martha is a happy tourist. Martha neither is a rich tourist nor does not hate Bernard.	Martha neither is not happy, not quiet, not rich nor is not hated by Bernard.	neutral	% SZS status Satisfiable	room(martha)&(![X]:(room(X)=>(X='martha')))& (((~((rich(martha)&tourist(martha))\|(~hate(bernard,martha))))<=>(?[X,Y]:((X!=martha)&(client(bernard,Y))&(like(X,Y)))))& (happy(martha)&tourist(martha))& (~((rich(martha)&tourist(martha))\|(~hate(bernard,martha)))))	room(martha)&(![X]:(room(X)=>(X='martha')))& (~((~happy(martha)&~quiet(martha)&~rich(martha))\|(~hate(martha,bernard))))	entailment	entailment	entailment
Kristen is the only person in the room. If “Kristen is not tall” then “Kristen is a quiet european” otherwise “only one person outside the room is not Kristen”. If “Kristen who is a scotch connoisseur, is not a quiet person” then “only one person in the room does not practice digital art”. More than one person outside the room is not hated by Norman. Kristen is the least quiet in the room. Only one person in the room is hated by Norman. Kristen neither practices digital art nor does not hate Jacob.	Kristen who is a scotch connoisseur, is a quiet european.	neutral	% SZS status Satisfiable	room(kristen)&(![X]:(room(X)=>(X='kristen')))& ((((~tall(kristen))=>(quiet(kristen)&european(kristen)))\|((~(~tall(kristen)))=>(((?[X]:(~room(X)&X!=kristen))&(![X,Y]:((X!=kristen&Y!=kristen)=>(X=Y)))))))& (((is_a_scotch_connoisseur(kristen))&(~(quiet(kristen)&person(kristen))))=>(((?[X]:(room(X)&does_not_practice_digital_art(X)))&(![X,Y]:((does_not_practice_digital_art(X)&does_not_practice_digital_art(Y))=>(X=Y))))))& ((?[X,Y]:(~room(X)&~room(Y)&(~hate(X,norman)&~hate(Y,norman))&(X!=Y))))& (![X]:(quieter(kristen,X)))& (((?[X]:(room(X)&hate(X,norman)))&(![X,Y]:((hate(X,norman)&hate(Y,norman))=>(X=Y)))))& (~((practices_digital_art(kristen))\|(~hate(jacob,kristen)))))	room(kristen)&(![X]:(room(X)=>(X='kristen')))& ((is_a_scotch_connoisseur(kristen))&(quiet(kristen)&european(kristen)))	contradiction	contradiction	contradiction
Robert is the only person in the room. Robert is not rich, not brave. Someone who is a brave tourist hate someone who hates Edward. Someone who is allergic to anything is taller than someone who is not allergic to anything. Robert is the richest in the room. It is not the case that 'more than one person outside the room is a rich tourist'.	Robert neither is a client of Google nor is not a tall creative rich tourist.	contradiction	-	room(robert)&(![X]:(room(X)=>(X='robert')))& ((~rich(robert)&~brave(robert))& (?[X,Y]:((brave(X)&tourist(X))&(hate(edward,Y))&(hate(X,Y))))& (?[X,Y]:((is_allergic_to_anything(X))&(is_not_allergic_to_anything(Y))&(taller(X,Y))))& (![X]:(richer(X,robert)))& (~((?[X,Y]:(~room(X)&~room(Y)&(rich(X)&tourist(X)&rich(Y)&tourist(Y))&(X!=Y))))))	room(robert)&(![X]:(room(X)=>(X='robert')))& (~((is_a_client_of_Google(robert))\|(~(tall(robert)&creative(robert)&rich(robert)&tourist(robert)))))	contradiction	contradiction	contradiction
Andrew, Seth, Preston are the only persons in the room. "Seth and Andrew are respectively creative and quiet" if "Preston is a tall european and is liked by Darren". "Preston and Andrew are not quiet" if "Seth is liked by Darren or does not like Darren or both". Darren is richer than Andrew. Someone in the room is liked by Darren. Preston and Andrew like Darren. Seth is the tallest in the room. Andrew is the least tall in the room. Andrew who enjoys watercolor painting, is not tall. Someone who is not Preston is a sibling of someone who is liked by Darren. Preston is the richest in the room. Seth likes Darren. Only one person outside the room does not enjoy mountain biking.	Andrew who likes Darren, is not a tall quiet person.	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(person_type, type, ( person: $i > $o)). tff(mary_type, type, ( mary: $i)). tff(tall_type, type, ( tall: $i > $o)). tff(quiet_type, type, ( quiet: $i > $o)). tff(preda_type, type, ( preda: $i > $o)). tff(like_type, type, ( like: ( $i * $i ) > $o)). tff(paul_type, type, ( paul: $i)). tff(alice_type, type, ( alice: $i)). tff(richer_type, type, ( richer: ( $i * $i ) > $o)). tff(fred_type, type, ( fred: $i)). tff(sibling_type, type, ( sibling: ( $i * $i ) > $o)). tff(predb_type, type, ( predb: $i > $o)). tff(taller_type, type, ( taller: ( $i * $i ) > $o)). tff(creative_type, type, ( creative: $i > $o)). tff(european_type, type, ( european: $i > $o)). tff(1,plain, ((~tall(mary)) <=> (~tall(mary))), inference(rewrite,[status(thm)],[])). tff(2,plain, ((~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)))) & ((((((((((((((tall(fred) & european(fred)) & like(fred, alice)) => (creative(paul) & quiet(mary))) & ((like(paul, alice) \| (~like(alice, paul))) => ((~quiet(fred)) & (~quiet(mary))))) & richer(mary, alice)) & ?[X: $i] : (room(X) => like(X, alice))) & (like(alice, fred) & like(alice, mary))) & ![X: $i] : taller(X, paul)) & ![X: $i] : taller(mary, X)) & (predb(mary) & (~tall(mary)))) & ?[X: $i, Y: $i] : (((~(X = fred)) & like(Y, alice)) & sibling(X, Y))) & ![X: $i] : richer(X, fred)) & like(alice, paul)) & (?[X: $i] : ((~room(X)) & (~preda(X))) & ![X: $i, Y: $i] : (((~preda(X)) & (~preda(Y))) => (X = Y))))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)))) & (like(alice, mary) & (~((tall(mary) & quiet(mary)) & person(mary))))))) <=> (~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((~(tall(fred) & european(fred) & like(fred, alice))) \| (creative(paul) & quiet(mary))) & ((~(like(paul, alice) \| (~like(alice, paul)))) \| ((~quiet(fred)) & (~quiet(mary)))) & richer(mary, alice) & ?[X: $i] : ((~room(X)) \| like(X, alice)) & like(alice, fred) & like(alice, mary) & ![X: $i] : taller(X, paul) & ![X: $i] : taller(mary, X) & predb(mary) & (~tall(mary)) & ?[X: $i, Y: $i] : ((~(X = fred)) & like(Y, alice) & sibling(X, Y)) & ![X: $i] : richer(X, fred) & like(alice, paul) & ?[X: $i] : ((~room(X)) & (~preda(X))) & ![X: $i, Y: $i] : ((~((~preda(X)) & (~preda(Y)))) \| (X = Y)))) \| (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & like(alice, mary) & (~(tall(mary) & quiet(mary) & person(mary))))))), inference(rewrite,[status(thm)],[])). tff(3,axiom,(~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)))) & ((((((((((((((tall(fred) & european(fred)) & like(fred, alice)) => (creative(paul) & quiet(mary))) & ((like(paul, alice) \| (~like(alice, paul))) => ((~quiet(fred)) & (~quiet(mary))))) & richer(mary, alice)) & ?[X: $i] : (room(X) => like(X, alice))) & (like(alice, fred) & like(alice, mary))) & ![X: $i] : taller(X, paul)) & ![X: $i] : taller(mary, X)) & (predb(mary) & (~tall(mary)))) & ?[X: $i, Y: $i] : (((~(X = fred)) & like(Y, alice)) & sibling(X, Y))) & ![X: $i] : richer(X, fred)) & like(alice, paul)) & (?[X: $i] : ((~room(X)) & (~preda(X))) & ![X: $i, Y: $i] : (((~preda(X)) & (~preda(Y))) => (X = Y))))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)))) & (like(alice, mary) & (~((tall(mary) & quiet(mary)) & person(mary))))))), file('/mnt/tmpfs//7014820077480244263605382.p','negated')). tff(4,plain, (~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((~(tall(fred) & european(fred) & like(fred, alice))) \| (creative(paul) & quiet(mary))) & ((~(like(paul, alice) \| (~like(alice, paul)))) \| ((~quiet(fred)) & (~quiet(mary)))) & richer(mary, alice) & ?[X: $i] : ((~room(X)) \| like(X, alice)) & like(alice, fred) & like(alice, mary) & ![X: $i] : taller(X, paul) & ![X: $i] : taller(mary, X) & predb(mary) & (~tall(mary)) & ?[X: $i, Y: $i] : ((~(X = fred)) & like(Y, alice) & sibling(X, Y)) & ![X: $i] : richer(X, fred) & like(alice, paul) & ?[X: $i] : ((~room(X)) & (~preda(X))) & ![X: $i, Y: $i] : ((~((~preda(X)) & (~preda(Y)))) \| (X = Y)))) \| (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & like(alice, mary) & (~(tall(mary) & quiet(mary) & person(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))) & ((~(tall(fred) & european(fred) & like(fred, alice))) \| (creative(paul) & quiet(mary))) & ((~(like(paul, alice) \| (~like(alice, paul)))) \| ((~quiet(fred)) & (~quiet(mary)))) & richer(mary, alice) & ?[X: $i] : ((~room(X)) \| like(X, alice)) & like(alice, fred) & like(alice, mary) & ![X: $i] : taller(X, paul) & ![X: $i] : taller(mary, X) & predb(mary) & (~tall(mary)) & ?[X: $i, Y: $i] : ((~(X = fred)) & like(Y, alice) & sibling(X, Y)) & ![X: $i] : richer(X, fred) & like(alice, paul) & ?[X: $i] : ((~room(X)) & (~preda(X))) & ![X: $i, Y: $i] : ((~((~preda(X)) & (~preda(Y)))) \| (X = Y))), inference(or_elim,[status(thm)],[4])). tff(6,plain, (~tall(mary)), inference(and_elim,[status(thm)],[5])). tff(7,plain, (~tall(mary)), inference(modus_ponens,[status(thm)],[6, 1])). tff(8,plain, (((~quiet(mary)) \| (~tall(mary)) \| (~person(mary))) \| tall(mary)), inference(tautology,[status(thm)],[])). tff(9,plain, ((~quiet(mary)) \| (~tall(mary)) \| (~person(mary))), inference(unit_resolution,[status(thm)],[8, 7])). tff(10,plain, (like(alice, mary) <=> like(alice, mary)), inference(rewrite,[status(thm)],[])). tff(11,plain, (like(alice, mary)), inference(and_elim,[status(thm)],[5])). tff(12,plain, (like(alice, mary)), 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, (((~((~quiet(mary)) \| (~tall(mary)) \| (~person(mary)))) \| (~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!4 = \|'fred'\|) \| (X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|) \| (~room(X!4)))) \| (~like(alice, mary))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!4 = \|'fred'\|) \| (X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|) \| (~room(X!4)))) \| (~like(alice, mary)) \| (~((~quiet(mary)) \| (~tall(mary)) \| (~person(mary)))))), inference(rewrite,[status(thm)],[])). tff(23,plain, ((~((X!4 = \|'fred'\|) \| (X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|) \| (~room(X!4)))) <=> (~((X!4 = \|'fred'\|) \| (X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|) \| (~room(X!4))))), inference(rewrite,[status(thm)],[])). tff(24,plain, ((tall(mary) & quiet(mary) & person(mary)) <=> (~((~quiet(mary)) \| (~tall(mary)) \| (~person(mary))))), inference(rewrite,[status(thm)],[])). tff(25,plain, (((tall(mary) & quiet(mary) & person(mary)) \| (~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!4 = \|'fred'\|) \| (X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|) \| (~room(X!4)))) \| (~like(alice, mary))) <=> ((~((~quiet(mary)) \| (~tall(mary)) \| (~person(mary)))) \| (~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!4 = \|'fred'\|) \| (X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|) \| (~room(X!4)))) \| (~like(alice, mary)))), inference(monotonicity,[status(thm)],[24, 23])). tff(26,plain, (((tall(mary) & quiet(mary) & person(mary)) \| (~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!4 = \|'fred'\|) \| (X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|) \| (~room(X!4)))) \| (~like(alice, mary))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!4 = \|'fred'\|) \| (X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|) \| (~room(X!4)))) \| (~like(alice, mary)) \| (~((~quiet(mary)) \| (~tall(mary)) \| (~person(mary)))))), inference(transitivity,[status(thm)],[25, 22])). tff(27,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!4 = \|'fred'\|) \| (X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|) \| (~room(X!4)))) \| (~like(alice, mary)) \| (tall(mary) & quiet(mary) & person(mary))) <=> ((tall(mary) & quiet(mary) & person(mary)) \| (~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!4 = \|'fred'\|) \| (X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|) \| (~room(X!4)))) \| (~like(alice, mary)))), inference(rewrite,[status(thm)],[])). tff(28,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!4 = \|'fred'\|) \| (X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|) \| (~room(X!4)))) \| (~like(alice, mary)) \| (tall(mary) & quiet(mary) & person(mary))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!4 = \|'fred'\|) \| (X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|) \| (~room(X!4)))) \| (~like(alice, mary)) \| (tall(mary) & quiet(mary) & person(mary)))), inference(monotonicity,[status(thm)],[23])). tff(29,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!4 = \|'fred'\|) \| (X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|) \| (~room(X!4)))) \| (~like(alice, mary)) \| (tall(mary) & quiet(mary) & person(mary))) <=> ((tall(mary) & quiet(mary) & person(mary)) \| (~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!4 = \|'fred'\|) \| (X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|) \| (~room(X!4)))) \| (~like(alice, mary)))), inference(transitivity,[status(thm)],[28, 27])). tff(30,plain, ((room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & like(alice, mary) & (~(tall(mary) & quiet(mary) & person(mary)))) <=> (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & like(alice, mary) & (~(tall(mary) & quiet(mary) & person(mary))))), inference(rewrite,[status(thm)],[])). tff(31,plain, ((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & like(alice, mary) & (~(tall(mary) & quiet(mary) & person(mary))))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & like(alice, mary) & (~(tall(mary) & quiet(mary) & person(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))) & like(alice, mary) & (~(tall(mary) & quiet(mary) & person(mary))))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & like(alice, mary) & (~(tall(mary) & quiet(mary) & person(mary)))))), inference(rewrite,[status(thm)],[])). tff(33,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & like(alice, mary) & (~(tall(mary) & quiet(mary) & person(mary))))), inference(or_elim,[status(thm)],[4])). tff(34,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & like(alice, mary) & (~(tall(mary) & quiet(mary) & person(mary))))), inference(modus_ponens,[status(thm)],[33, 31])). tff(35,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & like(alice, mary) & (~(tall(mary) & quiet(mary) & person(mary))))), inference(modus_ponens,[status(thm)],[34, 32])). tff(36,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & like(alice, mary) & (~(tall(mary) & quiet(mary) & person(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 (forall ((X $i)) (or (= X \|'fred'\|) (= X \|'paul'\|) (= X \|'mary'\|) (not (room X))))) (a!5 (not (or (= X!4 \|'fred'\|) (= X!4 \|'paul'\|) (= X!4 \|'mary'\|) (not (room X!4))))) (a!6 (refl (~ (not (like alice mary)) (not (like alice mary))))) (a!7 (refl (~ (and (tall mary) (quiet mary) (person mary)) (and (tall mary) (quiet mary) (person mary)))))) (let ((a!8 (and (room mary) (room paul) (room fred) a!4 (like alice mary) (not (and (tall mary) (quiet mary) (person mary)))))) (let ((a!9 (~ (not a!8) (or (not (room mary)) (not (room paul)) (not (room fred)) a!5 (not (like alice mary)) (and (tall mary) (quiet mary) (person mary)))))) (nnf-neg a!1 a!2 a!3 (sk (~ (not a!4) a!5)) a!6 a!7 a!9))))	room(andrew)&room(seth)&room(preston)&(![X]:(room(X)=>(X='andrew'\|X='seth'\|X='preston')))& ((((tall(preston)&european(preston))&(like(preston,darren)))=>((creative(seth))&(quiet(andrew))))& ((((like(seth,darren))\|(~like(darren,seth))))=>(~quiet(preston)&~quiet(andrew)))& (richer(andrew,darren))& (?[X]:(room(X)=>(like(X,darren))))& (like(darren,preston)&like(darren,andrew))& (![X]:(taller(X,seth)))& (![X]:(taller(andrew,X)))& ((enjoys_watercolor_painting(andrew))&(~tall(andrew)))& (?[X,Y]:((X!=preston)&(like(Y,darren))&(sibling(X,Y))))& (![X]:(richer(X,preston)))& (like(darren,seth))& (((?[X]:(~room(X)&does_not_enjoy_mountain_biking(X)))&(![X,Y]:((does_not_enjoy_mountain_biking(X)&does_not_enjoy_mountain_biking(Y))=>(X=Y))))))	room(andrew)&room(seth)&room(preston)&(![X]:(room(X)=>(X='andrew'\|X='seth'\|X='preston')))& ((like(darren,andrew))&(~(tall(andrew)&quiet(andrew)&person(andrew))))	entailment	contradiction	entailment
Bret is the only person in the room. “Only one person outside the room is not rich” only if “no one outside the room who is hated by Kenneth is not Bret”. “Bret is the richest in the room” unless “no one outside the room is a quiet tourist”. Geraldine and Bret hate each other. Only one person outside the room is not a quiet tourist. Bret hates Geraldine. Bret is the least quiet in the room.	Bret neither is not quiet, not happy, not rich nor is quieter than Kenneth.	entailment	% SZS status Unsatisfiable % SZS output start Proof tff(quieter_type, type, ( quieter: ( $i * $i ) > $o)). tff(lucy_type, type, ( lucy: $i)). tff(tptp_fun__mary__type, type, ( tptp_fun__mary_: $i)). tff(mary_type, type, ( mary: $i)). tff(room_type, type, ( room: $i > $o)). tff(tourist_type, type, ( tourist: $i > $o)). tff(quiet_type, type, ( quiet: $i > $o)). tff(hate_type, type, ( hate: ( $i * $i ) > $o)). tff(john_type, type, ( john: $i)). tff(richer_type, type, ( richer: ( $i * $i ) > $o)). tff(rich_type, type, ( rich: $i > $o)). tff(happy_type, type, ( happy: $i > $o)). tff(susan_type, type, ( susan: $i)). tff(alice_type, type, ( alice: $i)). tff(fred_type, type, ( fred: $i)). tff(paul_type, type, ( paul: $i)). tff(tptp_fun_X_2_type, type, ( tptp_fun_X_2: $i)). tff(tptp_fun_X_3_type, type, ( tptp_fun_X_3: $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] : ((~room(X)) & (~rich(X))) & ![X: $i, Y: $i] : (((~rich(X)) & (~rich(Y))) => (X = Y))) => (~?[X: $i] : ((~room(X)) => (hate(X, lucy) => (~(X = mary)))))) & ((~(~?[X: $i] : ((~room(X)) => (quiet(X) & tourist(X))))) => ![X: $i] : richer(X, mary))) & (hate(john, mary) & hate(mary, john))) & (?[X: $i] : ((~room(X)) & (~(quiet(X) & tourist(X)))) & ![X: $i, Y: $i] : (((~(quiet(X) & tourist(X))) & (~(quiet(Y) & tourist(Y)))) => (X = Y)))) & hate(john, mary)) & ![X: $i] : quieter(mary, X))) => ((room(mary) & ![X: $i] : (room(X) => (X = \|'mary'\|))) & (~((((~quiet(mary)) & (~happy(mary))) & (~rich(mary))) \| quieter(lucy, mary)))))) <=> (~((~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ((~(?[X: $i] : ((~room(X)) & (~rich(X))) & ![X: $i, Y: $i] : ((~((~rich(X)) & (~rich(Y)))) \| (X = Y)))) \| (~?[X: $i] : (room(X) \| (~(X = mary)) \| (~hate(X, lucy))))) & ((~?[X: $i] : (room(X) \| (quiet(X) & tourist(X)))) \| ![X: $i] : richer(X, mary)) & hate(john, mary) & hate(mary, john) & ?[X: $i] : ((~room(X)) & (~(quiet(X) & tourist(X)))) & ![X: $i, Y: $i] : ((~((~(quiet(X) & tourist(X))) & (~(quiet(Y) & tourist(Y))))) \| (X = Y)) & ![X: $i] : quieter(mary, X))) \| (room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~(quieter(lucy, mary) \| ((~quiet(mary)) & (~happy(mary)) & (~rich(mary))))))))), inference(rewrite,[status(thm)],[])). tff(5,axiom,(~(((room(mary) & ![X: $i] : (room(X) => (X = \|'mary'\|))) & (((((((?[X: $i] : ((~room(X)) & (~rich(X))) & ![X: $i, Y: $i] : (((~rich(X)) & (~rich(Y))) => (X = Y))) => (~?[X: $i] : ((~room(X)) => (hate(X, lucy) => (~(X = mary)))))) & ((~(~?[X: $i] : ((~room(X)) => (quiet(X) & tourist(X))))) => ![X: $i] : richer(X, mary))) & (hate(john, mary) & hate(mary, john))) & (?[X: $i] : ((~room(X)) & (~(quiet(X) & tourist(X)))) & ![X: $i, Y: $i] : (((~(quiet(X) & tourist(X))) & (~(quiet(Y) & tourist(Y)))) => (X = Y)))) & hate(john, mary)) & ![X: $i] : quieter(mary, X))) => ((room(mary) & ![X: $i] : (room(X) => (X = \|'mary'\|))) & (~((((~quiet(mary)) & (~happy(mary))) & (~rich(mary))) \| quieter(lucy, mary)))))), file('/mnt/tmpfs//2035283749261098200807117.p','negated')). tff(6,plain, (~((~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ((~(?[X: $i] : ((~room(X)) & (~rich(X))) & ![X: $i, Y: $i] : ((~((~rich(X)) & (~rich(Y)))) \| (X = Y)))) \| (~?[X: $i] : (room(X) \| (~(X = mary)) \| (~hate(X, lucy))))) & ((~?[X: $i] : (room(X) \| (quiet(X) & tourist(X)))) \| ![X: $i] : richer(X, mary)) & hate(john, mary) & hate(mary, john) & ?[X: $i] : ((~room(X)) & (~(quiet(X) & tourist(X)))) & ![X: $i, Y: $i] : ((~((~(quiet(X) & tourist(X))) & (~(quiet(Y) & tourist(Y))))) \| (X = Y)) & ![X: $i] : quieter(mary, X))) \| (room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~(quieter(lucy, mary) \| ((~quiet(mary)) & (~happy(mary)) & (~rich(mary)))))))), inference(modus_ponens,[status(thm)],[5, 4])). tff(7,plain, (room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ((~(?[X: $i] : ((~room(X)) & (~rich(X))) & ![X: $i, Y: $i] : ((~((~rich(X)) & (~rich(Y)))) \| (X = Y)))) \| (~?[X: $i] : (room(X) \| (~(X = mary)) \| (~hate(X, lucy))))) & ((~?[X: $i] : (room(X) \| (quiet(X) & tourist(X)))) \| ![X: $i] : richer(X, mary)) & hate(john, mary) & hate(mary, john) & ?[X: $i] : ((~room(X)) & (~(quiet(X) & tourist(X)))) & ![X: $i, Y: $i] : ((~((~(quiet(X) & tourist(X))) & (~(quiet(Y) & tourist(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, (\|'mary'\| = mary), inference(symmetry,[status(thm)],[18])). tff(20,plain, (quieter(\|'mary'\|, lucy) <=> quieter(mary, lucy)), inference(monotonicity,[status(thm)],[19])). tff(21,plain, (quieter(mary, lucy) <=> quieter(\|'mary'\|, lucy)), inference(symmetry,[status(thm)],[20])). tff(22,plain, (^[X: $i] : refl(quieter(mary, X) <=> quieter(mary, X))), inference(bind,[status(th)],[])). tff(23,plain, (![X: $i] : quieter(mary, X) <=> ![X: $i] : quieter(mary, X)), inference(quant_intro,[status(thm)],[22])). tff(24,plain, (![X: $i] : quieter(mary, X) <=> ![X: $i] : quieter(mary, X)), inference(rewrite,[status(thm)],[])). tff(25,plain, (![X: $i] : quieter(mary, X)), inference(and_elim,[status(thm)],[7])). tff(26,plain, (![X: $i] : quieter(mary, X)), inference(modus_ponens,[status(thm)],[25, 24])). tff(27,plain,( ![X: $i] : quieter(mary, X)), inference(skolemize,[status(sab)],[26])). tff(28,plain, (![X: $i] : quieter(mary, X)), inference(modus_ponens,[status(thm)],[27, 23])). tff(29,plain, ((~![X: $i] : quieter(mary, X)) \| quieter(mary, lucy)), inference(quant_inst,[status(thm)],[])). tff(30,plain, (quieter(mary, lucy)), inference(unit_resolution,[status(thm)],[29, 28])). tff(31,plain, (quieter(\|'mary'\|, lucy)), inference(modus_ponens,[status(thm)],[30, 21])). tff(32,plain, ((lucy = mary) <=> (mary = lucy)), inference(commutativity,[status(thm)],[])). tff(33,plain, ((lucy = \|'mary'\|) <=> (lucy = mary)), inference(monotonicity,[status(thm)],[19])). tff(34,plain, ((lucy = \|'mary'\|) <=> (mary = lucy)), inference(transitivity,[status(thm)],[33, 32])). tff(35,plain, ((mary = lucy) <=> (lucy = \|'mary'\|)), inference(symmetry,[status(thm)],[34])). tff(36,plain, ((~(mary = lucy)) <=> (~(lucy = \|'mary'\|))), inference(monotonicity,[status(thm)],[35])). tff(37,plain, ((~(mary = lucy)) <=> (~(mary = lucy))), 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//2035283749261098200807117.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 = 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)],[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))) & (~(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))) & (~(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)],[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))) & (~(susan = alice))), 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))) & (~(susan = fred))), 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))) & (~(susan = paul))), 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))) & (~(susan = mary))), 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))) & (~(john = lucy))), 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))) & (~(john = susan))), 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))) & (~(john = alice))), 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))) & (~(john = fred))), 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))) & (~(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)],[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))) & (~(alice = lucy))), 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))) & (~(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 = 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)],[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))) & (~(alice = paul))), 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))) & (~(alice = mary))), 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))) & (~(fred = lucy))), 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))) & (~(fred = susan))), 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))) & (~(fred = john))), 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))) & (~(fred = alice))), 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))) & (~(fred = paul))), 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))) & (~(fred = mary))), 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))) & (~(paul = lucy))), 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))) & (~(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 = lucy)), inference(and_elim,[status(thm)],[74])). tff(76,plain, (~(mary = lucy)), inference(modus_ponens,[status(thm)],[75, 37])). tff(77,plain, (~(lucy = \|'mary'\|)), inference(modus_ponens,[status(thm)],[76, 36])). tff(78,plain, (quieter(lucy, \|'mary'\|) <=> quieter(lucy, mary)), inference(monotonicity,[status(thm)],[19])). tff(79,plain, (quieter(lucy, mary) <=> quieter(lucy, \|'mary'\|)), inference(symmetry,[status(thm)],[78])). tff(80,assumption,(~((~quiet(X!2)) \| (~tourist(X!2)))), introduced(assumption)). tff(81,plain, (((~quiet(X!2)) \| (~tourist(X!2))) \| quiet(X!2)), inference(tautology,[status(thm)],[])). tff(82,plain, (quiet(X!2)), inference(unit_resolution,[status(thm)],[81, 80])). tff(83,plain, (((~quiet(X!2)) \| (~tourist(X!2))) \| tourist(X!2)), inference(tautology,[status(thm)],[])). tff(84,plain, (tourist(X!2)), inference(unit_resolution,[status(thm)],[83, 80])). tff(85,plain, ((~(~((~quiet(X!2)) \| (~tourist(X!2))))) <=> ((~quiet(X!2)) \| (~tourist(X!2)))), inference(rewrite,[status(thm)],[])). tff(86,plain, ((quiet(X!2) & tourist(X!2)) <=> (~((~quiet(X!2)) \| (~tourist(X!2))))), inference(rewrite,[status(thm)],[])). tff(87,plain, ((~(quiet(X!2) & tourist(X!2))) <=> (~(~((~quiet(X!2)) \| (~tourist(X!2)))))), inference(monotonicity,[status(thm)],[86])). tff(88,plain, ((~(quiet(X!2) & tourist(X!2))) <=> ((~quiet(X!2)) \| (~tourist(X!2)))), inference(transitivity,[status(thm)],[87, 85])). tff(89,plain, (?[X: $i] : ((~room(X)) & (~(quiet(X) & tourist(X)))) <=> ?[X: $i] : ((~room(X)) & (~(quiet(X) & tourist(X))))), inference(rewrite,[status(thm)],[])). tff(90,plain, (?[X: $i] : ((~room(X)) & (~(quiet(X) & tourist(X))))), inference(and_elim,[status(thm)],[7])). tff(91,plain, (?[X: $i] : ((~room(X)) & (~(quiet(X) & tourist(X))))), inference(modus_ponens,[status(thm)],[90, 89])). tff(92,plain,( (~room(X!2)) & (~(quiet(X!2) & tourist(X!2)))), inference(skolemize,[status(sab)],[91])). tff(93,plain, (~(quiet(X!2) & tourist(X!2))), inference(and_elim,[status(thm)],[92])). tff(94,plain, ((~quiet(X!2)) \| (~tourist(X!2))), inference(modus_ponens,[status(thm)],[93, 88])). tff(95,plain, ($false), inference(unit_resolution,[status(thm)],[94, 84, 82])). tff(96,plain,((~quiet(X!2)) \| (~tourist(X!2))), inference(lemma,lemma(discharge,[]))). tff(97,assumption,(~quiet(\|'mary'\|)), introduced(assumption)). tff(98,plain, (((~quiet(\|'mary'\|)) \| (~tourist(\|'mary'\|))) \| quiet(\|'mary'\|)), inference(tautology,[status(thm)],[])). tff(99,plain, ((~quiet(\|'mary'\|)) \| (~tourist(\|'mary'\|))), inference(unit_resolution,[status(thm)],[98, 97])). tff(100,assumption,((~quiet(X!2)) \| (~tourist(X!2))), introduced(assumption)). tff(101,assumption,(X!2 = \|'mary'\|), introduced(assumption)). tff(102,plain, (X!2 = mary), inference(transitivity,[status(thm)],[101, 19])). tff(103,plain, (room(X!2) <=> room(mary)), inference(monotonicity,[status(thm)],[102])). tff(104,plain, (room(mary) <=> room(X!2)), inference(symmetry,[status(thm)],[103])). tff(105,plain, (room(X!2)), inference(modus_ponens,[status(thm)],[14, 104])). tff(106,plain, (~room(X!2)), inference(and_elim,[status(thm)],[92])). tff(107,plain, ($false), inference(unit_resolution,[status(thm)],[106, 105])). tff(108,plain,(~(X!2 = \|'mary'\|)), inference(lemma,lemma(discharge,[]))). tff(109,plain, (^[X: $i, Y: $i] : refl(((X = Y) \| (~((~quiet(Y)) \| (~tourist(Y)))) \| (~((~quiet(X)) \| (~tourist(X))))) <=> ((X = Y) \| (~((~quiet(Y)) \| (~tourist(Y)))) \| (~((~quiet(X)) \| (~tourist(X))))))), inference(bind,[status(th)],[])). tff(110,plain, (![X: $i, Y: $i] : ((X = Y) \| (~((~quiet(Y)) \| (~tourist(Y)))) \| (~((~quiet(X)) \| (~tourist(X))))) <=> ![X: $i, Y: $i] : ((X = Y) \| (~((~quiet(Y)) \| (~tourist(Y)))) \| (~((~quiet(X)) \| (~tourist(X)))))), inference(quant_intro,[status(thm)],[109])). tff(111,plain, (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((quiet(X) & tourist(X)) <=> (~((~quiet(X)) \| (~tourist(X))))), ((~(quiet(X) & tourist(X))) <=> (~(~((~quiet(X)) \| (~tourist(X))))))), rewrite((~(~((~quiet(X)) \| (~tourist(X))))) <=> ((~quiet(X)) \| (~tourist(X)))), ((~(quiet(X) & tourist(X))) <=> ((~quiet(X)) \| (~tourist(X))))), trans(monotonicity(rewrite((quiet(Y) & tourist(Y)) <=> (~((~quiet(Y)) \| (~tourist(Y))))), ((~(quiet(Y) & tourist(Y))) <=> (~(~((~quiet(Y)) \| (~tourist(Y))))))), rewrite((~(~((~quiet(Y)) \| (~tourist(Y))))) <=> ((~quiet(Y)) \| (~tourist(Y)))), ((~(quiet(Y) & tourist(Y))) <=> ((~quiet(Y)) \| (~tourist(Y))))), (((~(quiet(X) & tourist(X))) & (~(quiet(Y) & tourist(Y)))) <=> (((~quiet(X)) \| (~tourist(X))) & ((~quiet(Y)) \| (~tourist(Y)))))), rewrite((((~quiet(X)) \| (~tourist(X))) & ((~quiet(Y)) \| (~tourist(Y)))) <=> (~((~((~quiet(Y)) \| (~tourist(Y)))) \| (~((~quiet(X)) \| (~tourist(X))))))), (((~(quiet(X) & tourist(X))) & (~(quiet(Y) & tourist(Y)))) <=> (~((~((~quiet(Y)) \| (~tourist(Y)))) \| (~((~quiet(X)) \| (~tourist(X)))))))), ((~((~(quiet(X) & tourist(X))) & (~(quiet(Y) & tourist(Y))))) <=> (~(~((~((~quiet(Y)) \| (~tourist(Y)))) \| (~((~quiet(X)) \| (~tourist(X))))))))), rewrite((~(~((~((~quiet(Y)) \| (~tourist(Y)))) \| (~((~quiet(X)) \| (~tourist(X))))))) <=> ((~((~quiet(Y)) \| (~tourist(Y)))) \| (~((~quiet(X)) \| (~tourist(X)))))), ((~((~(quiet(X) & tourist(X))) & (~(quiet(Y) & tourist(Y))))) <=> ((~((~quiet(Y)) \| (~tourist(Y)))) \| (~((~quiet(X)) \| (~tourist(X))))))), (((~((~(quiet(X) & tourist(X))) & (~(quiet(Y) & tourist(Y))))) \| (X = Y)) <=> (((~((~quiet(Y)) \| (~tourist(Y)))) \| (~((~quiet(X)) \| (~tourist(X))))) \| (X = Y)))), rewrite((((~((~quiet(Y)) \| (~tourist(Y)))) \| (~((~quiet(X)) \| (~tourist(X))))) \| (X = Y)) <=> ((X = Y) \| (~((~quiet(Y)) \| (~tourist(Y)))) \| (~((~quiet(X)) \| (~tourist(X)))))), (((~((~(quiet(X) & tourist(X))) & (~(quiet(Y) & tourist(Y))))) \| (X = Y)) <=> ((X = Y) \| (~((~quiet(Y)) \| (~tourist(Y)))) \| (~((~quiet(X)) \| (~tourist(X)))))))), inference(bind,[status(th)],[])). tff(112,plain, (![X: $i, Y: $i] : ((~((~(quiet(X) & tourist(X))) & (~(quiet(Y) & tourist(Y))))) \| (X = Y)) <=> ![X: $i, Y: $i] : ((X = Y) \| (~((~quiet(Y)) \| (~tourist(Y)))) \| (~((~quiet(X)) \| (~tourist(X)))))), inference(quant_intro,[status(thm)],[111])). tff(113,plain, (![X: $i, Y: $i] : ((~((~(quiet(X) & tourist(X))) & (~(quiet(Y) & tourist(Y))))) \| (X = Y)) <=> ![X: $i, Y: $i] : ((~((~(quiet(X) & tourist(X))) & (~(quiet(Y) & tourist(Y))))) \| (X = Y))), inference(rewrite,[status(thm)],[])). tff(114,plain, (![X: $i, Y: $i] : ((~((~(quiet(X) & tourist(X))) & (~(quiet(Y) & tourist(Y))))) \| (X = Y))), inference(and_elim,[status(thm)],[7])). tff(115,plain, (![X: $i, Y: $i] : ((~((~(quiet(X) & tourist(X))) & (~(quiet(Y) & tourist(Y))))) \| (X = Y))), inference(modus_ponens,[status(thm)],[114, 113])). tff(116,plain,( ![X: $i, Y: $i] : ((~((~(quiet(X) & tourist(X))) & (~(quiet(Y) & tourist(Y))))) \| (X = Y))), inference(skolemize,[status(sab)],[115])). tff(117,plain, (![X: $i, Y: $i] : ((X = Y) \| (~((~quiet(Y)) \| (~tourist(Y)))) \| (~((~quiet(X)) \| (~tourist(X)))))), inference(modus_ponens,[status(thm)],[116, 112])). tff(118,plain, (![X: $i, Y: $i] : ((X = Y) \| (~((~quiet(Y)) \| (~tourist(Y)))) \| (~((~quiet(X)) \| (~tourist(X)))))), inference(modus_ponens,[status(thm)],[117, 110])). tff(119,plain, (((~![X: $i, Y: $i] : ((X = Y) \| (~((~quiet(Y)) \| (~tourist(Y)))) \| (~((~quiet(X)) \| (~tourist(X)))))) \| ((~((~quiet(X!2)) \| (~tourist(X!2)))) \| (~((~quiet(\|'mary'\|)) \| (~tourist(\|'mary'\|)))) \| (X!2 = \|'mary'\|))) <=> ((~![X: $i, Y: $i] : ((X = Y) \| (~((~quiet(Y)) \| (~tourist(Y)))) \| (~((~quiet(X)) \| (~tourist(X)))))) \| (~((~quiet(X!2)) \| (~tourist(X!2)))) \| (~((~quiet(\|'mary'\|)) \| (~tourist(\|'mary'\|)))) \| (X!2 = \|'mary'\|))), inference(rewrite,[status(thm)],[])). tff(120,plain, (((X!2 = \|'mary'\|) \| (~((~quiet(\|'mary'\|)) \| (~tourist(\|'mary'\|)))) \| (~((~quiet(X!2)) \| (~tourist(X!2))))) <=> ((~((~quiet(X!2)) \| (~tourist(X!2)))) \| (~((~quiet(\|'mary'\|)) \| (~tourist(\|'mary'\|)))) \| (X!2 = \|'mary'\|))), inference(rewrite,[status(thm)],[])). tff(121,plain, (((~![X: $i, Y: $i] : ((X = Y) \| (~((~quiet(Y)) \| (~tourist(Y)))) \| (~((~quiet(X)) \| (~tourist(X)))))) \| ((X!2 = \|'mary'\|) \| (~((~quiet(\|'mary'\|)) \| (~tourist(\|'mary'\|)))) \| (~((~quiet(X!2)) \| (~tourist(X!2)))))) <=> ((~![X: $i, Y: $i] : ((X = Y) \| (~((~quiet(Y)) \| (~tourist(Y)))) \| (~((~quiet(X)) \| (~tourist(X)))))) \| ((~((~quiet(X!2)) \| (~tourist(X!2)))) \| (~((~quiet(\|'mary'\|)) \| (~tourist(\|'mary'\|)))) \| (X!2 = \|'mary'\|)))), inference(monotonicity,[status(thm)],[120])). tff(122,plain, (((~![X: $i, Y: $i] : ((X = Y) \| (~((~quiet(Y)) \| (~tourist(Y)))) \| (~((~quiet(X)) \| (~tourist(X)))))) \| ((X!2 = \|'mary'\|) \| (~((~quiet(\|'mary'\|)) \| (~tourist(\|'mary'\|)))) \| (~((~quiet(X!2)) \| (~tourist(X!2)))))) <=> ((~![X: $i, Y: $i] : ((X = Y) \| (~((~quiet(Y)) \| (~tourist(Y)))) \| (~((~quiet(X)) \| (~tourist(X)))))) \| (~((~quiet(X!2)) \| (~tourist(X!2)))) \| (~((~quiet(\|'mary'\|)) \| (~tourist(\|'mary'\|)))) \| (X!2 = \|'mary'\|))), inference(transitivity,[status(thm)],[121, 119])). tff(123,plain, ((~![X: $i, Y: $i] : ((X = Y) \| (~((~quiet(Y)) \| (~tourist(Y)))) \| (~((~quiet(X)) \| (~tourist(X)))))) \| ((X!2 = \|'mary'\|) \| (~((~quiet(\|'mary'\|)) \| (~tourist(\|'mary'\|)))) \| (~((~quiet(X!2)) \| (~tourist(X!2)))))), inference(quant_inst,[status(thm)],[])). tff(124,plain, ((~![X: $i, Y: $i] : ((X = Y) \| (~((~quiet(Y)) \| (~tourist(Y)))) \| (~((~quiet(X)) \| (~tourist(X)))))) \| (~((~quiet(X!2)) \| (~tourist(X!2)))) \| (~((~quiet(\|'mary'\|)) \| (~tourist(\|'mary'\|)))) \| (X!2 = \|'mary'\|)), inference(modus_ponens,[status(thm)],[123, 122])). tff(125,plain, ($false), inference(unit_resolution,[status(thm)],[124, 118, 108, 100, 99])). tff(126,plain,((~((~quiet(X!2)) \| (~tourist(X!2)))) \| quiet(\|'mary'\|)), inference(lemma,lemma(discharge,[]))). tff(127,plain, (quiet(\|'mary'\|)), inference(unit_resolution,[status(thm)],[126, 96])). tff(128,plain, (quiet(\|'mary'\|) <=> quiet(mary)), inference(monotonicity,[status(thm)],[19])). tff(129,plain, (quiet(mary) <=> quiet(\|'mary'\|)), inference(symmetry,[status(thm)],[128])). tff(130,plain, ((~quiet(mary)) <=> (~quiet(\|'mary'\|))), inference(monotonicity,[status(thm)],[129])). tff(131,assumption,(~quiet(mary)), introduced(assumption)). tff(132,plain, (~quiet(\|'mary'\|)), inference(modus_ponens,[status(thm)],[131, 130])). tff(133,assumption,(quiet(\|'mary'\|)), introduced(assumption)). tff(134,plain, ($false), inference(unit_resolution,[status(thm)],[133, 132])). tff(135,plain,((~quiet(\|'mary'\|)) \| quiet(mary)), inference(lemma,lemma(discharge,[]))). tff(136,plain, (quiet(mary)), inference(unit_resolution,[status(thm)],[135, 127])). tff(137,plain, ((quiet(mary) \| happy(mary) \| rich(mary)) \| (~quiet(mary))), inference(tautology,[status(thm)],[])). tff(138,plain, (quiet(mary) \| happy(mary) \| rich(mary)), inference(unit_resolution,[status(thm)],[137, 136])). tff(139,assumption,(~((~room(X!3)) \| (X!3 = \|'mary'\|))), introduced(assumption)). tff(140,plain, (((~room(X!3)) \| (X!3 = \|'mary'\|)) \| (~(X!3 = \|'mary'\|))), inference(tautology,[status(thm)],[])). tff(141,plain, (~(X!3 = \|'mary'\|)), inference(unit_resolution,[status(thm)],[140, 139])). tff(142,plain, (((~room(X!3)) \| (X!3 = \|'mary'\|)) \| room(X!3)), inference(tautology,[status(thm)],[])). tff(143,plain, (room(X!3)), inference(unit_resolution,[status(thm)],[142, 139])). tff(144,plain, (((~![X: $i] : ((~room(X)) \| (X = \|'mary'\|))) \| ((~room(X!3)) \| (X!3 = \|'mary'\|))) <=> ((~![X: $i] : ((~room(X)) \| (X = \|'mary'\|))) \| (~room(X!3)) \| (X!3 = \|'mary'\|))), inference(rewrite,[status(thm)],[])). tff(145,plain, ((~![X: $i] : ((~room(X)) \| (X = \|'mary'\|))) \| ((~room(X!3)) \| (X!3 = \|'mary'\|))), inference(quant_inst,[status(thm)],[])). tff(146,plain, ((~![X: $i] : ((~room(X)) \| (X = \|'mary'\|))) \| (~room(X!3)) \| (X!3 = \|'mary'\|)), inference(modus_ponens,[status(thm)],[145, 144])). tff(147,plain, ($false), inference(unit_resolution,[status(thm)],[146, 11, 143, 141])). tff(148,plain,((~room(X!3)) \| (X!3 = \|'mary'\|)), inference(lemma,lemma(discharge,[]))). tff(149,plain, ((quieter(lucy, mary) \| (~(quiet(mary) \| happy(mary) \| rich(mary))) \| (~room(mary)) \| (~((~room(X!3)) \| (X!3 = \|'mary'\|)))) <=> (quieter(lucy, mary) \| (~room(mary)) \| (~((~room(X!3)) \| (X!3 = \|'mary'\|))) \| (~(quiet(mary) \| happy(mary) \| rich(mary))))), inference(rewrite,[status(thm)],[])). tff(150,plain, (((~quiet(mary)) & (~happy(mary)) & (~rich(mary))) <=> (~(quiet(mary) \| happy(mary) \| rich(mary)))), inference(rewrite,[status(thm)],[])). tff(151,plain, ((quieter(lucy, mary) \| ((~quiet(mary)) & (~happy(mary)) & (~rich(mary))) \| (~room(mary)) \| (~((~room(X!3)) \| (X!3 = \|'mary'\|)))) <=> (quieter(lucy, mary) \| (~(quiet(mary) \| happy(mary) \| rich(mary))) \| (~room(mary)) \| (~((~room(X!3)) \| (X!3 = \|'mary'\|))))), inference(monotonicity,[status(thm)],[150])). tff(152,plain, ((quieter(lucy, mary) \| ((~quiet(mary)) & (~happy(mary)) & (~rich(mary))) \| (~room(mary)) \| (~((~room(X!3)) \| (X!3 = \|'mary'\|)))) <=> (quieter(lucy, mary) \| (~room(mary)) \| (~((~room(X!3)) \| (X!3 = \|'mary'\|))) \| (~(quiet(mary) \| happy(mary) \| rich(mary))))), inference(transitivity,[status(thm)],[151, 149])). tff(153,plain, (((~room(mary)) \| (~((~room(X!3)) \| (X!3 = \|'mary'\|))) \| (quieter(lucy, mary) \| ((~quiet(mary)) & (~happy(mary)) & (~rich(mary))))) <=> (quieter(lucy, mary) \| ((~quiet(mary)) & (~happy(mary)) & (~rich(mary))) \| (~room(mary)) \| (~((~room(X!3)) \| (X!3 = \|'mary'\|))))), inference(rewrite,[status(thm)],[])). tff(154,plain, ((room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~(quieter(lucy, mary) \| ((~quiet(mary)) & (~happy(mary)) & (~rich(mary)))))) <=> (room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~(quieter(lucy, mary) \| ((~quiet(mary)) & (~happy(mary)) & (~rich(mary))))))), inference(rewrite,[status(thm)],[])). tff(155,plain, ((~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~(quieter(lucy, mary) \| ((~quiet(mary)) & (~happy(mary)) & (~rich(mary))))))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~(quieter(lucy, mary) \| ((~quiet(mary)) & (~happy(mary)) & (~rich(mary)))))))), inference(monotonicity,[status(thm)],[154])). tff(156,plain, ((~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~(quieter(lucy, mary) \| ((~quiet(mary)) & (~happy(mary)) & (~rich(mary))))))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~(quieter(lucy, mary) \| ((~quiet(mary)) & (~happy(mary)) & (~rich(mary)))))))), inference(rewrite,[status(thm)],[])). tff(157,plain, (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~(quieter(lucy, mary) \| ((~quiet(mary)) & (~happy(mary)) & (~rich(mary))))))), inference(or_elim,[status(thm)],[6])). tff(158,plain, (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~(quieter(lucy, mary) \| ((~quiet(mary)) & (~happy(mary)) & (~rich(mary))))))), inference(modus_ponens,[status(thm)],[157, 155])). tff(159,plain, (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~(quieter(lucy, mary) \| ((~quiet(mary)) & (~happy(mary)) & (~rich(mary))))))), inference(modus_ponens,[status(thm)],[158, 156])). tff(160,plain, (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~(quieter(lucy, mary) \| ((~quiet(mary)) & (~happy(mary)) & (~rich(mary))))))), inference(modus_ponens,[status(thm)],[159, 155])). unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary))))) (a!2 (forall ((X $i)) (or (not (room X)) (= X \|'mary'\|)))) (a!3 (not (or (not (room X!3)) (= X!3 \|'mary'\|)))) (a!4 (or (quieter lucy mary) (and (not (quiet mary)) (not (happy mary)) (not (rich mary)))))) (let ((a!5 (~ (not (and (room mary) a!2 (not a!4))) (or (not (room mary)) a!3 a!4)))) (nnf-neg a!1 (sk (~ (not a!2) a!3)) (refl (~ a!4 a!4)) a!5)))	room(bret)&(![X]:(room(X)=>(X='bret')))& (((((?[X]:(~room(X)&~rich(X)))&(![X,Y]:((~rich(X)&~rich(Y))=>(X=Y)))))=>(~?[X]:(~room(X)=>(((hate(X,kenneth))=>(X!=bret))))))& (~(~?[X]:(~room(X)=>(quiet(X)&tourist(X))))=>(![X]:(richer(X,bret))))& ((hate(geraldine,bret) & hate(bret,geraldine)))& (((?[X]:(~room(X)&~(quiet(X)&tourist(X))))&(![X,Y]:((~(quiet(X)&tourist(X))&~(quiet(Y)&tourist(Y)))=>(X=Y)))))& (hate(geraldine,bret))& (![X]:(quieter(bret,X))))	room(bret)&(![X]:(room(X)=>(X='bret')))& (~((~quiet(bret)&~happy(bret)&~rich(bret))\|(quieter(kenneth,bret))))	contradiction	contradiction	contradiction
Gregory, Ryan, Betty are the only persons in the room. Ryan does not hate Vivian and is a rich brave european. It is not the case that 'Afton is richer than Gregory'. Only one person outside the room is not quiet, not creative, not brave, not happy. Ryan and Gregory are respectively rich and quiet. Gregory is the richest in the room. Betty is richer than Afton.	Ryan neither is not rich, not creative, not quiet nor is not a creative quiet european.	neutral	% SZS status Satisfiable	room(gregory)&room(ryan)&room(betty)&(![X]:(room(X)=>(X='gregory'\|X='ryan'\|X='betty')))& (((~hate(vivian,ryan))&(rich(ryan)&brave(ryan)&european(ryan)))& (~(richer(gregory,afton)))& (((?[X]:(~room(X)&~quiet(X)&~creative(X)&~brave(X)&~happy(X)))&(![X,Y]:((~quiet(X)&~creative(X)&~brave(X)&~happy(X)&~quiet(Y)&~creative(Y)&~brave(Y)&~happy(Y))=>(X=Y)))))& ((rich(ryan))&(quiet(gregory)))& (![X]:(richer(X,gregory)))& (richer(afton,betty)))	room(gregory)&room(ryan)&room(betty)&(![X]:(room(X)=>(X='gregory'\|X='ryan'\|X='betty')))& (~((~rich(ryan)&~creative(ryan)&~quiet(ryan))\|(~(creative(ryan)&quiet(ryan)&european(ryan)))))	entailment	entailment	entailment
Olivia, Ruby are the only persons in the room. If "Olivia is hated by Terry" then "Olivia is the tallest in the room". Olivia is the tallest in the room. Someone who is not Olivia hate someone who is not rich.	Olivia does not hate Terry or hates Terry 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(rich_type, type, ( rich: $i > $o)). tff(mary_type, type, ( mary: $i)). tff(taller_type, type, ( taller: ( $i * $i ) > $o)). tff(lucy_type, type, ( lucy: $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'\|)))) & (((hate(mary, lucy) => ![X: $i] : taller(X, mary)) & ![X: $i] : taller(X, mary)) & ?[X: $i, Y: $i] : (((~(X = mary)) & (~rich(Y))) & hate(X, Y)))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = \|'mary'\|) \| (X = \|'paul'\|)))) & ((~hate(lucy, mary)) \| hate(lucy, mary))))) <=> (~((~(room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((~hate(mary, lucy)) \| ![X: $i] : taller(X, mary)) & ![X: $i] : taller(X, mary) & ?[X: $i, Y: $i] : ((~(X = mary)) & (~rich(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'\|)))) & (((hate(mary, lucy) => ![X: $i] : taller(X, mary)) & ![X: $i] : taller(X, mary)) & ?[X: $i, Y: $i] : (((~(X = mary)) & (~rich(Y))) & hate(X, Y)))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = \|'mary'\|) \| (X = \|'paul'\|)))) & ((~hate(lucy, mary)) \| hate(lucy, mary))))), file('/mnt/tmpfs//8205494026256371386644709.p','negated')). tff(4,plain, (~((~(room(mary) & room(paul) & ![X: $i] : ((X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((~hate(mary, lucy)) \| ![X: $i] : taller(X, mary)) & ![X: $i] : taller(X, mary) & ?[X: $i, Y: $i] : ((~(X = mary)) & (~rich(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))) & ((~hate(mary, lucy)) \| ![X: $i] : taller(X, mary)) & ![X: $i] : taller(X, mary) & ?[X: $i, Y: $i] : ((~(X = mary)) & (~rich(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(olivia)&room(ruby)&(![X]:(room(X)=>(X='olivia'\|X='ruby')))& (((hate(olivia,terry))=>(![X]:(taller(X,olivia))))& (![X]:(taller(X,olivia)))& (?[X,Y]:((X!=olivia)&(~rich(Y))&(hate(X,Y)))))	room(olivia)&room(ruby)&(![X]:(room(X)=>(X='olivia'\|X='ruby')))& (((~hate(terry,olivia))\|(hate(terry,olivia))))	contradiction	neutral	neutral
Mark is the only person in the room. 'Mark is the richest in the room' if 'Rick and Mark like each other'. Rick is a client of Mark. Mark is not liked by Tameika. More than one person outside the room is not liked by Rick. Mark is the quietest in the room. Mark is the least rich in the room. Rick is richer than Mark. Mark is liked by Rick and is not rich.	Someone who does not like Rick is richer than someone who is not a rich tourist.	entailment	% SZS status Unsatisfiable % SZS output start Proof tff(richer_type, type, ( richer: ( $i * $i ) > $o)). tff(mary_type, type, ( mary: $i)). tff(susan_type, type, ( susan: $i)). tff(tptp_fun__mary__type, type, ( tptp_fun__mary_: $i)). tff(room_type, type, ( room: $i > $o)). tff(rich_type, type, ( rich: $i > $o)). tff(like_type, type, ( like: ( $i * $i ) > $o)). tff(paul_type, type, ( paul: $i)). tff(quieter_type, type, ( quieter: ( $i * $i ) > $o)). tff(client_type, type, ( client: ( $i * $i ) > $o)). tff(tourist_type, type, ( tourist: $i > $o)). tff(john_type, type, ( john: $i)). tff(alice_type, type, ( alice: $i)). tff(fred_type, type, ( fred: $i)). tff(lucy_type, type, ( lucy: $i)). tff(tptp_fun_X_2_type, type, ( tptp_fun_X_2: $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'\|))) & (((((((((like(paul, mary) & like(mary, paul)) => ![X: $i] : richer(X, mary)) & client(mary, paul)) & (~like(mary, susan))) & ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & ((~like(X, paul)) & (~like(Y, paul)))) & (~(X = Y)))) & ![X: $i] : quieter(X, mary)) & ![X: $i] : richer(mary, X)) & richer(mary, paul)) & (like(mary, paul) & (~rich(mary))))) => ((room(mary) & ![X: $i] : (room(X) => (X = \|'mary'\|))) & ?[X: $i, Y: $i] : (((~like(paul, X)) & (~(rich(Y) & tourist(Y)))) & richer(X, Y))))) <=> (~((~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ((~(like(paul, mary) & like(mary, paul))) \| ![X: $i] : richer(X, mary)) & client(mary, paul) & (~like(mary, susan)) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~like(X, paul)) & (~like(Y, paul)) & (~(X = Y))) & ![X: $i] : quieter(X, mary) & ![X: $i] : richer(mary, X) & richer(mary, paul) & like(mary, paul) & (~rich(mary)))) \| (room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ?[X: $i, Y: $i] : ((~like(paul, X)) & (~(rich(Y) & tourist(Y))) & richer(X, Y)))))), inference(rewrite,[status(thm)],[])). tff(5,axiom,(~(((room(mary) & ![X: $i] : (room(X) => (X = \|'mary'\|))) & (((((((((like(paul, mary) & like(mary, paul)) => ![X: $i] : richer(X, mary)) & client(mary, paul)) & (~like(mary, susan))) & ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & ((~like(X, paul)) & (~like(Y, paul)))) & (~(X = Y)))) & ![X: $i] : quieter(X, mary)) & ![X: $i] : richer(mary, X)) & richer(mary, paul)) & (like(mary, paul) & (~rich(mary))))) => ((room(mary) & ![X: $i] : (room(X) => (X = \|'mary'\|))) & ?[X: $i, Y: $i] : (((~like(paul, X)) & (~(rich(Y) & tourist(Y)))) & richer(X, Y))))), file('/mnt/tmpfs//5032550460116761665319131.p','negated')). tff(6,plain, (~((~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ((~(like(paul, mary) & like(mary, paul))) \| ![X: $i] : richer(X, mary)) & client(mary, paul) & (~like(mary, susan)) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~like(X, paul)) & (~like(Y, paul)) & (~(X = Y))) & ![X: $i] : quieter(X, mary) & ![X: $i] : richer(mary, X) & richer(mary, paul) & like(mary, paul) & (~rich(mary)))) \| (room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ?[X: $i, Y: $i] : ((~like(paul, X)) & (~(rich(Y) & tourist(Y))) & richer(X, Y))))), inference(modus_ponens,[status(thm)],[5, 4])). tff(7,plain, (room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ((~(like(paul, mary) & like(mary, paul))) \| ![X: $i] : richer(X, mary)) & client(mary, paul) & (~like(mary, susan)) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~like(X, paul)) & (~like(Y, paul)) & (~(X = Y))) & ![X: $i] : quieter(X, mary) & ![X: $i] : richer(mary, X) & richer(mary, paul) & like(mary, paul) & (~rich(mary))), 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, (richer(susan, mary) <=> richer(susan, \|'mary'\|)), inference(monotonicity,[status(thm)],[18])). tff(20,plain, (richer(susan, \|'mary'\|) <=> richer(susan, mary)), inference(symmetry,[status(thm)],[19])). tff(21,plain, ((~richer(susan, \|'mary'\|)) <=> (~richer(susan, mary))), inference(monotonicity,[status(thm)],[20])). tff(22,plain, (richer(mary, susan) <=> richer(\|'mary'\|, susan)), inference(monotonicity,[status(thm)],[18])). tff(23,plain, (^[X: $i] : refl(richer(mary, X) <=> richer(mary, X))), inference(bind,[status(th)],[])). tff(24,plain, (![X: $i] : richer(mary, X) <=> ![X: $i] : richer(mary, X)), inference(quant_intro,[status(thm)],[23])). tff(25,plain, (![X: $i] : richer(mary, X) <=> ![X: $i] : richer(mary, X)), inference(rewrite,[status(thm)],[])). tff(26,plain, (![X: $i] : richer(mary, X)), inference(and_elim,[status(thm)],[7])). tff(27,plain, (![X: $i] : richer(mary, X)), inference(modus_ponens,[status(thm)],[26, 25])). tff(28,plain,( ![X: $i] : richer(mary, X)), inference(skolemize,[status(sab)],[27])). tff(29,plain, (![X: $i] : richer(mary, X)), inference(modus_ponens,[status(thm)],[28, 24])). tff(30,plain, ((~![X: $i] : richer(mary, X)) \| richer(mary, susan)), inference(quant_inst,[status(thm)],[])). tff(31,plain, (richer(mary, susan)), inference(unit_resolution,[status(thm)],[30, 29])). tff(32,plain, (richer(\|'mary'\|, susan)), inference(modus_ponens,[status(thm)],[31, 22])). tff(33,plain, ((susan = mary) <=> (mary = susan)), inference(commutativity,[status(thm)],[])). tff(34,plain, (\|'mary'\| = mary), inference(symmetry,[status(thm)],[18])). tff(35,plain, ((susan = \|'mary'\|) <=> (susan = mary)), inference(monotonicity,[status(thm)],[34])). tff(36,plain, ((susan = \|'mary'\|) <=> (mary = susan)), inference(transitivity,[status(thm)],[35, 33])). tff(37,plain, ((mary = susan) <=> (susan = \|'mary'\|)), inference(symmetry,[status(thm)],[36])). tff(38,plain, ((~(mary = susan)) <=> (~(susan = \|'mary'\|))), inference(monotonicity,[status(thm)],[37])). tff(39,plain, ((~(mary = susan)) <=> (~(mary = susan))), inference(rewrite,[status(thm)],[])). tff(40,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//5032550460116761665319131.p','b14')). 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))) & (~(lucy = alice))) & (~(lucy = john))), inference(and_elim,[status(thm)],[40])). tff(42,plain, ((((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(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)],[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))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = 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))) & (~(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)],[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))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = 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))) & (~(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)],[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))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))), 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))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))), 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))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = 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))) & (~(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)],[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))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = 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))) & (~(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)],[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))) & (~(john = fred))) & (~(john = alice))) & (~(john = 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))) & (~(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)],[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))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))), 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))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = 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))) & (~(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)],[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))) & (~(alice = susan))) & (~(alice = 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))) & (~(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)],[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))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = 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))) & (~(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)],[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))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))), 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))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))), 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))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))), 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))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))), 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))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))), 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))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))), 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))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))), 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))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))), 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))) & (~(paul = susan))) & (~(paul = lucy))), 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))) & (~(paul = john))) & (~(paul = susan))), 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))) & (~(paul = alice))) & (~(paul = john))), inference(and_elim,[status(thm)],[71])). tff(73,plain, (((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))), inference(and_elim,[status(thm)],[72])). tff(74,plain, ((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))), inference(and_elim,[status(thm)],[73])). tff(75,plain, (((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))), inference(and_elim,[status(thm)],[74])). tff(76,plain, ((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))), inference(and_elim,[status(thm)],[75])). tff(77,plain, (((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))), inference(and_elim,[status(thm)],[76])). tff(78,plain, (~(mary = susan)), inference(and_elim,[status(thm)],[77])). tff(79,plain, (~(mary = susan)), inference(modus_ponens,[status(thm)],[78, 39])). tff(80,plain, (~(susan = \|'mary'\|)), inference(modus_ponens,[status(thm)],[79, 38])). tff(81,plain, (![X: $i, Y: $i] : ((X = Y) \| (~richer(Y, X)) \| (~richer(X, Y))) <=> ![X: $i, Y: $i] : ((X = Y) \| (~richer(Y, X)) \| (~richer(X, Y)))), inference(rewrite,[status(thm)],[])). tff(82,plain, (![X: $i, Y: $i] : ((X = Y) \| (~richer(Y, X)) \| (~richer(X, Y))) <=> ![X: $i, Y: $i] : ((X = Y) \| (~richer(Y, X)) \| (~richer(X, Y)))), inference(rewrite,[status(thm)],[])). tff(83,plain, (^[X: $i, Y: $i] : trans(monotonicity(rewrite((richer(X, Y) => (~richer(Y, X))) <=> ((~richer(Y, X)) \| (~richer(X, Y)))), (((~(X = Y)) => (richer(X, Y) => (~richer(Y, X)))) <=> ((~(X = Y)) => ((~richer(Y, X)) \| (~richer(X, Y)))))), rewrite(((~(X = Y)) => ((~richer(Y, X)) \| (~richer(X, Y)))) <=> ((X = Y) \| (~richer(Y, X)) \| (~richer(X, Y)))), (((~(X = Y)) => (richer(X, Y) => (~richer(Y, X)))) <=> ((X = Y) \| (~richer(Y, X)) \| (~richer(X, Y)))))), inference(bind,[status(th)],[])). tff(84,plain, (![X: $i, Y: $i] : ((~(X = Y)) => (richer(X, Y) => (~richer(Y, X)))) <=> ![X: $i, Y: $i] : ((X = Y) \| (~richer(Y, X)) \| (~richer(X, Y)))), inference(quant_intro,[status(thm)],[83])). tff(85,axiom,(![X: $i, Y: $i] : ((~(X = Y)) => (richer(X, Y) => (~richer(Y, X))))), file('/mnt/tmpfs//5032550460116761665319131.p','b7')). tff(86,plain, (![X: $i, Y: $i] : ((X = Y) \| (~richer(Y, X)) \| (~richer(X, Y)))), inference(modus_ponens,[status(thm)],[85, 84])). tff(87,plain, (![X: $i, Y: $i] : ((X = Y) \| (~richer(Y, X)) \| (~richer(X, Y)))), inference(modus_ponens,[status(thm)],[86, 82])). tff(88,plain,( ![X: $i, Y: $i] : ((X = Y) \| (~richer(Y, X)) \| (~richer(X, Y)))), inference(skolemize,[status(sab)],[87])). tff(89,plain, (![X: $i, Y: $i] : ((X = Y) \| (~richer(Y, X)) \| (~richer(X, Y)))), inference(modus_ponens,[status(thm)],[88, 81])). tff(90,plain, (((~![X: $i, Y: $i] : ((X = Y) \| (~richer(Y, X)) \| (~richer(X, Y)))) \| ((~richer(susan, \|'mary'\|)) \| (susan = \|'mary'\|) \| (~richer(\|'mary'\|, susan)))) <=> ((~![X: $i, Y: $i] : ((X = Y) \| (~richer(Y, X)) \| (~richer(X, Y)))) \| (~richer(susan, \|'mary'\|)) \| (susan = \|'mary'\|) \| (~richer(\|'mary'\|, susan)))), inference(rewrite,[status(thm)],[])). tff(91,plain, (((susan = \|'mary'\|) \| (~richer(\|'mary'\|, susan)) \| (~richer(susan, \|'mary'\|))) <=> ((~richer(susan, \|'mary'\|)) \| (susan = \|'mary'\|) \| (~richer(\|'mary'\|, susan)))), inference(rewrite,[status(thm)],[])). tff(92,plain, (((~![X: $i, Y: $i] : ((X = Y) \| (~richer(Y, X)) \| (~richer(X, Y)))) \| ((susan = \|'mary'\|) \| (~richer(\|'mary'\|, susan)) \| (~richer(susan, \|'mary'\|)))) <=> ((~![X: $i, Y: $i] : ((X = Y) \| (~richer(Y, X)) \| (~richer(X, Y)))) \| ((~richer(susan, \|'mary'\|)) \| (susan = \|'mary'\|) \| (~richer(\|'mary'\|, susan))))), inference(monotonicity,[status(thm)],[91])). tff(93,plain, (((~![X: $i, Y: $i] : ((X = Y) \| (~richer(Y, X)) \| (~richer(X, Y)))) \| ((susan = \|'mary'\|) \| (~richer(\|'mary'\|, susan)) \| (~richer(susan, \|'mary'\|)))) <=> ((~![X: $i, Y: $i] : ((X = Y) \| (~richer(Y, X)) \| (~richer(X, Y)))) \| (~richer(susan, \|'mary'\|)) \| (susan = \|'mary'\|) \| (~richer(\|'mary'\|, susan)))), inference(transitivity,[status(thm)],[92, 90])). tff(94,plain, ((~![X: $i, Y: $i] : ((X = Y) \| (~richer(Y, X)) \| (~richer(X, Y)))) \| ((susan = \|'mary'\|) \| (~richer(\|'mary'\|, susan)) \| (~richer(susan, \|'mary'\|)))), inference(quant_inst,[status(thm)],[])). tff(95,plain, ((~![X: $i, Y: $i] : ((X = Y) \| (~richer(Y, X)) \| (~richer(X, Y)))) \| (~richer(susan, \|'mary'\|)) \| (susan = \|'mary'\|) \| (~richer(\|'mary'\|, susan))), inference(modus_ponens,[status(thm)],[94, 93])). tff(96,plain, ((~richer(susan, \|'mary'\|)) \| (susan = \|'mary'\|) \| (~richer(\|'mary'\|, susan))), inference(unit_resolution,[status(thm)],[95, 89])). tff(97,plain, ((~richer(susan, \|'mary'\|)) \| (~richer(\|'mary'\|, susan))), inference(unit_resolution,[status(thm)],[96, 80])). tff(98,plain, (~richer(susan, \|'mary'\|)), inference(unit_resolution,[status(thm)],[97, 32])). tff(99,plain, (~richer(susan, mary)), inference(modus_ponens,[status(thm)],[98, 21])). tff(100,plain, (like(paul, \|'mary'\|) <=> like(paul, mary)), inference(monotonicity,[status(thm)],[34])). tff(101,plain, (richer(\|'mary'\|, \|'mary'\|) <=> richer(mary, \|'mary'\|)), inference(monotonicity,[status(thm)],[34])). tff(102,plain, (richer(mary, \|'mary'\|) <=> richer(\|'mary'\|, \|'mary'\|)), inference(symmetry,[status(thm)],[101])). tff(103,plain, ((~![X: $i] : richer(mary, X)) \| richer(mary, \|'mary'\|)), inference(quant_inst,[status(thm)],[])). tff(104,plain, (richer(mary, \|'mary'\|)), inference(unit_resolution,[status(thm)],[103, 29])). tff(105,plain, (richer(\|'mary'\|, \|'mary'\|)), inference(modus_ponens,[status(thm)],[104, 102])). tff(106,plain, (rich(\|'mary'\|) <=> rich(mary)), inference(monotonicity,[status(thm)],[34])). tff(107,plain, (rich(mary) <=> rich(\|'mary'\|)), inference(symmetry,[status(thm)],[106])). tff(108,plain, ((~rich(mary)) <=> (~rich(\|'mary'\|))), inference(monotonicity,[status(thm)],[107])). tff(109,plain, ((~rich(mary)) <=> (~rich(mary))), inference(rewrite,[status(thm)],[])). tff(110,plain, (~rich(mary)), inference(and_elim,[status(thm)],[7])). tff(111,plain, (~rich(mary)), inference(modus_ponens,[status(thm)],[110, 109])). tff(112,plain, (~rich(\|'mary'\|)), inference(modus_ponens,[status(thm)],[111, 108])). tff(113,plain, (((~rich(\|'mary'\|)) \| (~tourist(\|'mary'\|))) \| rich(\|'mary'\|)), inference(tautology,[status(thm)],[])). tff(114,plain, ((~rich(\|'mary'\|)) \| (~tourist(\|'mary'\|))), inference(unit_resolution,[status(thm)],[113, 112])). tff(115,assumption,(~((~room(X!2)) \| (X!2 = \|'mary'\|))), introduced(assumption)). tff(116,plain, (((~room(X!2)) \| (X!2 = \|'mary'\|)) \| (~(X!2 = \|'mary'\|))), inference(tautology,[status(thm)],[])). tff(117,plain, (~(X!2 = \|'mary'\|)), inference(unit_resolution,[status(thm)],[116, 115])). tff(118,plain, (((~room(X!2)) \| (X!2 = \|'mary'\|)) \| room(X!2)), inference(tautology,[status(thm)],[])). tff(119,plain, (room(X!2)), inference(unit_resolution,[status(thm)],[118, 115])). tff(120,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(121,plain, ((~![X: $i] : ((~room(X)) \| (X = \|'mary'\|))) \| ((~room(X!2)) \| (X!2 = \|'mary'\|))), inference(quant_inst,[status(thm)],[])). tff(122,plain, ((~![X: $i] : ((~room(X)) \| (X = \|'mary'\|))) \| (~room(X!2)) \| (X!2 = \|'mary'\|)), inference(modus_ponens,[status(thm)],[121, 120])). tff(123,plain, ($false), inference(unit_resolution,[status(thm)],[122, 11, 119, 117])). tff(124,plain,((~room(X!2)) \| (X!2 = \|'mary'\|)), inference(lemma,lemma(discharge,[]))). tff(125,plain, (((~room(mary)) \| (~((~room(X!2)) \| (X!2 = \|'mary'\|))) \| ![X: $i, Y: $i] : (like(paul, X) \| (~richer(X, Y)) \| (~((~rich(Y)) \| (~tourist(Y)))))) <=> ((~room(mary)) \| (~((~room(X!2)) \| (X!2 = \|'mary'\|))) \| ![X: $i, Y: $i] : (like(paul, X) \| (~richer(X, Y)) \| (~((~rich(Y)) \| (~tourist(Y))))))), inference(rewrite,[status(thm)],[])). tff(126,plain, (((~room(mary)) \| (~((~room(X!2)) \| (X!2 = \|'mary'\|))) \| ![X: $i, Y: $i] : (~((~like(paul, X)) & (~(rich(Y) & tourist(Y))) & richer(X, Y)))) <=> ((~room(mary)) \| (~((~room(X!2)) \| (X!2 = \|'mary'\|))) \| ![X: $i, Y: $i] : (like(paul, X) \| (~richer(X, Y)) \| (~((~rich(Y)) \| (~tourist(Y))))))), inference(rewrite,[status(thm)],[])). tff(127,plain, (((~room(mary)) \| (~((~room(X!2)) \| (X!2 = \|'mary'\|))) \| ![X: $i, Y: $i] : (~((~like(paul, X)) & (~(rich(Y) & tourist(Y))) & richer(X, Y)))) <=> ((~room(mary)) \| (~((~room(X!2)) \| (X!2 = \|'mary'\|))) \| ![X: $i, Y: $i] : (~((~like(paul, X)) & (~(rich(Y) & tourist(Y))) & richer(X, Y))))), inference(rewrite,[status(thm)],[])). tff(128,plain, ((room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ?[X: $i, Y: $i] : ((~like(paul, X)) & (~(rich(Y) & tourist(Y))) & richer(X, Y))) <=> (room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ?[X: $i, Y: $i] : ((~like(paul, X)) & (~(rich(Y) & tourist(Y))) & richer(X, Y)))), inference(rewrite,[status(thm)],[])). tff(129,plain, ((~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ?[X: $i, Y: $i] : ((~like(paul, X)) & (~(rich(Y) & tourist(Y))) & richer(X, Y)))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ?[X: $i, Y: $i] : ((~like(paul, X)) & (~(rich(Y) & tourist(Y))) & richer(X, Y))))), inference(monotonicity,[status(thm)],[128])). tff(130,plain, ((~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ?[X: $i, Y: $i] : ((~like(paul, X)) & (~(rich(Y) & tourist(Y))) & richer(X, Y)))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ?[X: $i, Y: $i] : ((~like(paul, X)) & (~(rich(Y) & tourist(Y))) & richer(X, Y))))), inference(rewrite,[status(thm)],[])). tff(131,plain, (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ?[X: $i, Y: $i] : ((~like(paul, X)) & (~(rich(Y) & tourist(Y))) & richer(X, Y)))), inference(or_elim,[status(thm)],[6])). tff(132,plain, (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ?[X: $i, Y: $i] : ((~like(paul, X)) & (~(rich(Y) & tourist(Y))) & richer(X, Y)))), inference(modus_ponens,[status(thm)],[131, 129])). tff(133,plain, (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ?[X: $i, Y: $i] : ((~like(paul, X)) & (~(rich(Y) & tourist(Y))) & richer(X, Y)))), inference(modus_ponens,[status(thm)],[132, 130])). tff(134,plain, (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ?[X: $i, Y: $i] : ((~like(paul, X)) & (~(rich(Y) & tourist(Y))) & richer(X, Y)))), inference(modus_ponens,[status(thm)],[133, 129])). unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary))))) (a!2 (forall ((X $i)) (or (not (room X)) (= X \|'mary'\|)))) (a!3 (not (or (not (room X!2)) (= X!2 \|'mary'\|)))) (a!4 (lambda ((X $i) (Y $i)) (let ((a!1 (and (not (like paul X)) (not (and (rich Y) (tourist Y))) (richer X Y)))) (refl (~ (not a!1) (not a!1)))))) (a!5 (exists ((X $i) (Y $i)) (and (not (like paul X)) (not (and (rich Y) (tourist Y))) (richer X Y)))) (a!6 (forall ((X $i) (Y $i)) (let ((a!1 (and (not (like paul X)) (not (and (rich Y) (tourist Y))) (richer 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(mark)&(![X]:(room(X)=>(X='mark')))& ((((like(rick,mark) & like(mark,rick)))=>(![X]:(richer(X,mark))))& (client(mark,rick))& (~like(mark,tameika))& ((?[X,Y]:(~room(X)&~room(Y)&(~like(X,rick)&~like(Y,rick))&(X!=Y))))& (![X]:(quieter(X,mark)))& (![X]:(richer(mark,X)))& (richer(mark,rick))& ((like(mark,rick))&(~rich(mark))))	room(mark)&(![X]:(room(X)=>(X='mark')))& (?[X,Y]:((~like(rick,X))&(~(rich(Y)&tourist(Y)))&(richer(X,Y))))	contradiction	neutral	neutral
“Jacque is not a tall person” if “Timothy is taller than Lauren”. Timothy is taller than Michael. Jacque is a quiet person.	Jacque is hated by Timothy or is a tall quiet european or both.	neutral	% SZS status Satisfiable	room(michael)&room(jacque)&room(lauren)&room(robert)&(![X]:(room(X)=>(X='michael'\|X='jacque'\|X='lauren'\|X='robert')))& (((taller(lauren,timothy))=>(~(tall(jacque)&person(jacque))))& (taller(michael,timothy))& (quiet(jacque)&person(jacque)))	room(michael)&room(jacque)&room(lauren)&room(robert)&(![X]:(room(X)=>(X='michael'\|X='jacque'\|X='lauren'\|X='robert')))& (((hate(jacque,timothy))\|(tall(jacque)&quiet(jacque)&european(jacque))))	neutral	entailment	neutral
Dorothy who is not liked by Dave, likes Dave.	Dorothy is not liked by Dave.	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(like_type, type, ( like: ( $i * $i ) > $o)). tff(lucy_type, type, ( lucy: $i)). tff(fred_type, type, ( fred: $i)). tff(alice_type, type, ( alice: $i)). tff(paul_type, type, ( paul: $i)). tff(mary_type, type, ( mary: $i)). tff(1,plain, ((~like(fred, lucy)) <=> (~like(fred, 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'\|)))) & ((~like(fred, lucy)) & like(lucy, fred))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)) \| (X = \|'alice'\|)))) & (~like(fred, lucy))))) <=> (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~like(fred, lucy)) & like(lucy, fred))) \| (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~like(fred, 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'\|)))) & ((~like(fred, lucy)) & like(lucy, fred))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)) \| (X = \|'alice'\|)))) & (~like(fred, lucy))))), file('/mnt/tmpfs//52933916311353811320550.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(fred, lucy)) & like(lucy, fred))) \| (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~like(fred, 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))) & (~like(fred, lucy)) & like(lucy, fred)), inference(or_elim,[status(thm)],[4])). tff(6,plain, (~like(fred, lucy)), inference(and_elim,[status(thm)],[5])). tff(7,plain, (~like(fred, lucy)), inference(modus_ponens,[status(thm)],[6, 1])). tff(8,plain, (room(alice) <=> room(alice)), inference(rewrite,[status(thm)],[])). tff(9,plain, (room(alice)), inference(and_elim,[status(thm)],[5])). tff(10,plain, (room(alice)), inference(modus_ponens,[status(thm)],[9, 8])). tff(11,plain, (room(fred) <=> room(fred)), inference(rewrite,[status(thm)],[])). tff(12,plain, (room(fred)), inference(and_elim,[status(thm)],[5])). tff(13,plain, (room(fred)), inference(modus_ponens,[status(thm)],[12, 11])). tff(14,plain, (room(paul) <=> room(paul)), inference(rewrite,[status(thm)],[])). tff(15,plain, (room(paul)), inference(and_elim,[status(thm)],[5])). tff(16,plain, (room(paul)), inference(modus_ponens,[status(thm)],[15, 14])). tff(17,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(18,plain, (room(mary)), inference(and_elim,[status(thm)],[5])). tff(19,plain, (room(mary)), inference(modus_ponens,[status(thm)],[18, 17])). tff(20,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~room(alice)) \| (~((X!0 = \|'alice'\|) \| (X!0 = \|'fred'\|) \| (X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0)))) \| like(fred, lucy)) <=> (like(fred, lucy) \| (~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(21,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(22,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~room(alice)) \| (~((X!0 = \|'alice'\|) \| (X!0 = \|'fred'\|) \| (X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0)))) \| like(fred, lucy)) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~room(alice)) \| (~((X!0 = \|'alice'\|) \| (X!0 = \|'fred'\|) \| (X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (~room(X!0)))) \| like(fred, lucy))), inference(monotonicity,[status(thm)],[21])). 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)))) \| like(fred, lucy)) <=> (like(fred, lucy) \| (~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)],[22, 20])). tff(24,plain, ((room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~like(fred, lucy))) <=> (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~like(fred, lucy)))), inference(rewrite,[status(thm)],[])). tff(25,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~like(fred, lucy)))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~like(fred, lucy))))), inference(monotonicity,[status(thm)],[24])). tff(26,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~like(fred, lucy)))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~like(fred, lucy))))), 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))) & (~like(fred, lucy)))), inference(or_elim,[status(thm)],[4])). tff(28,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~like(fred, lucy)))), inference(modus_ponens,[status(thm)],[27, 25])). tff(29,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (~like(fred, lucy)))), 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))) & (~like(fred, lucy)))), inference(modus_ponens,[status(thm)],[29, 25])). 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)))))) (let ((a!7 (not (and (room mary) (room paul) (room fred) (room alice) a!5 (not (like fred lucy)))))) (let ((a!8 (~ a!7 (or (not (room mary)) (not (room paul)) (not (room fred)) (not (room alice)) a!6 (like fred lucy))))) (nnf-neg a!1 a!2 a!3 a!4 (sk (~ (not a!5) a!6)) (refl (~ (like fred lucy) (like fred lucy))) a!8))))	room(deborah)&room(richard)&room(dorothy)&room(esther)&(![X]:(room(X)=>(X='deborah'\|X='richard'\|X='dorothy'\|X='esther')))& ((~like(dorothy,dave))&(like(dave,dorothy)))	room(deborah)&room(richard)&room(dorothy)&room(esther)&(![X]:(room(X)=>(X='deborah'\|X='richard'\|X='dorothy'\|X='esther')))& (~like(dorothy,dave))	entailment	contradiction	entailment
Josephine, Allison are the only persons in the room. Allison likes Samantha or is a sibling of Samantha or both if Samantha is a sibling of Allison and vice versa. More than one person in the room is not liked by Samantha if no one in the room who is not Allison does not like Samantha. If Josephine is not liked by Samantha or is not quiet or both then Allison is the least quiet in the room. More than one person in the room is not liked by Samantha. Allison is the least quiet in the room. Allison and Josephine are happy quiet tourist. Samantha is quieter than Josephine. Allison does not travel domestically frequently. Josephine who does not like Samantha, is not liked by Samantha.	Josephine is not a quiet tall person and is quieter than Samantha.	contradiction	-	room(josephine)&room(allison)&(![X]:(room(X)=>(X='josephine'\|X='allison')))& (((sibling(allison,samantha))<=>(((like(samantha,allison))\|(sibling(samantha,allison)))))& ((~?[X]:(room(X)=>(((X!=allison)=>(~like(samantha,X))))))=>((?[X,Y]:(room(X)&room(Y)&(~like(X,samantha)&~like(Y,samantha))&(X!=Y)))))& ((((~like(josephine,samantha))\|(~quiet(josephine))))=>(![X]:(quieter(allison,X))))& ((?[X,Y]:(room(X)&room(Y)&(~like(X,samantha)&~like(Y,samantha))&(X!=Y))))& (![X]:(quieter(allison,X)))& (happy(allison)&quiet(allison)&tourist(allison)&happy(josephine)&quiet(josephine)&tourist(josephine))& (quieter(josephine,samantha))& (does_not_travel_domestically_frequently(allison))& ((~like(samantha,josephine))&(~like(josephine,samantha))))	room(josephine)&room(allison)&(![X]:(room(X)=>(X='josephine'\|X='allison')))& ((~(quiet(josephine)&tall(josephine)&person(josephine)))&(quieter(samantha,josephine)))	neutral	entailment	contradiction
Regina, Dale, Jack, Tracy are the only persons in the room. 'Someone who is not quiet is taller than someone who is not a creative person' unless 'it is not the case that 'Jack is the least tall in the room''. If 'only one person outside the room is a sibling of Henry' then 'someone who is a client of Microsoft is quieter than someone who is not Regina'. 'Jack is a brave tall creative european and is not a creative european' if 'Dale is the least tall in the room' and vice versa. 'Henry is a sibling of Tracy' if 'Jack either is a creative tall european or is a client of Microsoft' and vice versa. Regina is the least tall in the room. It is not the case that 'no one outside the room who is quieter than Henry is not a brave european'. Everyone outside the room is not a tall quiet brave creative european. More than one person outside the room is not Jack. Everyone outside the room is not a client of Microsoft. Tracy is not Jack.	Tracy who is not creative, is a quiet tall person.	neutral	% SZS status Satisfiable	room(regina)&room(dale)&room(jack)&room(tracy)&(![X]:(room(X)=>(X='regina'\|X='dale'\|X='jack'\|X='tracy')))& ((~(~(![X]:(taller(jack,X))))=>(?[X,Y]:((~quiet(X))&(~(creative(Y)&person(Y)))&(taller(X,Y)))))& ((((?[X]:(~room(X)&sibling(henry,X)))&(![X,Y]:((sibling(henry,X)&sibling(henry,Y))=>(X=Y)))))=>(?[X,Y]:((is_a_client_of_Microsoft(X))&(Y!=regina)&(quieter(X,Y)))))& ((![X]:(taller(dale,X)))<=>((brave(jack)&tall(jack)&creative(jack)&european(jack))&(~(creative(jack)&european(jack)))))& (((((creative(jack)&tall(jack)&european(jack))\|(is_a_client_of_Microsoft(jack)))&(~((creative(jack)&tall(jack)&european(jack))\|(is_a_client_of_Microsoft(jack))))))<=>(sibling(tracy,henry)))& (![X]:(taller(regina,X)))& (~(~?[X]:(~room(X)=>(((quieter(henry,X))=>(~(brave(X)&european(X))))))))& (![X]:(~room(X)=>(~(tall(X)&quiet(X)&brave(X)&creative(X)&european(X)))))& ((?[X,Y]:(~room(X)&~room(Y)&(X!=jack&Y!=jack)&(X!=Y))))& (![X]:(~room(X)=>(is_not_a_client_of_Microsoft(X))))& (tracy!=jack))	room(regina)&room(dale)&room(jack)&room(tracy)&(![X]:(room(X)=>(X='regina'\|X='dale'\|X='jack'\|X='tracy')))& ((~creative(tracy))&(quiet(tracy)&tall(tracy)&person(tracy)))	neutral	contradiction	contradiction
Josephine, Carmen, Madeline, Rita are the only persons in the room. Only one person outside the room is a quiet brave tall person if only one person outside the room is not quiet. Someone outside the room does not like Marisol if Madeline is a client of Marisol or is not liked by Marisol or both. Madeline is a tall quiet brave person and enjoys gardening. Madeline is the tallest in the room. Madeline is not a quiet person or enjoys gardening or both. Someone outside the room does not like Marisol. Someone outside the room does not like Marisol.	Rita who is a tall brave person, is a client of Randy.	neutral	% SZS status Satisfiable	room(josephine)&room(carmen)&room(madeline)&room(rita)&(![X]:(room(X)=>(X='josephine'\|X='carmen'\|X='madeline'\|X='rita')))& (((((?[X]:(~room(X)&~quiet(X)))&(![X,Y]:((~quiet(X)&~quiet(Y))=>(X=Y)))))=>(((?[X]:(~room(X)&quiet(X)&brave(X)&tall(X)&person(X)))&(![X,Y]:((quiet(X)&brave(X)&tall(X)&person(X)&quiet(Y)&brave(Y)&tall(Y)&person(Y))=>(X=Y))))))& ((((client(marisol,madeline))\|(~like(madeline,marisol))))=>(?[X]:(~room(X)=>(~like(marisol,X)))))& ((tall(madeline)&quiet(madeline)&brave(madeline)&person(madeline))&(enjoys_gardening(madeline)))& (![X]:(taller(X,madeline)))& (((~(quiet(madeline)&person(madeline)))\|(enjoys_gardening(madeline))))& (?[X]:(~room(X)=>(~like(marisol,X))))& (?[X]:(~room(X)=>(~like(marisol,X)))))	room(josephine)&room(carmen)&room(madeline)&room(rita)&(![X]:(room(X)=>(X='josephine'\|X='carmen'\|X='madeline'\|X='rita')))& ((tall(rita)&brave(rita)&person(rita))&(client(randy,rita)))	neutral	neutral	contradiction
Michael, Donna, Ana, Sasha are the only persons in the room. Sasha likes Gary and is a brave european. Donna who does not like Gary, does not collect comic books. Everyone outside the room who is not Ana likes Gary. Michael is not liked by Gary or does not like Gary or both. Michael is the richest in the room. Sasha likes Gary and is not rich, not creative. Only one person in the room does not collect comic books. Donna and Michael like each other. Sasha is liked by Gary or is not Ana or both.	Michael is a creative happy brave european and is liked by Gary.	neutral	% SZS status Satisfiable	room(michael)&room(donna)&room(ana)&room(sasha)&(![X]:(room(X)=>(X='michael'\|X='donna'\|X='ana'\|X='sasha')))& (((like(gary,sasha))&(brave(sasha)&european(sasha)))& ((~like(gary,donna))&(does_not_collect_comic_books(donna)))& (![X]:(~room(X)=>(((X!=ana)=>(like(gary,X))))))& (((~like(michael,gary))\|(~like(gary,michael))))& (![X]:(richer(X,michael)))& ((like(gary,sasha))&(~rich(sasha)&~creative(sasha)))& (((?[X]:(room(X)&does_not_collect_comic_books(X)))&(![X,Y]:((does_not_collect_comic_books(X)&does_not_collect_comic_books(Y))=>(X=Y)))))& ((like(donna,michael) & like(michael,donna)))& (((like(sasha,gary))\|(sasha!=ana))))	room(michael)&room(donna)&room(ana)&room(sasha)&(![X]:(room(X)=>(X='michael'\|X='donna'\|X='ana'\|X='sasha')))& ((creative(michael)&happy(michael)&brave(michael)&european(michael))&(like(michael,gary)))	contradiction	contradiction	contradiction
Duane, Jerold, Mark, Cody are the only persons in the room. “Cody is a sibling of Earl and is not a rich brave quiet tall european” if “Jerold and Duane are not creative, not quiet”. “Duane who is not hated by Erin, does not hate Earl” if “someone outside the room who is hated by Erin is a quiet creative tall european”. Jerold and Cody are not creative. Jerold is the quietest in the room. Duane is not hated by Erin or is not a tall european or both. Everyone outside the room is not creative, not brave.	Mark neither is not quiet, not creative, not brave nor likes Erin.	neutral	% SZS status Satisfiable	room(duane)&room(jerold)&room(mark)&room(cody)&(![X]:(room(X)=>(X='duane'\|X='jerold'\|X='mark'\|X='cody')))& (((~creative(jerold)&~quiet(jerold)&~creative(duane)&~quiet(duane))=>((sibling(earl,cody))&(~(rich(cody)&brave(cody)&quiet(cody)&tall(cody)&european(cody)))))& ((?[X]:(~room(X)=>(((hate(X,erin))=>(quiet(X)&creative(X)&tall(X)&european(X))))))=>((~hate(duane,erin))&(~hate(earl,duane))))& (~creative(jerold)&~creative(cody))& (![X]:(quieter(X,jerold)))& (((~hate(duane,erin))\|(~(tall(duane)&european(duane)))))& (![X]:(~room(X)=>(~creative(X)&~brave(X)))))	room(duane)&room(jerold)&room(mark)&room(cody)&(![X]:(room(X)=>(X='duane'\|X='jerold'\|X='mark'\|X='cody')))& (~((~quiet(mark)&~creative(mark)&~brave(mark))\|(like(erin,mark))))	neutral	neutral	contradiction
William, Robert are the only persons in the room. Only one person in the room is not tall, not happy, not creative.	Robert is not creative or is not tall or both.	neutral	% SZS status Satisfiable	room(william)&room(robert)&(![X]:(room(X)=>(X='william'\|X='robert')))& (((?[X]:(room(X)&~tall(X)&~happy(X)&~creative(X)))&(![X,Y]:((~tall(X)&~happy(X)&~creative(X)&~tall(Y)&~happy(Y)&~creative(Y))=>(X=Y)))))	room(william)&room(robert)&(![X]:(room(X)=>(X='william'\|X='robert')))& (((~creative(robert))\|(~tall(robert))))	entailment	entailment	contradiction
Deborah, Matthew, Charlene, Margaret are the only persons in the room. Everyone in the room who is not a tall tourist is not liked by Marie. Only one person in the room is not liked by Marie. Someone who is liked by Marie is a client of someone who is not Matthew. Only one person outside the room is not happy, not tall.	Someone who is not a creative happy tourist like someone who likes Marie.	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_X_0_type, type, ( tptp_fun_X_0: $i)). tff(tptp_fun__paul__type, type, ( tptp_fun__paul_: $i)). tff(tptp_fun__mary__type, type, ( tptp_fun__mary_: $i)). tff(like_type, type, ( like: ( $i * $i ) > $o)). tff(lucy_type, type, ( lucy: $i)). tff(tall_type, type, ( tall: $i > $o)). tff(happy_type, type, ( happy: $i > $o)). tff(client_type, type, ( client: ( $i * $i ) > $o)). tff(paul_type, type, ( paul: $i)). tff(tourist_type, type, ( tourist: $i > $o)). 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(creative_type, type, ( creative: $i > $o)). tff(john_type, type, ( john: $i)). tff(susan_type, type, ( susan: $i)). tff(tptp_fun_X_4_type, type, ( tptp_fun_X_4: $i)). tff(1,assumption,(X!0 = \|'mary'\|), introduced(assumption)). tff(2,plain, (\|'mary'\| = X!0), inference(symmetry,[status(thm)],[1])). tff(3,plain, (like(\|'mary'\|, lucy) <=> like(X!0, lucy)), inference(monotonicity,[status(thm)],[2])). tff(4,plain, (like(X!0, lucy) <=> like(\|'mary'\|, lucy)), inference(symmetry,[status(thm)],[3])). tff(5,plain, ((~like(X!0, lucy)) <=> (~like(\|'mary'\|, lucy))), inference(monotonicity,[status(thm)],[4])). tff(6,plain, (?[X: $i] : (room(X) & (~like(X, lucy))) <=> ?[X: $i] : (room(X) & (~like(X, lucy)))), inference(rewrite,[status(thm)],[])). tff(7,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) => ((~(tall(X) & tourist(X))) => (~like(X, lucy)))) & (?[X: $i] : (room(X) & (~like(X, lucy))) & ![X: $i, Y: $i] : (((~like(X, lucy)) & (~like(Y, lucy))) => (X = Y)))) & ?[X: $i, Y: $i] : ((like(X, lucy) & (~(Y = paul))) & client(X, Y))) & (?[X: $i] : (((~room(X)) & (~happy(X))) & (~tall(X))) & ![X: $i, Y: $i] : (((((~happy(X)) & (~tall(X))) & (~happy(Y))) & (~tall(Y))) => (X = Y))))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)) \| (X = \|'alice'\|)))) & ?[X: $i, Y: $i] : (((~((creative(X) & happy(X)) & tourist(X))) & like(lucy, Y)) & like(X, Y))))) <=> (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ![X: $i] : ((~like(X, lucy)) \| (tall(X) & tourist(X)) \| (~room(X))) & ?[X: $i] : (room(X) & (~like(X, lucy))) & ![X: $i, Y: $i] : ((~((~like(X, lucy)) & (~like(Y, lucy)))) \| (X = Y)) & ?[X: $i, Y: $i] : (like(X, lucy) & (~(Y = paul)) & client(X, Y)) & ?[X: $i] : ((~room(X)) & (~happy(X)) & (~tall(X))) & ![X: $i, Y: $i] : ((~((~happy(X)) & (~tall(X)) & (~happy(Y)) & (~tall(Y)))) \| (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] : ((~(creative(X) & happy(X) & tourist(X))) & like(lucy, Y) & like(X, Y)))))), inference(rewrite,[status(thm)],[])). tff(8,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) => ((~(tall(X) & tourist(X))) => (~like(X, lucy)))) & (?[X: $i] : (room(X) & (~like(X, lucy))) & ![X: $i, Y: $i] : (((~like(X, lucy)) & (~like(Y, lucy))) => (X = Y)))) & ?[X: $i, Y: $i] : ((like(X, lucy) & (~(Y = paul))) & client(X, Y))) & (?[X: $i] : (((~room(X)) & (~happy(X))) & (~tall(X))) & ![X: $i, Y: $i] : (((((~happy(X)) & (~tall(X))) & (~happy(Y))) & (~tall(Y))) => (X = Y))))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)) \| (X = \|'alice'\|)))) & ?[X: $i, Y: $i] : (((~((creative(X) & happy(X)) & tourist(X))) & like(lucy, Y)) & like(X, Y))))), file('/mnt/tmpfs//1154774462978702311438543.p','negated')). 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] : ((~like(X, lucy)) \| (tall(X) & tourist(X)) \| (~room(X))) & ?[X: $i] : (room(X) & (~like(X, lucy))) & ![X: $i, Y: $i] : ((~((~like(X, lucy)) & (~like(Y, lucy)))) \| (X = Y)) & ?[X: $i, Y: $i] : (like(X, lucy) & (~(Y = paul)) & client(X, Y)) & ?[X: $i] : ((~room(X)) & (~happy(X)) & (~tall(X))) & ![X: $i, Y: $i] : ((~((~happy(X)) & (~tall(X)) & (~happy(Y)) & (~tall(Y)))) \| (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] : ((~(creative(X) & happy(X) & tourist(X))) & like(lucy, Y) & like(X, Y))))), inference(modus_ponens,[status(thm)],[8, 7])). tff(10,plain, (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ![X: $i] : ((~like(X, lucy)) \| (tall(X) & tourist(X)) \| (~room(X))) & ?[X: $i] : (room(X) & (~like(X, lucy))) & ![X: $i, Y: $i] : ((~((~like(X, lucy)) & (~like(Y, lucy)))) \| (X = Y)) & ?[X: $i, Y: $i] : (like(X, lucy) & (~(Y = paul)) & client(X, Y)) & ?[X: $i] : ((~room(X)) & (~happy(X)) & (~tall(X))) & ![X: $i, Y: $i] : ((~((~happy(X)) & (~tall(X)) & (~happy(Y)) & (~tall(Y)))) \| (X = Y))), inference(or_elim,[status(thm)],[9])). tff(11,plain, (?[X: $i] : (room(X) & (~like(X, lucy)))), inference(and_elim,[status(thm)],[10])). tff(12,plain, (?[X: $i] : (room(X) & (~like(X, lucy)))), inference(modus_ponens,[status(thm)],[11, 6])). tff(13,plain,( room(X!0) & (~like(X!0, lucy))), inference(skolemize,[status(sab)],[12])). tff(14,plain, (~like(X!0, lucy)), inference(and_elim,[status(thm)],[13])). tff(15,plain, (~like(\|'mary'\|, lucy)), inference(modus_ponens,[status(thm)],[14, 5])). tff(16,plain, ((lucy = \|'mary'\|) <=> (lucy = X!0)), inference(monotonicity,[status(thm)],[2])). tff(17,plain, ((lucy = X!0) <=> (lucy = \|'mary'\|)), inference(symmetry,[status(thm)],[16])). tff(18,plain, ((~(lucy = X!0)) <=> (~(lucy = \|'mary'\|))), inference(monotonicity,[status(thm)],[17])). tff(19,plain, ((fred = mary) <=> (mary = fred)), inference(commutativity,[status(thm)],[])). tff(20,assumption,(lucy = X!0), introduced(assumption)). tff(21,plain, ((lucy = fred) <=> (fred = lucy)), inference(commutativity,[status(thm)],[])). tff(22,assumption,(~(paul = \|'mary'\|)), introduced(assumption)). tff(23,plain, ((alice = mary) <=> (mary = alice)), inference(commutativity,[status(thm)],[])). tff(24,assumption,(~(mary = \|'fred'\|)), introduced(assumption)). tff(25,plain, ((lucy = paul) <=> (paul = lucy)), inference(commutativity,[status(thm)],[])). tff(26,plain, ((paul = mary) <=> (mary = paul)), inference(commutativity,[status(thm)],[])). tff(27,assumption,(~(fred = \|'mary'\|)), introduced(assumption)). tff(28,assumption,(~(mary = \|'alice'\|)), introduced(assumption)). tff(29,assumption,(~(alice = \|'alice'\|)), introduced(assumption)). tff(30,plain, ((alice = paul) <=> (paul = alice)), inference(commutativity,[status(thm)],[])). tff(31,plain, (X!0 = lucy), inference(symmetry,[status(thm)],[20])). tff(32,assumption,(mary = \|'mary'\|), introduced(assumption)). tff(33,plain, (\|'mary'\| = mary), inference(symmetry,[status(thm)],[32])). tff(34,plain, ((alice = \|'mary'\|) <=> (alice = mary)), inference(monotonicity,[status(thm)],[33])). tff(35,plain, ((alice = \|'mary'\|) <=> (mary = alice)), inference(transitivity,[status(thm)],[34, 23])). tff(36,plain, ((mary = alice) <=> (alice = \|'mary'\|)), inference(symmetry,[status(thm)],[35])). tff(37,plain, ((~(mary = alice)) <=> (~(alice = \|'mary'\|))), inference(monotonicity,[status(thm)],[36])). tff(38,plain, ((~(mary = alice)) <=> (~(mary = alice))), inference(rewrite,[status(thm)],[])). tff(39,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//1154774462978702311438543.p','b14')). 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))) & (~(lucy = 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))) & (~(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)],[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))) & (~(lucy = fred))), 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))) & (~(lucy = mary))) & (~(lucy = paul))), 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))) & (~(susan = lucy))) & (~(lucy = mary))), 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))) & (~(susan = john))) & (~(susan = lucy))), 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))) & (~(susan = alice))) & (~(susan = 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))) & (~(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)],[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))) & (~(susan = paul))) & (~(susan = fred))), 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))) & (~(susan = mary))) & (~(susan = paul))), 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))) & (~(john = lucy))) & (~(susan = mary))), 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))) & (~(john = susan))) & (~(john = lucy))), 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))) & (~(john = alice))) & (~(john = susan))), 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))) & (~(john = fred))) & (~(john = alice))), 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))) & (~(john = fred))), 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))) & (~(john = mary))) & (~(john = paul))), 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))) & (~(alice = lucy))) & (~(john = mary))), 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))) & (~(alice = susan))) & (~(alice = lucy))), 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))) & (~(alice = susan))), 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))) & (~(alice = fred))) & (~(alice = john))), 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))) & (~(alice = paul))) & (~(alice = fred))), 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))) & (~(alice = mary))) & (~(alice = paul))), 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))) & (~(fred = lucy))) & (~(alice = mary))), 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))) & (~(fred = susan))) & (~(fred = lucy))), 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))) & (~(fred = john))) & (~(fred = susan))), 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))) & (~(fred = alice))) & (~(fred = john))), 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))) & (~(fred = paul))) & (~(fred = alice))), 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))) & (~(fred = mary))) & (~(fred = paul))), 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))) & (~(paul = lucy))) & (~(fred = mary))), 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))) & (~(paul = susan))) & (~(paul = lucy))), 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))) & (~(paul = susan))), 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))) & (~(paul = john))), 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))) & (~(paul = alice))), inference(and_elim,[status(thm)],[71])). tff(73,plain, ((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))), inference(and_elim,[status(thm)],[72])). tff(74,plain, (((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))), inference(and_elim,[status(thm)],[73])). tff(75,plain, ((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))), inference(and_elim,[status(thm)],[74])). tff(76,plain, (((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))), inference(and_elim,[status(thm)],[75])). tff(77,plain, ((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))), inference(and_elim,[status(thm)],[76])). tff(78,plain, (((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))), inference(and_elim,[status(thm)],[77])). tff(79,plain, (~(mary = alice)), inference(and_elim,[status(thm)],[78])). tff(80,plain, (~(mary = alice)), inference(modus_ponens,[status(thm)],[79, 38])). tff(81,plain, (~(alice = \|'mary'\|)), inference(modus_ponens,[status(thm)],[80, 37])). tff(82,plain, ((lucy = mary) <=> (mary = lucy)), inference(commutativity,[status(thm)],[])). tff(83,plain, ((X!0 = \|'mary'\|) <=> (lucy = mary)), inference(monotonicity,[status(thm)],[31, 33])). tff(84,plain, ((X!0 = \|'mary'\|) <=> (mary = lucy)), inference(transitivity,[status(thm)],[83, 82])). tff(85,plain, ((mary = lucy) <=> (X!0 = \|'mary'\|)), inference(symmetry,[status(thm)],[84])). tff(86,plain, ((~(mary = lucy)) <=> (~(X!0 = \|'mary'\|))), inference(monotonicity,[status(thm)],[85])). tff(87,plain, ((~(mary = lucy)) <=> (~(mary = lucy))), inference(rewrite,[status(thm)],[])). tff(88,plain, (~(mary = lucy)), inference(and_elim,[status(thm)],[75])). tff(89,plain, (~(mary = lucy)), inference(modus_ponens,[status(thm)],[88, 87])). tff(90,plain, (~(X!0 = \|'mary'\|)), inference(modus_ponens,[status(thm)],[89, 86])). tff(91,plain, ((lucy = alice) <=> (alice = lucy)), inference(commutativity,[status(thm)],[])). tff(92,assumption,(~(alice = \|'mary'\|)), introduced(assumption)). tff(93,plain, ((alice = fred) <=> (fred = alice)), inference(commutativity,[status(thm)],[])). tff(94,assumption,(~(X!0 = \|'mary'\|)), introduced(assumption)). tff(95,assumption,(~(X!0 = \|'alice'\|)), introduced(assumption)). tff(96,plain, ((fred = paul) <=> (paul = fred)), inference(commutativity,[status(thm)],[])). tff(97,assumption,(~(fred = \|'paul'\|)), introduced(assumption)). tff(98,assumption,(X!0 = \|'fred'\|), introduced(assumption)). tff(99,plain, (\|'fred'\| = X!0), inference(symmetry,[status(thm)],[98])). tff(100,plain, (\|'fred'\| = lucy), inference(transitivity,[status(thm)],[99, 31])). tff(101,plain, ((paul = \|'fred'\|) <=> (paul = lucy)), inference(monotonicity,[status(thm)],[100])). tff(102,plain, ((paul = lucy) <=> (paul = \|'fred'\|)), inference(symmetry,[status(thm)],[101])). tff(103,plain, ((~(paul = lucy)) <=> (~(paul = \|'fred'\|))), inference(monotonicity,[status(thm)],[102])). tff(104,plain, ((~(paul = lucy)) <=> (~(paul = lucy))), inference(rewrite,[status(thm)],[])). tff(105,plain, (~(paul = lucy)), inference(and_elim,[status(thm)],[69])). tff(106,plain, (~(paul = lucy)), inference(modus_ponens,[status(thm)],[105, 104])). tff(107,plain, (~(paul = \|'fred'\|)), inference(modus_ponens,[status(thm)],[106, 103])). tff(108,plain, ((fred = \|'fred'\|) <=> (fred = lucy)), inference(monotonicity,[status(thm)],[100])). tff(109,plain, ((fred = lucy) <=> (fred = \|'fred'\|)), inference(symmetry,[status(thm)],[108])). tff(110,plain, ((~(fred = lucy)) <=> (~(fred = \|'fred'\|))), inference(monotonicity,[status(thm)],[109])). tff(111,plain, ((~(fred = lucy)) <=> (~(fred = lucy))), inference(rewrite,[status(thm)],[])). tff(112,plain, (~(fred = lucy)), inference(and_elim,[status(thm)],[63])). tff(113,plain, (~(fred = lucy)), inference(modus_ponens,[status(thm)],[112, 111])). tff(114,plain, (~(fred = \|'fred'\|)), inference(modus_ponens,[status(thm)],[113, 110])). tff(115,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(116,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)],[115])). tff(117,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(118,plain, (![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))), inference(and_elim,[status(thm)],[10])). tff(119,plain, (![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))), inference(modus_ponens,[status(thm)],[118, 117])). tff(120,plain,( ![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))), inference(skolemize,[status(sab)],[119])). tff(121,plain, (![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))), inference(modus_ponens,[status(thm)],[120, 116])). tff(122,plain, (room(fred) <=> room(fred)), inference(rewrite,[status(thm)],[])). tff(123,plain, (room(fred)), inference(and_elim,[status(thm)],[10])). tff(124,plain, (room(fred)), inference(modus_ponens,[status(thm)],[123, 122])). tff(125,plain, (((~![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| ((~room(fred)) \| (fred = \|'alice'\|) \| (fred = \|'fred'\|) \| (fred = \|'paul'\|) \| (fred = \|'mary'\|))) <=> ((~![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| (~room(fred)) \| (fred = \|'alice'\|) \| (fred = \|'fred'\|) \| (fred = \|'paul'\|) \| (fred = \|'mary'\|))), inference(rewrite,[status(thm)],[])). tff(126,plain, (((fred = \|'alice'\|) \| (fred = \|'fred'\|) \| (fred = \|'paul'\|) \| (fred = \|'mary'\|) \| (~room(fred))) <=> ((~room(fred)) \| (fred = \|'alice'\|) \| (fred = \|'fred'\|) \| (fred = \|'paul'\|) \| (fred = \|'mary'\|))), inference(rewrite,[status(thm)],[])). tff(127,plain, (((~![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| ((fred = \|'alice'\|) \| (fred = \|'fred'\|) \| (fred = \|'paul'\|) \| (fred = \|'mary'\|) \| (~room(fred)))) <=> ((~![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| ((~room(fred)) \| (fred = \|'alice'\|) \| (fred = \|'fred'\|) \| (fred = \|'paul'\|) \| (fred = \|'mary'\|)))), inference(monotonicity,[status(thm)],[126])). tff(128,plain, (((~![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| ((fred = \|'alice'\|) \| (fred = \|'fred'\|) \| (fred = \|'paul'\|) \| (fred = \|'mary'\|) \| (~room(fred)))) <=> ((~![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| (~room(fred)) \| (fred = \|'alice'\|) \| (fred = \|'fred'\|) \| (fred = \|'paul'\|) \| (fred = \|'mary'\|))), inference(transitivity,[status(thm)],[127, 125])). tff(129,plain, ((~![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| ((fred = \|'alice'\|) \| (fred = \|'fred'\|) \| (fred = \|'paul'\|) \| (fred = \|'mary'\|) \| (~room(fred)))), inference(quant_inst,[status(thm)],[])). tff(130,plain, ((~![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| (~room(fred)) \| (fred = \|'alice'\|) \| (fred = \|'fred'\|) \| (fred = \|'paul'\|) \| (fred = \|'mary'\|)), inference(modus_ponens,[status(thm)],[129, 128])). tff(131,plain, ((fred = \|'alice'\|) \| (fred = \|'fred'\|) \| (fred = \|'paul'\|) \| (fred = \|'mary'\|)), inference(unit_resolution,[status(thm)],[130, 124, 121])). tff(132,plain, (fred = \|'alice'\|), inference(unit_resolution,[status(thm)],[131, 114, 97, 27])). tff(133,plain, (\|'alice'\| = fred), inference(symmetry,[status(thm)],[132])). tff(134,plain, ((paul = \|'alice'\|) <=> (paul = fred)), inference(monotonicity,[status(thm)],[133])). tff(135,plain, ((paul = fred) <=> (paul = \|'alice'\|)), inference(symmetry,[status(thm)],[134])). tff(136,plain, ((~(paul = fred)) <=> (~(paul = \|'alice'\|))), inference(monotonicity,[status(thm)],[135])). tff(137,plain, ((~(paul = fred)) <=> (~(paul = fred))), inference(rewrite,[status(thm)],[])). tff(138,plain, (~(paul = fred)), inference(and_elim,[status(thm)],[73])). tff(139,plain, (~(paul = fred)), inference(modus_ponens,[status(thm)],[138, 137])). tff(140,plain, (~(paul = \|'alice'\|)), inference(modus_ponens,[status(thm)],[139, 136])). tff(141,plain, ((alice = \|'fred'\|) <=> (alice = lucy)), inference(monotonicity,[status(thm)],[100])). tff(142,plain, ((alice = lucy) <=> (alice = \|'fred'\|)), inference(symmetry,[status(thm)],[141])). tff(143,plain, ((~(alice = lucy)) <=> (~(alice = \|'fred'\|))), inference(monotonicity,[status(thm)],[142])). tff(144,plain, ((~(alice = lucy)) <=> (~(alice = lucy))), inference(rewrite,[status(thm)],[])). tff(145,plain, (~(alice = lucy)), inference(and_elim,[status(thm)],[57])). tff(146,plain, (~(alice = lucy)), inference(modus_ponens,[status(thm)],[145, 144])). tff(147,plain, (~(alice = \|'fred'\|)), inference(modus_ponens,[status(thm)],[146, 143])). tff(148,plain, (room(alice) <=> room(alice)), inference(rewrite,[status(thm)],[])). tff(149,plain, (room(alice)), inference(and_elim,[status(thm)],[10])). tff(150,plain, (room(alice)), inference(modus_ponens,[status(thm)],[149, 148])). tff(151,plain, (((~![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| ((~room(alice)) \| (alice = \|'alice'\|) \| (alice = \|'fred'\|) \| (alice = \|'paul'\|) \| (alice = \|'mary'\|))) <=> ((~![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| (~room(alice)) \| (alice = \|'alice'\|) \| (alice = \|'fred'\|) \| (alice = \|'paul'\|) \| (alice = \|'mary'\|))), inference(rewrite,[status(thm)],[])). tff(152,plain, (((alice = \|'alice'\|) \| (alice = \|'fred'\|) \| (alice = \|'paul'\|) \| (alice = \|'mary'\|) \| (~room(alice))) <=> ((~room(alice)) \| (alice = \|'alice'\|) \| (alice = \|'fred'\|) \| (alice = \|'paul'\|) \| (alice = \|'mary'\|))), inference(rewrite,[status(thm)],[])). tff(153,plain, (((~![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| ((alice = \|'alice'\|) \| (alice = \|'fred'\|) \| (alice = \|'paul'\|) \| (alice = \|'mary'\|) \| (~room(alice)))) <=> ((~![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| ((~room(alice)) \| (alice = \|'alice'\|) \| (alice = \|'fred'\|) \| (alice = \|'paul'\|) \| (alice = \|'mary'\|)))), inference(monotonicity,[status(thm)],[152])). tff(154,plain, (((~![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| ((alice = \|'alice'\|) \| (alice = \|'fred'\|) \| (alice = \|'paul'\|) \| (alice = \|'mary'\|) \| (~room(alice)))) <=> ((~![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| (~room(alice)) \| (alice = \|'alice'\|) \| (alice = \|'fred'\|) \| (alice = \|'paul'\|) \| (alice = \|'mary'\|))), inference(transitivity,[status(thm)],[153, 151])). tff(155,plain, ((~![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| ((alice = \|'alice'\|) \| (alice = \|'fred'\|) \| (alice = \|'paul'\|) \| (alice = \|'mary'\|) \| (~room(alice)))), inference(quant_inst,[status(thm)],[])). tff(156,plain, ((~![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| (~room(alice)) \| (alice = \|'alice'\|) \| (alice = \|'fred'\|) \| (alice = \|'paul'\|) \| (alice = \|'mary'\|)), inference(modus_ponens,[status(thm)],[155, 154])). tff(157,plain, ((alice = \|'alice'\|) \| (alice = \|'fred'\|) \| (alice = \|'paul'\|) \| (alice = \|'mary'\|)), inference(unit_resolution,[status(thm)],[156, 150, 121])). tff(158,plain, (alice = \|'paul'\|), inference(unit_resolution,[status(thm)],[157, 147, 29, 92])). tff(159,plain, (\|'paul'\| = alice), inference(symmetry,[status(thm)],[158])). tff(160,plain, ((paul = \|'paul'\|) <=> (paul = alice)), inference(monotonicity,[status(thm)],[159])). tff(161,plain, ((paul = alice) <=> (paul = \|'paul'\|)), inference(symmetry,[status(thm)],[160])). tff(162,plain, ((~(paul = alice)) <=> (~(paul = \|'paul'\|))), inference(monotonicity,[status(thm)],[161])). tff(163,plain, ((~(paul = alice)) <=> (~(paul = alice))), inference(rewrite,[status(thm)],[])). tff(164,plain, (~(paul = alice)), inference(and_elim,[status(thm)],[72])). tff(165,plain, (~(paul = alice)), inference(modus_ponens,[status(thm)],[164, 163])). tff(166,plain, (~(paul = \|'paul'\|)), inference(modus_ponens,[status(thm)],[165, 162])). tff(167,plain, (room(paul) <=> room(paul)), inference(rewrite,[status(thm)],[])). tff(168,plain, (room(paul)), inference(and_elim,[status(thm)],[10])). tff(169,plain, (room(paul)), inference(modus_ponens,[status(thm)],[168, 167])). tff(170,plain, (((~![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| ((~room(paul)) \| (paul = \|'alice'\|) \| (paul = \|'fred'\|) \| (paul = \|'paul'\|) \| (paul = \|'mary'\|))) <=> ((~![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| (~room(paul)) \| (paul = \|'alice'\|) \| (paul = \|'fred'\|) \| (paul = \|'paul'\|) \| (paul = \|'mary'\|))), inference(rewrite,[status(thm)],[])). tff(171,plain, (((paul = \|'alice'\|) \| (paul = \|'fred'\|) \| (paul = \|'paul'\|) \| (paul = \|'mary'\|) \| (~room(paul))) <=> ((~room(paul)) \| (paul = \|'alice'\|) \| (paul = \|'fred'\|) \| (paul = \|'paul'\|) \| (paul = \|'mary'\|))), inference(rewrite,[status(thm)],[])). tff(172,plain, (((~![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| ((paul = \|'alice'\|) \| (paul = \|'fred'\|) \| (paul = \|'paul'\|) \| (paul = \|'mary'\|) \| (~room(paul)))) <=> ((~![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| ((~room(paul)) \| (paul = \|'alice'\|) \| (paul = \|'fred'\|) \| (paul = \|'paul'\|) \| (paul = \|'mary'\|)))), inference(monotonicity,[status(thm)],[171])). tff(173,plain, (((~![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| ((paul = \|'alice'\|) \| (paul = \|'fred'\|) \| (paul = \|'paul'\|) \| (paul = \|'mary'\|) \| (~room(paul)))) <=> ((~![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| (~room(paul)) \| (paul = \|'alice'\|) \| (paul = \|'fred'\|) \| (paul = \|'paul'\|) \| (paul = \|'mary'\|))), inference(transitivity,[status(thm)],[172, 170])). tff(174,plain, ((~![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| ((paul = \|'alice'\|) \| (paul = \|'fred'\|) \| (paul = \|'paul'\|) \| (paul = \|'mary'\|) \| (~room(paul)))), inference(quant_inst,[status(thm)],[])). tff(175,plain, ((~![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| (~room(paul)) \| (paul = \|'alice'\|) \| (paul = \|'fred'\|) \| (paul = \|'paul'\|) \| (paul = \|'mary'\|)), inference(modus_ponens,[status(thm)],[174, 173])). tff(176,plain, ((paul = \|'alice'\|) \| (paul = \|'fred'\|) \| (paul = \|'paul'\|) \| (paul = \|'mary'\|)), inference(unit_resolution,[status(thm)],[175, 169, 121])). tff(177,plain, ($false), inference(unit_resolution,[status(thm)],[176, 166, 140, 107, 22])). tff(178,plain,((~(X!0 = \|'fred'\|)) \| (paul = \|'mary'\|) \| (alice = \|'alice'\|) \| (alice = \|'mary'\|) \| (fred = \|'paul'\|) \| (fred = \|'mary'\|) \| (~(lucy = X!0))), inference(lemma,lemma(discharge,[]))). tff(179,plain, (~(X!0 = \|'fred'\|)), inference(unit_resolution,[status(thm)],[178, 97, 29, 92, 22, 27, 20])). tff(180,plain, (room(X!0)), inference(and_elim,[status(thm)],[13])). tff(181,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(182,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(183,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)],[182, 181])). tff(184,plain, ((X!0 = \|'alice'\|) \| (X!0 = \|'fred'\|) \| (X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|)), inference(unit_resolution,[status(thm)],[183, 121, 180])). tff(185,plain, (X!0 = \|'paul'\|), inference(unit_resolution,[status(thm)],[184, 179, 95, 94])). tff(186,plain, (\|'paul'\| = X!0), inference(symmetry,[status(thm)],[185])). tff(187,plain, (\|'paul'\| = lucy), inference(transitivity,[status(thm)],[186, 31])). tff(188,plain, ((paul = \|'paul'\|) <=> (paul = lucy)), inference(monotonicity,[status(thm)],[187])). tff(189,plain, ((paul = lucy) <=> (paul = \|'paul'\|)), inference(symmetry,[status(thm)],[188])). tff(190,plain, ((~(paul = lucy)) <=> (~(paul = \|'paul'\|))), inference(monotonicity,[status(thm)],[189])). tff(191,plain, (~(paul = \|'paul'\|)), inference(modus_ponens,[status(thm)],[106, 190])). tff(192,plain, ((alice = \|'paul'\|) <=> (alice = lucy)), inference(monotonicity,[status(thm)],[187])). tff(193,plain, ((alice = lucy) <=> (alice = \|'paul'\|)), inference(symmetry,[status(thm)],[192])). tff(194,plain, ((~(alice = lucy)) <=> (~(alice = \|'paul'\|))), inference(monotonicity,[status(thm)],[193])). tff(195,plain, (~(alice = \|'paul'\|)), inference(modus_ponens,[status(thm)],[146, 194])). tff(196,plain, (alice = \|'fred'\|), inference(unit_resolution,[status(thm)],[157, 195, 29, 92])). tff(197,plain, (\|'fred'\| = alice), inference(symmetry,[status(thm)],[196])). tff(198,plain, ((paul = \|'fred'\|) <=> (paul = alice)), inference(monotonicity,[status(thm)],[197])). tff(199,plain, ((paul = alice) <=> (paul = \|'fred'\|)), inference(symmetry,[status(thm)],[198])). tff(200,plain, ((~(paul = alice)) <=> (~(paul = \|'fred'\|))), inference(monotonicity,[status(thm)],[199])). tff(201,plain, (~(paul = \|'fred'\|)), inference(modus_ponens,[status(thm)],[165, 200])). tff(202,plain, (paul = \|'alice'\|), inference(unit_resolution,[status(thm)],[176, 201, 191, 22])). tff(203,plain, (\|'alice'\| = paul), inference(symmetry,[status(thm)],[202])). tff(204,plain, ((fred = \|'alice'\|) <=> (fred = paul)), inference(monotonicity,[status(thm)],[203])). tff(205,plain, ((fred = \|'alice'\|) <=> (paul = fred)), inference(transitivity,[status(thm)],[204, 96])). tff(206,plain, ((paul = fred) <=> (fred = \|'alice'\|)), inference(symmetry,[status(thm)],[205])). tff(207,plain, ((~(paul = fred)) <=> (~(fred = \|'alice'\|))), inference(monotonicity,[status(thm)],[206])). tff(208,plain, (~(fred = \|'alice'\|)), inference(modus_ponens,[status(thm)],[139, 207])). tff(209,plain, ((fred = \|'fred'\|) <=> (fred = alice)), inference(monotonicity,[status(thm)],[197])). tff(210,plain, ((fred = alice) <=> (fred = \|'fred'\|)), inference(symmetry,[status(thm)],[209])). tff(211,plain, ((~(fred = alice)) <=> (~(fred = \|'fred'\|))), inference(monotonicity,[status(thm)],[210])). tff(212,plain, ((~(fred = alice)) <=> (~(fred = alice))), inference(rewrite,[status(thm)],[])). tff(213,plain, (~(fred = alice)), inference(and_elim,[status(thm)],[66])). tff(214,plain, (~(fred = alice)), inference(modus_ponens,[status(thm)],[213, 212])). tff(215,plain, (~(fred = \|'fred'\|)), inference(modus_ponens,[status(thm)],[214, 211])). tff(216,plain, (fred = \|'alice'\|), inference(unit_resolution,[status(thm)],[131, 215, 97, 27])). tff(217,plain, ($false), inference(unit_resolution,[status(thm)],[216, 208])). tff(218,plain,((fred = \|'paul'\|) \| (fred = \|'mary'\|) \| (paul = \|'mary'\|) \| (alice = \|'alice'\|) \| (alice = \|'mary'\|) \| (~(lucy = X!0)) \| (X!0 = \|'alice'\|) \| (X!0 = \|'mary'\|)), inference(lemma,lemma(discharge,[]))). tff(219,plain, (fred = \|'paul'\|), inference(unit_resolution,[status(thm)],[218, 95, 22, 29, 92, 20, 27, 94])). tff(220,plain, (\|'paul'\| = fred), inference(symmetry,[status(thm)],[219])). tff(221,plain, ((alice = \|'paul'\|) <=> (alice = fred)), inference(monotonicity,[status(thm)],[220])). tff(222,plain, ((alice = \|'paul'\|) <=> (fred = alice)), inference(transitivity,[status(thm)],[221, 93])). tff(223,plain, ((fred = alice) <=> (alice = \|'paul'\|)), inference(symmetry,[status(thm)],[222])). tff(224,plain, ((~(fred = alice)) <=> (~(alice = \|'paul'\|))), inference(monotonicity,[status(thm)],[223])). tff(225,plain, (~(alice = \|'paul'\|)), inference(modus_ponens,[status(thm)],[214, 224])). tff(226,plain, (alice = \|'fred'\|), inference(unit_resolution,[status(thm)],[157, 225, 29, 92])). tff(227,plain, (\|'fred'\| = alice), inference(symmetry,[status(thm)],[226])). tff(228,plain, ((X!0 = \|'fred'\|) <=> (lucy = alice)), inference(monotonicity,[status(thm)],[31, 227])). tff(229,plain, ((X!0 = \|'fred'\|) <=> (alice = lucy)), inference(transitivity,[status(thm)],[228, 91])). tff(230,plain, ((alice = lucy) <=> (X!0 = \|'fred'\|)), inference(symmetry,[status(thm)],[229])). tff(231,plain, ((~(alice = lucy)) <=> (~(X!0 = \|'fred'\|))), inference(monotonicity,[status(thm)],[230])). tff(232,plain, (~(X!0 = \|'fred'\|)), inference(modus_ponens,[status(thm)],[146, 231])). tff(233,plain, ((X!0 = \|'paul'\|) <=> (lucy = fred)), inference(monotonicity,[status(thm)],[31, 220])). tff(234,plain, ((X!0 = \|'paul'\|) <=> (fred = lucy)), inference(transitivity,[status(thm)],[233, 21])). tff(235,plain, ((fred = lucy) <=> (X!0 = \|'paul'\|)), inference(symmetry,[status(thm)],[234])). tff(236,plain, ((~(fred = lucy)) <=> (~(X!0 = \|'paul'\|))), inference(monotonicity,[status(thm)],[235])). tff(237,plain, (~(X!0 = \|'paul'\|)), inference(modus_ponens,[status(thm)],[113, 236])). tff(238,plain, (X!0 = \|'fred'\|), inference(unit_resolution,[status(thm)],[184, 237, 95, 94])). tff(239,plain, ($false), inference(unit_resolution,[status(thm)],[238, 232])). tff(240,plain,((X!0 = \|'alice'\|) \| (~(lucy = X!0)) \| (X!0 = \|'mary'\|) \| (alice = \|'alice'\|) \| (alice = \|'mary'\|) \| (paul = \|'mary'\|) \| (fred = \|'mary'\|)), inference(lemma,lemma(discharge,[]))). tff(241,plain, (X!0 = \|'alice'\|), inference(unit_resolution,[status(thm)],[240, 90, 20, 29, 81, 22, 27])). tff(242,plain, (\|'alice'\| = X!0), inference(symmetry,[status(thm)],[241])). tff(243,plain, (\|'alice'\| = lucy), inference(transitivity,[status(thm)],[242, 31])). tff(244,plain, ((paul = \|'alice'\|) <=> (paul = lucy)), inference(monotonicity,[status(thm)],[243])). tff(245,plain, ((paul = lucy) <=> (paul = \|'alice'\|)), inference(symmetry,[status(thm)],[244])). tff(246,plain, ((~(paul = lucy)) <=> (~(paul = \|'alice'\|))), inference(monotonicity,[status(thm)],[245])). tff(247,plain, (~(paul = \|'alice'\|)), inference(modus_ponens,[status(thm)],[106, 246])). tff(248,plain, ((fred = \|'alice'\|) <=> (fred = lucy)), inference(monotonicity,[status(thm)],[243])). tff(249,plain, ((fred = lucy) <=> (fred = \|'alice'\|)), inference(symmetry,[status(thm)],[248])). tff(250,plain, ((~(fred = lucy)) <=> (~(fred = \|'alice'\|))), inference(monotonicity,[status(thm)],[249])). tff(251,plain, (~(fred = \|'alice'\|)), inference(modus_ponens,[status(thm)],[113, 250])). tff(252,assumption,(~(paul = \|'alice'\|)), introduced(assumption)). tff(253,assumption,(fred = \|'fred'\|), introduced(assumption)). tff(254,plain, (\|'fred'\| = fred), inference(symmetry,[status(thm)],[253])). tff(255,plain, ((paul = \|'fred'\|) <=> (paul = fred)), inference(monotonicity,[status(thm)],[254])). tff(256,plain, ((paul = fred) <=> (paul = \|'fred'\|)), inference(symmetry,[status(thm)],[255])). tff(257,plain, ((~(paul = fred)) <=> (~(paul = \|'fred'\|))), inference(monotonicity,[status(thm)],[256])). tff(258,plain, (~(paul = \|'fred'\|)), inference(modus_ponens,[status(thm)],[139, 257])). tff(259,plain, (paul = \|'paul'\|), inference(unit_resolution,[status(thm)],[176, 258, 252, 22])). tff(260,plain, (\|'paul'\| = paul), inference(symmetry,[status(thm)],[259])). tff(261,plain, ((alice = \|'paul'\|) <=> (alice = paul)), inference(monotonicity,[status(thm)],[260])). tff(262,plain, ((alice = \|'paul'\|) <=> (paul = alice)), inference(transitivity,[status(thm)],[261, 30])). tff(263,plain, ((paul = alice) <=> (alice = \|'paul'\|)), inference(symmetry,[status(thm)],[262])). tff(264,plain, ((~(paul = alice)) <=> (~(alice = \|'paul'\|))), inference(monotonicity,[status(thm)],[263])). tff(265,plain, (~(alice = \|'paul'\|)), inference(modus_ponens,[status(thm)],[165, 264])). tff(266,plain, ((alice = \|'fred'\|) <=> (alice = fred)), inference(monotonicity,[status(thm)],[254])). tff(267,plain, ((alice = \|'fred'\|) <=> (fred = alice)), inference(transitivity,[status(thm)],[266, 93])). tff(268,plain, ((fred = alice) <=> (alice = \|'fred'\|)), inference(symmetry,[status(thm)],[267])). tff(269,plain, ((~(fred = alice)) <=> (~(alice = \|'fred'\|))), inference(monotonicity,[status(thm)],[268])). tff(270,plain, (~(alice = \|'fred'\|)), inference(modus_ponens,[status(thm)],[214, 269])). tff(271,plain, (alice = \|'paul'\|), inference(unit_resolution,[status(thm)],[157, 270, 29, 92])). tff(272,plain, ($false), inference(unit_resolution,[status(thm)],[271, 265])). tff(273,plain,((~(fred = \|'fred'\|)) \| (alice = \|'alice'\|) \| (alice = \|'mary'\|) \| (paul = \|'alice'\|) \| (paul = \|'mary'\|)), inference(lemma,lemma(discharge,[]))). tff(274,plain, (~(fred = \|'fred'\|)), inference(unit_resolution,[status(thm)],[273, 81, 29, 247, 22])). tff(275,plain, (fred = \|'paul'\|), inference(unit_resolution,[status(thm)],[131, 274, 251, 27])). tff(276,plain, (\|'paul'\| = fred), inference(symmetry,[status(thm)],[275])). tff(277,plain, ((paul = \|'paul'\|) <=> (paul = fred)), inference(monotonicity,[status(thm)],[276])). tff(278,plain, ((paul = fred) <=> (paul = \|'paul'\|)), inference(symmetry,[status(thm)],[277])). tff(279,plain, ((~(paul = fred)) <=> (~(paul = \|'paul'\|))), inference(monotonicity,[status(thm)],[278])). tff(280,plain, (~(paul = \|'paul'\|)), inference(modus_ponens,[status(thm)],[139, 279])). tff(281,plain, (paul = \|'fred'\|), inference(unit_resolution,[status(thm)],[176, 280, 247, 22])). tff(282,plain, (\|'fred'\| = paul), inference(symmetry,[status(thm)],[281])). tff(283,plain, ((alice = \|'fred'\|) <=> (alice = paul)), inference(monotonicity,[status(thm)],[282])). tff(284,plain, ((alice = \|'fred'\|) <=> (paul = alice)), inference(transitivity,[status(thm)],[283, 30])). tff(285,plain, ((paul = alice) <=> (alice = \|'fred'\|)), inference(symmetry,[status(thm)],[284])). tff(286,plain, ((~(paul = alice)) <=> (~(alice = \|'fred'\|))), inference(monotonicity,[status(thm)],[285])). tff(287,plain, (~(alice = \|'fred'\|)), inference(modus_ponens,[status(thm)],[165, 286])). tff(288,plain, ((alice = \|'paul'\|) <=> (alice = fred)), inference(monotonicity,[status(thm)],[276])). tff(289,plain, ((alice = \|'paul'\|) <=> (fred = alice)), inference(transitivity,[status(thm)],[288, 93])). tff(290,plain, ((fred = alice) <=> (alice = \|'paul'\|)), inference(symmetry,[status(thm)],[289])). tff(291,plain, ((~(fred = alice)) <=> (~(alice = \|'paul'\|))), inference(monotonicity,[status(thm)],[290])). tff(292,plain, (~(alice = \|'paul'\|)), inference(modus_ponens,[status(thm)],[214, 291])). tff(293,plain, (alice = \|'fred'\|), inference(unit_resolution,[status(thm)],[157, 292, 29, 81])). tff(294,plain, ($false), inference(unit_resolution,[status(thm)],[293, 287])). tff(295,plain,((~(mary = \|'mary'\|)) \| (alice = \|'alice'\|) \| (paul = \|'mary'\|) \| (fred = \|'mary'\|) \| (~(lucy = X!0))), inference(lemma,lemma(discharge,[]))). tff(296,plain, (~(mary = \|'mary'\|)), inference(unit_resolution,[status(thm)],[295, 29, 22, 27, 20])). tff(297,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(298,plain, (room(mary)), inference(and_elim,[status(thm)],[10])). tff(299,plain, (room(mary)), inference(modus_ponens,[status(thm)],[298, 297])). tff(300,plain, (((~![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| ((~room(mary)) \| (mary = \|'alice'\|) \| (mary = \|'fred'\|) \| (mary = \|'paul'\|) \| (mary = \|'mary'\|))) <=> ((~![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| (~room(mary)) \| (mary = \|'alice'\|) \| (mary = \|'fred'\|) \| (mary = \|'paul'\|) \| (mary = \|'mary'\|))), inference(rewrite,[status(thm)],[])). tff(301,plain, (((mary = \|'alice'\|) \| (mary = \|'fred'\|) \| (mary = \|'paul'\|) \| (mary = \|'mary'\|) \| (~room(mary))) <=> ((~room(mary)) \| (mary = \|'alice'\|) \| (mary = \|'fred'\|) \| (mary = \|'paul'\|) \| (mary = \|'mary'\|))), inference(rewrite,[status(thm)],[])). tff(302,plain, (((~![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| ((mary = \|'alice'\|) \| (mary = \|'fred'\|) \| (mary = \|'paul'\|) \| (mary = \|'mary'\|) \| (~room(mary)))) <=> ((~![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| ((~room(mary)) \| (mary = \|'alice'\|) \| (mary = \|'fred'\|) \| (mary = \|'paul'\|) \| (mary = \|'mary'\|)))), inference(monotonicity,[status(thm)],[301])). tff(303,plain, (((~![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| ((mary = \|'alice'\|) \| (mary = \|'fred'\|) \| (mary = \|'paul'\|) \| (mary = \|'mary'\|) \| (~room(mary)))) <=> ((~![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| (~room(mary)) \| (mary = \|'alice'\|) \| (mary = \|'fred'\|) \| (mary = \|'paul'\|) \| (mary = \|'mary'\|))), inference(transitivity,[status(thm)],[302, 300])). tff(304,plain, ((~![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| ((mary = \|'alice'\|) \| (mary = \|'fred'\|) \| (mary = \|'paul'\|) \| (mary = \|'mary'\|) \| (~room(mary)))), inference(quant_inst,[status(thm)],[])). tff(305,plain, ((~![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| (~room(mary)) \| (mary = \|'alice'\|) \| (mary = \|'fred'\|) \| (mary = \|'paul'\|) \| (mary = \|'mary'\|)), inference(modus_ponens,[status(thm)],[304, 303])). tff(306,plain, ((mary = \|'alice'\|) \| (mary = \|'fred'\|) \| (mary = \|'paul'\|) \| (mary = \|'mary'\|)), inference(unit_resolution,[status(thm)],[305, 299, 121])). tff(307,plain, (mary = \|'paul'\|), inference(unit_resolution,[status(thm)],[306, 296, 24, 28])). tff(308,plain, (\|'paul'\| = mary), inference(symmetry,[status(thm)],[307])). tff(309,plain, ((fred = \|'paul'\|) <=> (fred = mary)), inference(monotonicity,[status(thm)],[308])). tff(310,plain, ((fred = \|'paul'\|) <=> (mary = fred)), inference(transitivity,[status(thm)],[309, 19])). tff(311,plain, ((mary = fred) <=> (fred = \|'paul'\|)), inference(symmetry,[status(thm)],[310])). tff(312,plain, ((~(mary = fred)) <=> (~(fred = \|'paul'\|))), inference(monotonicity,[status(thm)],[311])). tff(313,plain, ((~(mary = fred)) <=> (~(mary = fred))), inference(rewrite,[status(thm)],[])). tff(314,plain, ((~(mary = paul)) & (~(mary = fred))), inference(and_elim,[status(thm)],[78])). tff(315,plain, (~(mary = fred)), inference(and_elim,[status(thm)],[314])). tff(316,plain, (~(mary = fred)), inference(modus_ponens,[status(thm)],[315, 313])). tff(317,plain, (~(fred = \|'paul'\|)), inference(modus_ponens,[status(thm)],[316, 312])). tff(318,plain, ((paul = \|'paul'\|) <=> (paul = mary)), inference(monotonicity,[status(thm)],[308])). tff(319,plain, ((paul = \|'paul'\|) <=> (mary = paul)), inference(transitivity,[status(thm)],[318, 26])). tff(320,plain, ((mary = paul) <=> (paul = \|'paul'\|)), inference(symmetry,[status(thm)],[319])). tff(321,plain, ((~(mary = paul)) <=> (~(paul = \|'paul'\|))), inference(monotonicity,[status(thm)],[320])). tff(322,plain, ((~(mary = paul)) <=> (~(mary = paul))), inference(rewrite,[status(thm)],[])). tff(323,plain, (~(mary = paul)), inference(and_elim,[status(thm)],[314])). tff(324,plain, (~(mary = paul)), inference(modus_ponens,[status(thm)],[323, 322])). tff(325,plain, (~(paul = \|'paul'\|)), inference(modus_ponens,[status(thm)],[324, 321])). tff(326,plain, ((alice = \|'paul'\|) <=> (alice = mary)), inference(monotonicity,[status(thm)],[308])). tff(327,plain, ((alice = \|'paul'\|) <=> (mary = alice)), inference(transitivity,[status(thm)],[326, 23])). tff(328,plain, ((mary = alice) <=> (alice = \|'paul'\|)), inference(symmetry,[status(thm)],[327])). tff(329,plain, ((~(mary = alice)) <=> (~(alice = \|'paul'\|))), inference(monotonicity,[status(thm)],[328])). tff(330,plain, (~(alice = \|'paul'\|)), inference(modus_ponens,[status(thm)],[80, 329])). tff(331,assumption,(~(paul = \|'paul'\|)), introduced(assumption)). tff(332,assumption,(alice = \|'fred'\|), introduced(assumption)). tff(333,plain, (\|'fred'\| = alice), inference(symmetry,[status(thm)],[332])). tff(334,plain, ((paul = \|'fred'\|) <=> (paul = alice)), inference(monotonicity,[status(thm)],[333])). tff(335,plain, ((paul = alice) <=> (paul = \|'fred'\|)), inference(symmetry,[status(thm)],[334])). tff(336,plain, ((~(paul = alice)) <=> (~(paul = \|'fred'\|))), inference(monotonicity,[status(thm)],[335])). tff(337,plain, (~(paul = \|'fred'\|)), inference(modus_ponens,[status(thm)],[165, 336])). tff(338,plain, (paul = \|'alice'\|), inference(unit_resolution,[status(thm)],[176, 337, 331, 22])). tff(339,plain, (\|'alice'\| = paul), inference(symmetry,[status(thm)],[338])). tff(340,plain, ((fred = \|'alice'\|) <=> (fred = paul)), inference(monotonicity,[status(thm)],[339])). tff(341,plain, ((fred = \|'alice'\|) <=> (paul = fred)), inference(transitivity,[status(thm)],[340, 96])). tff(342,plain, ((paul = fred) <=> (fred = \|'alice'\|)), inference(symmetry,[status(thm)],[341])). tff(343,plain, ((~(paul = fred)) <=> (~(fred = \|'alice'\|))), inference(monotonicity,[status(thm)],[342])). tff(344,plain, (~(fred = \|'alice'\|)), inference(modus_ponens,[status(thm)],[139, 343])). tff(345,plain, ((fred = \|'fred'\|) <=> (fred = alice)), inference(monotonicity,[status(thm)],[333])). tff(346,plain, ((fred = alice) <=> (fred = \|'fred'\|)), inference(symmetry,[status(thm)],[345])). tff(347,plain, ((~(fred = alice)) <=> (~(fred = \|'fred'\|))), inference(monotonicity,[status(thm)],[346])). tff(348,plain, (~(fred = \|'fred'\|)), inference(modus_ponens,[status(thm)],[214, 347])). tff(349,plain, (fred = \|'alice'\|), inference(unit_resolution,[status(thm)],[131, 348, 97, 27])). tff(350,plain, ($false), inference(unit_resolution,[status(thm)],[349, 344])). tff(351,plain,((~(alice = \|'fred'\|)) \| (fred = \|'paul'\|) \| (fred = \|'mary'\|) \| (paul = \|'paul'\|) \| (paul = \|'mary'\|)), inference(lemma,lemma(discharge,[]))). tff(352,plain, (~(alice = \|'fred'\|)), inference(unit_resolution,[status(thm)],[351, 317, 27, 325, 22])). tff(353,plain, (alice = \|'mary'\|), inference(unit_resolution,[status(thm)],[157, 352, 29, 330])). tff(354,plain, (\|'mary'\| = alice), inference(symmetry,[status(thm)],[353])). tff(355,plain, ((X!0 = \|'mary'\|) <=> (lucy = alice)), inference(monotonicity,[status(thm)],[31, 354])). tff(356,plain, ((X!0 = \|'mary'\|) <=> (alice = lucy)), inference(transitivity,[status(thm)],[355, 91])). tff(357,plain, ((alice = lucy) <=> (X!0 = \|'mary'\|)), inference(symmetry,[status(thm)],[356])). tff(358,plain, ((~(alice = lucy)) <=> (~(X!0 = \|'mary'\|))), inference(monotonicity,[status(thm)],[357])). tff(359,plain, (~(X!0 = \|'mary'\|)), inference(modus_ponens,[status(thm)],[146, 358])). tff(360,plain, ((X!0 = \|'paul'\|) <=> (lucy = mary)), inference(monotonicity,[status(thm)],[31, 308])). tff(361,plain, ((X!0 = \|'paul'\|) <=> (mary = lucy)), inference(transitivity,[status(thm)],[360, 82])). tff(362,plain, ((mary = lucy) <=> (X!0 = \|'paul'\|)), inference(symmetry,[status(thm)],[361])). tff(363,plain, ((~(mary = lucy)) <=> (~(X!0 = \|'paul'\|))), inference(monotonicity,[status(thm)],[362])). tff(364,plain, (~(X!0 = \|'paul'\|)), inference(modus_ponens,[status(thm)],[89, 363])). tff(365,assumption,(paul = \|'fred'\|), introduced(assumption)). tff(366,plain, (\|'fred'\| = paul), inference(symmetry,[status(thm)],[365])). tff(367,plain, ((fred = \|'fred'\|) <=> (fred = paul)), inference(monotonicity,[status(thm)],[366])). tff(368,plain, ((fred = \|'fred'\|) <=> (paul = fred)), inference(transitivity,[status(thm)],[367, 96])). tff(369,plain, ((paul = fred) <=> (fred = \|'fred'\|)), inference(symmetry,[status(thm)],[368])). tff(370,plain, ((~(paul = fred)) <=> (~(fred = \|'fred'\|))), inference(monotonicity,[status(thm)],[369])). tff(371,plain, (~(fred = \|'fred'\|)), inference(modus_ponens,[status(thm)],[139, 370])). tff(372,plain, (fred = \|'alice'\|), inference(unit_resolution,[status(thm)],[131, 371, 97, 27])). tff(373,plain, (\|'alice'\| = fred), inference(symmetry,[status(thm)],[372])). tff(374,plain, ((X!0 = \|'alice'\|) <=> (lucy = fred)), inference(monotonicity,[status(thm)],[31, 373])). tff(375,plain, ((X!0 = \|'alice'\|) <=> (fred = lucy)), inference(transitivity,[status(thm)],[374, 21])). tff(376,plain, ((fred = lucy) <=> (X!0 = \|'alice'\|)), inference(symmetry,[status(thm)],[375])). tff(377,plain, ((~(fred = lucy)) <=> (~(X!0 = \|'alice'\|))), inference(monotonicity,[status(thm)],[376])). tff(378,plain, (~(X!0 = \|'alice'\|)), inference(modus_ponens,[status(thm)],[113, 377])). tff(379,assumption,(~(X!0 = \|'paul'\|)), introduced(assumption)). tff(380,plain, ((X!0 = \|'fred'\|) <=> (lucy = paul)), inference(monotonicity,[status(thm)],[31, 366])). tff(381,plain, ((X!0 = \|'fred'\|) <=> (paul = lucy)), inference(transitivity,[status(thm)],[380, 25])). tff(382,plain, ((paul = lucy) <=> (X!0 = \|'fred'\|)), inference(symmetry,[status(thm)],[381])). tff(383,plain, ((~(paul = lucy)) <=> (~(X!0 = \|'fred'\|))), inference(monotonicity,[status(thm)],[382])). tff(384,plain, (~(X!0 = \|'fred'\|)), inference(modus_ponens,[status(thm)],[106, 383])). tff(385,plain, (X!0 = \|'alice'\|), inference(unit_resolution,[status(thm)],[184, 384, 379, 94])). tff(386,plain, ($false), inference(unit_resolution,[status(thm)],[385, 378])). tff(387,plain,((~(paul = \|'fred'\|)) \| (~(lucy = X!0)) \| (X!0 = \|'paul'\|) \| (X!0 = \|'mary'\|) \| (fred = \|'paul'\|) \| (fred = \|'mary'\|)), inference(lemma,lemma(discharge,[]))). tff(388,plain, (~(paul = \|'fred'\|)), inference(unit_resolution,[status(thm)],[387, 364, 20, 359, 317, 27])). tff(389,plain, (paul = \|'alice'\|), inference(unit_resolution,[status(thm)],[176, 388, 325, 22])). tff(390,plain, (\|'alice'\| = paul), inference(symmetry,[status(thm)],[389])). tff(391,plain, ((fred = \|'alice'\|) <=> (fred = paul)), inference(monotonicity,[status(thm)],[390])). tff(392,plain, ((fred = \|'alice'\|) <=> (paul = fred)), inference(transitivity,[status(thm)],[391, 96])). tff(393,plain, ((paul = fred) <=> (fred = \|'alice'\|)), inference(symmetry,[status(thm)],[392])). tff(394,plain, ((~(paul = fred)) <=> (~(fred = \|'alice'\|))), inference(monotonicity,[status(thm)],[393])). tff(395,plain, (~(fred = \|'alice'\|)), inference(modus_ponens,[status(thm)],[139, 394])). tff(396,plain, (fred = \|'fred'\|), inference(unit_resolution,[status(thm)],[131, 395, 317, 27])). tff(397,plain, (\|'fred'\| = fred), inference(symmetry,[status(thm)],[396])). tff(398,plain, ((X!0 = \|'fred'\|) <=> (lucy = fred)), inference(monotonicity,[status(thm)],[31, 397])). tff(399,plain, ((X!0 = \|'fred'\|) <=> (fred = lucy)), inference(transitivity,[status(thm)],[398, 21])). tff(400,plain, ((fred = lucy) <=> (X!0 = \|'fred'\|)), inference(symmetry,[status(thm)],[399])). tff(401,plain, ((~(fred = lucy)) <=> (~(X!0 = \|'fred'\|))), inference(monotonicity,[status(thm)],[400])). tff(402,plain, (~(X!0 = \|'fred'\|)), inference(modus_ponens,[status(thm)],[113, 401])). tff(403,plain, ((X!0 = \|'alice'\|) <=> (lucy = paul)), inference(monotonicity,[status(thm)],[31, 390])). tff(404,plain, ((X!0 = \|'alice'\|) <=> (paul = lucy)), inference(transitivity,[status(thm)],[403, 25])). tff(405,plain, ((paul = lucy) <=> (X!0 = \|'alice'\|)), inference(symmetry,[status(thm)],[404])). tff(406,plain, ((~(paul = lucy)) <=> (~(X!0 = \|'alice'\|))), inference(monotonicity,[status(thm)],[405])). tff(407,plain, (~(X!0 = \|'alice'\|)), inference(modus_ponens,[status(thm)],[106, 406])). tff(408,plain, (X!0 = \|'fred'\|), inference(unit_resolution,[status(thm)],[184, 407, 364, 359])). tff(409,plain, ($false), inference(unit_resolution,[status(thm)],[408, 402])). tff(410,plain,((alice = \|'alice'\|) \| (~(lucy = X!0)) \| (fred = \|'mary'\|) \| (paul = \|'mary'\|) \| (mary = \|'fred'\|) \| (mary = \|'alice'\|)), inference(lemma,lemma(discharge,[]))). tff(411,plain, (alice = \|'alice'\|), inference(unit_resolution,[status(thm)],[410, 28, 27, 22, 24, 20])). tff(412,plain, (\|'alice'\| = alice), inference(symmetry,[status(thm)],[411])). tff(413,plain, ((fred = \|'alice'\|) <=> (fred = alice)), inference(monotonicity,[status(thm)],[412])). tff(414,plain, ((fred = alice) <=> (fred = \|'alice'\|)), inference(symmetry,[status(thm)],[413])). tff(415,plain, ((~(fred = alice)) <=> (~(fred = \|'alice'\|))), inference(monotonicity,[status(thm)],[414])). tff(416,plain, (~(fred = \|'alice'\|)), inference(modus_ponens,[status(thm)],[214, 415])). tff(417,plain, ((paul = \|'alice'\|) <=> (paul = alice)), inference(monotonicity,[status(thm)],[412])). tff(418,plain, ((paul = alice) <=> (paul = \|'alice'\|)), inference(symmetry,[status(thm)],[417])). tff(419,plain, ((~(paul = alice)) <=> (~(paul = \|'alice'\|))), inference(monotonicity,[status(thm)],[418])). tff(420,plain, (~(paul = \|'alice'\|)), inference(modus_ponens,[status(thm)],[165, 419])). tff(421,plain, ((X!0 = \|'alice'\|) <=> (lucy = alice)), inference(monotonicity,[status(thm)],[31, 412])). tff(422,plain, ((X!0 = \|'alice'\|) <=> (alice = lucy)), inference(transitivity,[status(thm)],[421, 91])). tff(423,plain, ((alice = lucy) <=> (X!0 = \|'alice'\|)), inference(symmetry,[status(thm)],[422])). tff(424,plain, ((~(alice = lucy)) <=> (~(X!0 = \|'alice'\|))), inference(monotonicity,[status(thm)],[423])). tff(425,plain, (~(X!0 = \|'alice'\|)), inference(modus_ponens,[status(thm)],[146, 424])). tff(426,plain, ((mary = \|'paul'\|) <=> (mary = paul)), inference(monotonicity,[status(thm)],[260])). tff(427,plain, ((mary = paul) <=> (mary = \|'paul'\|)), inference(symmetry,[status(thm)],[426])). tff(428,plain, ((~(mary = paul)) <=> (~(mary = \|'paul'\|))), inference(monotonicity,[status(thm)],[427])). tff(429,plain, (~(mary = \|'paul'\|)), inference(modus_ponens,[status(thm)],[324, 428])). tff(430,plain, (mary = \|'mary'\|), inference(unit_resolution,[status(thm)],[306, 429, 24, 28])). tff(431,plain, (\|'mary'\| = mary), inference(symmetry,[status(thm)],[430])). tff(432,plain, ((X!0 = \|'mary'\|) <=> (lucy = mary)), inference(monotonicity,[status(thm)],[31, 431])). tff(433,plain, ((X!0 = \|'mary'\|) <=> (mary = lucy)), inference(transitivity,[status(thm)],[432, 82])). tff(434,plain, ((mary = lucy) <=> (X!0 = \|'mary'\|)), inference(symmetry,[status(thm)],[433])). tff(435,plain, ((~(mary = lucy)) <=> (~(X!0 = \|'mary'\|))), inference(monotonicity,[status(thm)],[434])). tff(436,plain, (~(X!0 = \|'mary'\|)), inference(modus_ponens,[status(thm)],[89, 435])). tff(437,plain, ((X!0 = \|'fred'\|) <=> (lucy = fred)), inference(monotonicity,[status(thm)],[31, 254])). tff(438,plain, ((X!0 = \|'fred'\|) <=> (fred = lucy)), inference(transitivity,[status(thm)],[437, 21])). tff(439,plain, ((fred = lucy) <=> (X!0 = \|'fred'\|)), inference(symmetry,[status(thm)],[438])). tff(440,plain, ((~(fred = lucy)) <=> (~(X!0 = \|'fred'\|))), inference(monotonicity,[status(thm)],[439])). tff(441,plain, (~(X!0 = \|'fred'\|)), inference(modus_ponens,[status(thm)],[113, 440])). tff(442,plain, ((X!0 = \|'paul'\|) <=> (lucy = paul)), inference(monotonicity,[status(thm)],[31, 260])). tff(443,plain, ((X!0 = \|'paul'\|) <=> (paul = lucy)), inference(transitivity,[status(thm)],[442, 25])). tff(444,plain, ((paul = lucy) <=> (X!0 = \|'paul'\|)), inference(symmetry,[status(thm)],[443])). tff(445,plain, ((~(paul = lucy)) <=> (~(X!0 = \|'paul'\|))), inference(monotonicity,[status(thm)],[444])). tff(446,plain, (~(X!0 = \|'paul'\|)), inference(modus_ponens,[status(thm)],[106, 445])). tff(447,plain, (X!0 = \|'mary'\|), inference(unit_resolution,[status(thm)],[184, 446, 95, 441])). tff(448,plain, ($false), inference(unit_resolution,[status(thm)],[447, 436])). tff(449,plain,((~(fred = \|'fred'\|)) \| (~(lucy = X!0)) \| (X!0 = \|'alice'\|) \| (mary = \|'fred'\|) \| (mary = \|'alice'\|) \| (paul = \|'alice'\|) \| (paul = \|'mary'\|)), inference(lemma,lemma(discharge,[]))). tff(450,plain, (~(fred = \|'fred'\|)), inference(unit_resolution,[status(thm)],[449, 425, 20, 24, 28, 420, 22])). tff(451,plain, (fred = \|'paul'\|), inference(unit_resolution,[status(thm)],[131, 450, 416, 27])). tff(452,plain, (\|'paul'\| = fred), inference(symmetry,[status(thm)],[451])). tff(453,plain, ((X!0 = \|'paul'\|) <=> (lucy = fred)), inference(monotonicity,[status(thm)],[31, 452])). tff(454,plain, ((X!0 = \|'paul'\|) <=> (fred = lucy)), inference(transitivity,[status(thm)],[453, 21])). tff(455,plain, ((fred = lucy) <=> (X!0 = \|'paul'\|)), inference(symmetry,[status(thm)],[454])). tff(456,plain, ((~(fred = lucy)) <=> (~(X!0 = \|'paul'\|))), inference(monotonicity,[status(thm)],[455])). tff(457,plain, (~(X!0 = \|'paul'\|)), inference(modus_ponens,[status(thm)],[113, 456])). tff(458,plain, ((mary = \|'paul'\|) <=> (mary = fred)), inference(monotonicity,[status(thm)],[452])). tff(459,plain, ((mary = fred) <=> (mary = \|'paul'\|)), inference(symmetry,[status(thm)],[458])). tff(460,plain, ((~(mary = fred)) <=> (~(mary = \|'paul'\|))), inference(monotonicity,[status(thm)],[459])). tff(461,plain, (~(mary = \|'paul'\|)), inference(modus_ponens,[status(thm)],[316, 460])). tff(462,plain, (mary = \|'mary'\|), inference(unit_resolution,[status(thm)],[306, 461, 24, 28])). tff(463,plain, (\|'mary'\| = mary), inference(symmetry,[status(thm)],[462])). tff(464,plain, ((X!0 = \|'mary'\|) <=> (lucy = mary)), inference(monotonicity,[status(thm)],[31, 463])). tff(465,plain, ((X!0 = \|'mary'\|) <=> (mary = lucy)), inference(transitivity,[status(thm)],[464, 82])). tff(466,plain, ((mary = lucy) <=> (X!0 = \|'mary'\|)), inference(symmetry,[status(thm)],[465])). tff(467,plain, ((~(mary = lucy)) <=> (~(X!0 = \|'mary'\|))), inference(monotonicity,[status(thm)],[466])). tff(468,plain, (~(X!0 = \|'mary'\|)), inference(modus_ponens,[status(thm)],[89, 467])). tff(469,plain, ((paul = \|'paul'\|) <=> (paul = fred)), inference(monotonicity,[status(thm)],[452])). tff(470,plain, ((paul = fred) <=> (paul = \|'paul'\|)), inference(symmetry,[status(thm)],[469])). tff(471,plain, ((~(paul = fred)) <=> (~(paul = \|'paul'\|))), inference(monotonicity,[status(thm)],[470])). tff(472,plain, (~(paul = \|'paul'\|)), inference(modus_ponens,[status(thm)],[139, 471])). tff(473,plain, (paul = \|'fred'\|), inference(unit_resolution,[status(thm)],[176, 472, 420, 22])). tff(474,plain, (\|'fred'\| = paul), inference(symmetry,[status(thm)],[473])). tff(475,plain, ((X!0 = \|'fred'\|) <=> (lucy = paul)), inference(monotonicity,[status(thm)],[31, 474])). tff(476,plain, ((X!0 = \|'fred'\|) <=> (paul = lucy)), inference(transitivity,[status(thm)],[475, 25])). tff(477,plain, ((paul = lucy) <=> (X!0 = \|'fred'\|)), inference(symmetry,[status(thm)],[476])). tff(478,plain, ((~(paul = lucy)) <=> (~(X!0 = \|'fred'\|))), inference(monotonicity,[status(thm)],[477])). tff(479,plain, (~(X!0 = \|'fred'\|)), inference(modus_ponens,[status(thm)],[106, 478])). tff(480,plain, ($false), inference(unit_resolution,[status(thm)],[184, 479, 468, 425, 457])). tff(481,plain,((mary = \|'alice'\|) \| (~(lucy = X!0)) \| (paul = \|'mary'\|) \| (mary = \|'fred'\|) \| (fred = \|'mary'\|)), inference(lemma,lemma(discharge,[]))). tff(482,plain, (mary = \|'alice'\|), inference(unit_resolution,[status(thm)],[481, 27, 22, 24, 20])). tff(483,plain, (\|'alice'\| = mary), inference(symmetry,[status(thm)],[482])). tff(484,plain, ((paul = \|'alice'\|) <=> (paul = mary)), inference(monotonicity,[status(thm)],[483])). tff(485,plain, ((paul = \|'alice'\|) <=> (mary = paul)), inference(transitivity,[status(thm)],[484, 26])). tff(486,plain, ((mary = paul) <=> (paul = \|'alice'\|)), inference(symmetry,[status(thm)],[485])). tff(487,plain, ((~(mary = paul)) <=> (~(paul = \|'alice'\|))), inference(monotonicity,[status(thm)],[486])). tff(488,plain, (~(paul = \|'alice'\|)), inference(modus_ponens,[status(thm)],[324, 487])). tff(489,plain, ((fred = \|'alice'\|) <=> (fred = mary)), inference(monotonicity,[status(thm)],[483])). tff(490,plain, ((fred = \|'alice'\|) <=> (mary = fred)), inference(transitivity,[status(thm)],[489, 19])). tff(491,plain, ((mary = fred) <=> (fred = \|'alice'\|)), inference(symmetry,[status(thm)],[490])). tff(492,plain, ((~(mary = fred)) <=> (~(fred = \|'alice'\|))), inference(monotonicity,[status(thm)],[491])). tff(493,plain, (~(fred = \|'alice'\|)), inference(modus_ponens,[status(thm)],[316, 492])). tff(494,plain, ((alice = \|'alice'\|) <=> (alice = mary)), inference(monotonicity,[status(thm)],[483])). tff(495,plain, ((alice = \|'alice'\|) <=> (mary = alice)), inference(transitivity,[status(thm)],[494, 23])). tff(496,plain, ((mary = alice) <=> (alice = \|'alice'\|)), inference(symmetry,[status(thm)],[495])). tff(497,plain, ((~(mary = alice)) <=> (~(alice = \|'alice'\|))), inference(monotonicity,[status(thm)],[496])). tff(498,plain, (~(alice = \|'alice'\|)), inference(modus_ponens,[status(thm)],[80, 497])). tff(499,plain, ((X!0 = \|'alice'\|) <=> (lucy = mary)), inference(monotonicity,[status(thm)],[31, 483])). tff(500,plain, ((X!0 = \|'alice'\|) <=> (mary = lucy)), inference(transitivity,[status(thm)],[499, 82])). tff(501,plain, ((mary = lucy) <=> (X!0 = \|'alice'\|)), inference(symmetry,[status(thm)],[500])). tff(502,plain, ((~(mary = lucy)) <=> (~(X!0 = \|'alice'\|))), inference(monotonicity,[status(thm)],[501])). tff(503,plain, (~(X!0 = \|'alice'\|)), inference(modus_ponens,[status(thm)],[89, 502])). tff(504,assumption,(fred = \|'paul'\|), introduced(assumption)). tff(505,plain, (\|'paul'\| = fred), inference(symmetry,[status(thm)],[504])). tff(506,plain, ((alice = \|'paul'\|) <=> (alice = fred)), inference(monotonicity,[status(thm)],[505])). tff(507,plain, ((alice = \|'paul'\|) <=> (fred = alice)), inference(transitivity,[status(thm)],[506, 93])). tff(508,plain, ((fred = alice) <=> (alice = \|'paul'\|)), inference(symmetry,[status(thm)],[507])). tff(509,plain, ((~(fred = alice)) <=> (~(alice = \|'paul'\|))), inference(monotonicity,[status(thm)],[508])). tff(510,plain, (~(alice = \|'paul'\|)), inference(modus_ponens,[status(thm)],[214, 509])). tff(511,plain, ((paul = \|'paul'\|) <=> (paul = fred)), inference(monotonicity,[status(thm)],[505])). tff(512,plain, ((paul = fred) <=> (paul = \|'paul'\|)), inference(symmetry,[status(thm)],[511])). tff(513,plain, ((~(paul = fred)) <=> (~(paul = \|'paul'\|))), inference(monotonicity,[status(thm)],[512])). tff(514,plain, (~(paul = \|'paul'\|)), inference(modus_ponens,[status(thm)],[139, 513])). tff(515,plain, (paul = \|'fred'\|), inference(unit_resolution,[status(thm)],[176, 514, 252, 22])). tff(516,plain, (\|'fred'\| = paul), inference(symmetry,[status(thm)],[515])). tff(517,plain, ((alice = \|'fred'\|) <=> (alice = paul)), inference(monotonicity,[status(thm)],[516])). tff(518,plain, ((alice = \|'fred'\|) <=> (paul = alice)), inference(transitivity,[status(thm)],[517, 30])). tff(519,plain, ((paul = alice) <=> (alice = \|'fred'\|)), inference(symmetry,[status(thm)],[518])). tff(520,plain, ((~(paul = alice)) <=> (~(alice = \|'fred'\|))), inference(monotonicity,[status(thm)],[519])). tff(521,plain, (~(alice = \|'fred'\|)), inference(modus_ponens,[status(thm)],[165, 520])). tff(522,plain, (alice = \|'mary'\|), inference(unit_resolution,[status(thm)],[157, 521, 29, 510])). tff(523,plain, (\|'mary'\| = alice), inference(symmetry,[status(thm)],[522])). tff(524,plain, ((X!0 = \|'mary'\|) <=> (lucy = alice)), inference(monotonicity,[status(thm)],[31, 523])). tff(525,plain, ((X!0 = \|'mary'\|) <=> (alice = lucy)), inference(transitivity,[status(thm)],[524, 91])). tff(526,plain, ((alice = lucy) <=> (X!0 = \|'mary'\|)), inference(symmetry,[status(thm)],[525])). tff(527,plain, ((~(alice = lucy)) <=> (~(X!0 = \|'mary'\|))), inference(monotonicity,[status(thm)],[526])). tff(528,plain, (~(X!0 = \|'mary'\|)), inference(modus_ponens,[status(thm)],[146, 527])). tff(529,plain, ((X!0 = \|'paul'\|) <=> (lucy = fred)), inference(monotonicity,[status(thm)],[31, 505])). tff(530,plain, ((X!0 = \|'paul'\|) <=> (fred = lucy)), inference(transitivity,[status(thm)],[529, 21])). tff(531,plain, ((fred = lucy) <=> (X!0 = \|'paul'\|)), inference(symmetry,[status(thm)],[530])). tff(532,plain, ((~(fred = lucy)) <=> (~(X!0 = \|'paul'\|))), inference(monotonicity,[status(thm)],[531])). tff(533,plain, (~(X!0 = \|'paul'\|)), inference(modus_ponens,[status(thm)],[113, 532])). tff(534,plain, ((X!0 = \|'fred'\|) <=> (lucy = paul)), inference(monotonicity,[status(thm)],[31, 516])). tff(535,plain, ((X!0 = \|'fred'\|) <=> (paul = lucy)), inference(transitivity,[status(thm)],[534, 25])). tff(536,plain, ((paul = lucy) <=> (X!0 = \|'fred'\|)), inference(symmetry,[status(thm)],[535])). tff(537,plain, ((~(paul = lucy)) <=> (~(X!0 = \|'fred'\|))), inference(monotonicity,[status(thm)],[536])). tff(538,plain, (~(X!0 = \|'fred'\|)), inference(modus_ponens,[status(thm)],[106, 537])). tff(539,plain, (X!0 = \|'mary'\|), inference(unit_resolution,[status(thm)],[184, 538, 95, 533])). tff(540,plain, ($false), inference(unit_resolution,[status(thm)],[539, 528])). tff(541,plain,((~(fred = \|'paul'\|)) \| (~(lucy = X!0)) \| (X!0 = \|'alice'\|) \| (alice = \|'alice'\|) \| (paul = \|'alice'\|) \| (paul = \|'mary'\|)), inference(lemma,lemma(discharge,[]))). tff(542,plain, (~(fred = \|'paul'\|)), inference(unit_resolution,[status(thm)],[541, 503, 20, 498, 488, 22])). tff(543,plain, (fred = \|'fred'\|), inference(unit_resolution,[status(thm)],[131, 542, 493, 27])). tff(544,plain, (\|'fred'\| = fred), inference(symmetry,[status(thm)],[543])). tff(545,plain, ((paul = \|'fred'\|) <=> (paul = fred)), inference(monotonicity,[status(thm)],[544])). tff(546,plain, ((paul = fred) <=> (paul = \|'fred'\|)), inference(symmetry,[status(thm)],[545])). tff(547,plain, ((~(paul = fred)) <=> (~(paul = \|'fred'\|))), inference(monotonicity,[status(thm)],[546])). tff(548,plain, (~(paul = \|'fred'\|)), inference(modus_ponens,[status(thm)],[139, 547])). tff(549,plain, (paul = \|'paul'\|), inference(unit_resolution,[status(thm)],[176, 548, 488, 22])). tff(550,plain, (\|'paul'\| = paul), inference(symmetry,[status(thm)],[549])). tff(551,plain, ((X!0 = \|'paul'\|) <=> (lucy = paul)), inference(monotonicity,[status(thm)],[31, 550])). tff(552,plain, ((X!0 = \|'paul'\|) <=> (paul = lucy)), inference(transitivity,[status(thm)],[551, 25])). tff(553,plain, ((paul = lucy) <=> (X!0 = \|'paul'\|)), inference(symmetry,[status(thm)],[552])). tff(554,plain, ((~(paul = lucy)) <=> (~(X!0 = \|'paul'\|))), inference(monotonicity,[status(thm)],[553])). tff(555,plain, (~(X!0 = \|'paul'\|)), inference(modus_ponens,[status(thm)],[106, 554])). tff(556,plain, ((X!0 = \|'fred'\|) <=> (lucy = fred)), inference(monotonicity,[status(thm)],[31, 544])). tff(557,plain, ((X!0 = \|'fred'\|) <=> (fred = lucy)), inference(transitivity,[status(thm)],[556, 21])). tff(558,plain, ((fred = lucy) <=> (X!0 = \|'fred'\|)), inference(symmetry,[status(thm)],[557])). tff(559,plain, ((~(fred = lucy)) <=> (~(X!0 = \|'fred'\|))), inference(monotonicity,[status(thm)],[558])). tff(560,plain, (~(X!0 = \|'fred'\|)), inference(modus_ponens,[status(thm)],[113, 559])). tff(561,plain, (alice = \|'mary'\|), inference(unit_resolution,[status(thm)],[273, 543, 498, 488, 22])). tff(562,plain, (\|'mary'\| = alice), inference(symmetry,[status(thm)],[561])). tff(563,plain, ((X!0 = \|'mary'\|) <=> (lucy = alice)), inference(monotonicity,[status(thm)],[31, 562])). tff(564,plain, ((X!0 = \|'mary'\|) <=> (alice = lucy)), inference(transitivity,[status(thm)],[563, 91])). tff(565,plain, ((alice = lucy) <=> (X!0 = \|'mary'\|)), inference(symmetry,[status(thm)],[564])). tff(566,plain, ((~(alice = lucy)) <=> (~(X!0 = \|'mary'\|))), inference(monotonicity,[status(thm)],[565])). tff(567,plain, (~(X!0 = \|'mary'\|)), inference(modus_ponens,[status(thm)],[146, 566])). tff(568,plain, (X!0 = \|'paul'\|), inference(unit_resolution,[status(thm)],[184, 567, 503, 560])). tff(569,plain, ($false), inference(unit_resolution,[status(thm)],[568, 555])). tff(570,plain,((fred = \|'mary'\|) \| (~(lucy = X!0)) \| (paul = \|'mary'\|) \| (mary = \|'fred'\|)), inference(lemma,lemma(discharge,[]))). tff(571,plain, (fred = \|'mary'\|), inference(unit_resolution,[status(thm)],[570, 24, 22, 20])). tff(572,plain, (\|'mary'\| = fred), inference(symmetry,[status(thm)],[571])). tff(573,plain, ((mary = \|'mary'\|) <=> (mary = fred)), inference(monotonicity,[status(thm)],[572])). tff(574,plain, ((mary = fred) <=> (mary = \|'mary'\|)), inference(symmetry,[status(thm)],[573])). tff(575,plain, ((~(mary = fred)) <=> (~(mary = \|'mary'\|))), inference(monotonicity,[status(thm)],[574])). tff(576,plain, (~(mary = \|'mary'\|)), inference(modus_ponens,[status(thm)],[316, 575])). tff(577,plain, ((alice = \|'mary'\|) <=> (alice = fred)), inference(monotonicity,[status(thm)],[572])). tff(578,plain, ((alice = \|'mary'\|) <=> (fred = alice)), inference(transitivity,[status(thm)],[577, 93])). tff(579,plain, ((fred = alice) <=> (alice = \|'mary'\|)), inference(symmetry,[status(thm)],[578])). tff(580,plain, ((~(fred = alice)) <=> (~(alice = \|'mary'\|))), inference(monotonicity,[status(thm)],[579])). tff(581,plain, (~(alice = \|'mary'\|)), inference(modus_ponens,[status(thm)],[214, 580])). tff(582,plain, ((X!0 = \|'mary'\|) <=> (lucy = fred)), inference(monotonicity,[status(thm)],[31, 572])). tff(583,plain, ((X!0 = \|'mary'\|) <=> (fred = lucy)), inference(transitivity,[status(thm)],[582, 21])). tff(584,plain, ((fred = lucy) <=> (X!0 = \|'mary'\|)), inference(symmetry,[status(thm)],[583])). tff(585,plain, ((~(fred = lucy)) <=> (~(X!0 = \|'mary'\|))), inference(monotonicity,[status(thm)],[584])). tff(586,plain, (~(X!0 = \|'mary'\|)), inference(modus_ponens,[status(thm)],[113, 585])). tff(587,assumption,(paul = \|'paul'\|), introduced(assumption)). tff(588,plain, (\|'paul'\| = paul), inference(symmetry,[status(thm)],[587])). tff(589,plain, ((alice = \|'paul'\|) <=> (alice = paul)), inference(monotonicity,[status(thm)],[588])). tff(590,plain, ((alice = \|'paul'\|) <=> (paul = alice)), inference(transitivity,[status(thm)],[589, 30])). tff(591,plain, ((paul = alice) <=> (alice = \|'paul'\|)), inference(symmetry,[status(thm)],[590])). tff(592,plain, ((~(paul = alice)) <=> (~(alice = \|'paul'\|))), inference(monotonicity,[status(thm)],[591])). tff(593,plain, (~(alice = \|'paul'\|)), inference(modus_ponens,[status(thm)],[165, 592])). tff(594,assumption,(~(mary = \|'mary'\|)), introduced(assumption)). tff(595,plain, ((mary = \|'paul'\|) <=> (mary = paul)), inference(monotonicity,[status(thm)],[588])). tff(596,plain, ((mary = paul) <=> (mary = \|'paul'\|)), inference(symmetry,[status(thm)],[595])). tff(597,plain, ((~(mary = paul)) <=> (~(mary = \|'paul'\|))), inference(monotonicity,[status(thm)],[596])). tff(598,plain, (~(mary = \|'paul'\|)), inference(modus_ponens,[status(thm)],[324, 597])). tff(599,plain, (mary = \|'alice'\|), inference(unit_resolution,[status(thm)],[306, 598, 24, 594])). tff(600,plain, (\|'alice'\| = mary), inference(symmetry,[status(thm)],[599])). tff(601,plain, ((alice = \|'alice'\|) <=> (alice = mary)), inference(monotonicity,[status(thm)],[600])). tff(602,plain, ((alice = \|'alice'\|) <=> (mary = alice)), inference(transitivity,[status(thm)],[601, 23])). tff(603,plain, ((mary = alice) <=> (alice = \|'alice'\|)), inference(symmetry,[status(thm)],[602])). tff(604,plain, ((~(mary = alice)) <=> (~(alice = \|'alice'\|))), inference(monotonicity,[status(thm)],[603])). tff(605,plain, (~(alice = \|'alice'\|)), inference(modus_ponens,[status(thm)],[80, 604])). tff(606,plain, (alice = \|'fred'\|), inference(unit_resolution,[status(thm)],[157, 605, 92, 593])). tff(607,plain, (\|'fred'\| = alice), inference(symmetry,[status(thm)],[606])). tff(608,plain, ((X!0 = \|'fred'\|) <=> (lucy = alice)), inference(monotonicity,[status(thm)],[31, 607])). tff(609,plain, ((X!0 = \|'fred'\|) <=> (alice = lucy)), inference(transitivity,[status(thm)],[608, 91])). tff(610,plain, ((alice = lucy) <=> (X!0 = \|'fred'\|)), inference(symmetry,[status(thm)],[609])). tff(611,plain, ((~(alice = lucy)) <=> (~(X!0 = \|'fred'\|))), inference(monotonicity,[status(thm)],[610])). tff(612,plain, (~(X!0 = \|'fred'\|)), inference(modus_ponens,[status(thm)],[146, 611])). tff(613,plain, ((X!0 = \|'paul'\|) <=> (lucy = paul)), inference(monotonicity,[status(thm)],[31, 588])). tff(614,plain, ((X!0 = \|'paul'\|) <=> (paul = lucy)), inference(transitivity,[status(thm)],[613, 25])). tff(615,plain, ((paul = lucy) <=> (X!0 = \|'paul'\|)), inference(symmetry,[status(thm)],[614])). tff(616,plain, ((~(paul = lucy)) <=> (~(X!0 = \|'paul'\|))), inference(monotonicity,[status(thm)],[615])). tff(617,plain, (~(X!0 = \|'paul'\|)), inference(modus_ponens,[status(thm)],[106, 616])). tff(618,plain, ((X!0 = \|'alice'\|) <=> (lucy = mary)), inference(monotonicity,[status(thm)],[31, 600])). tff(619,plain, ((X!0 = \|'alice'\|) <=> (mary = lucy)), inference(transitivity,[status(thm)],[618, 82])). tff(620,plain, ((mary = lucy) <=> (X!0 = \|'alice'\|)), inference(symmetry,[status(thm)],[619])). tff(621,plain, ((~(mary = lucy)) <=> (~(X!0 = \|'alice'\|))), inference(monotonicity,[status(thm)],[620])). tff(622,plain, (~(X!0 = \|'alice'\|)), inference(modus_ponens,[status(thm)],[89, 621])). tff(623,plain, (X!0 = \|'fred'\|), inference(unit_resolution,[status(thm)],[184, 622, 94, 617])). tff(624,plain, ($false), inference(unit_resolution,[status(thm)],[623, 612])). tff(625,plain,((~(paul = \|'paul'\|)) \| (~(lucy = X!0)) \| (X!0 = \|'mary'\|) \| (alice = \|'mary'\|) \| (mary = \|'fred'\|) \| (mary = \|'mary'\|)), inference(lemma,lemma(discharge,[]))). tff(626,plain, (~(paul = \|'paul'\|)), inference(unit_resolution,[status(thm)],[625, 586, 20, 581, 24, 576])). tff(627,assumption,(paul = \|'alice'\|), introduced(assumption)). tff(628,plain, (\|'alice'\| = paul), inference(symmetry,[status(thm)],[627])). tff(629,plain, ((alice = \|'alice'\|) <=> (alice = paul)), inference(monotonicity,[status(thm)],[628])). tff(630,plain, ((alice = \|'alice'\|) <=> (paul = alice)), inference(transitivity,[status(thm)],[629, 30])). tff(631,plain, ((paul = alice) <=> (alice = \|'alice'\|)), inference(symmetry,[status(thm)],[630])). tff(632,plain, ((~(paul = alice)) <=> (~(alice = \|'alice'\|))), inference(monotonicity,[status(thm)],[631])). tff(633,plain, (~(alice = \|'alice'\|)), inference(modus_ponens,[status(thm)],[165, 632])). tff(634,plain, ((mary = \|'alice'\|) <=> (mary = paul)), inference(monotonicity,[status(thm)],[628])). tff(635,plain, ((mary = paul) <=> (mary = \|'alice'\|)), inference(symmetry,[status(thm)],[634])). tff(636,plain, ((~(mary = paul)) <=> (~(mary = \|'alice'\|))), inference(monotonicity,[status(thm)],[635])). tff(637,plain, (~(mary = \|'alice'\|)), inference(modus_ponens,[status(thm)],[324, 636])). tff(638,plain, (mary = \|'paul'\|), inference(unit_resolution,[status(thm)],[306, 637, 24, 594])). tff(639,plain, (\|'paul'\| = mary), inference(symmetry,[status(thm)],[638])). tff(640,plain, ((alice = \|'paul'\|) <=> (alice = mary)), inference(monotonicity,[status(thm)],[639])). tff(641,plain, ((alice = \|'paul'\|) <=> (mary = alice)), inference(transitivity,[status(thm)],[640, 23])). tff(642,plain, ((mary = alice) <=> (alice = \|'paul'\|)), inference(symmetry,[status(thm)],[641])). tff(643,plain, ((~(mary = alice)) <=> (~(alice = \|'paul'\|))), inference(monotonicity,[status(thm)],[642])). tff(644,plain, (~(alice = \|'paul'\|)), inference(modus_ponens,[status(thm)],[80, 643])). tff(645,plain, (alice = \|'fred'\|), inference(unit_resolution,[status(thm)],[157, 644, 92, 633])). tff(646,plain, (\|'fred'\| = alice), inference(symmetry,[status(thm)],[645])). tff(647,plain, ((X!0 = \|'fred'\|) <=> (lucy = alice)), inference(monotonicity,[status(thm)],[31, 646])). tff(648,plain, ((X!0 = \|'fred'\|) <=> (alice = lucy)), inference(transitivity,[status(thm)],[647, 91])). tff(649,plain, ((alice = lucy) <=> (X!0 = \|'fred'\|)), inference(symmetry,[status(thm)],[648])). tff(650,plain, ((~(alice = lucy)) <=> (~(X!0 = \|'fred'\|))), inference(monotonicity,[status(thm)],[649])). tff(651,plain, (~(X!0 = \|'fred'\|)), inference(modus_ponens,[status(thm)],[146, 650])). tff(652,plain, ((X!0 = \|'alice'\|) <=> (lucy = paul)), inference(monotonicity,[status(thm)],[31, 628])). tff(653,plain, ((X!0 = \|'alice'\|) <=> (paul = lucy)), inference(transitivity,[status(thm)],[652, 25])). tff(654,plain, ((paul = lucy) <=> (X!0 = \|'alice'\|)), inference(symmetry,[status(thm)],[653])). tff(655,plain, ((~(paul = lucy)) <=> (~(X!0 = \|'alice'\|))), inference(monotonicity,[status(thm)],[654])). tff(656,plain, (~(X!0 = \|'alice'\|)), inference(modus_ponens,[status(thm)],[106, 655])). tff(657,plain, ((X!0 = \|'paul'\|) <=> (lucy = mary)), inference(monotonicity,[status(thm)],[31, 639])). tff(658,plain, ((X!0 = \|'paul'\|) <=> (mary = lucy)), inference(transitivity,[status(thm)],[657, 82])). tff(659,plain, ((mary = lucy) <=> (X!0 = \|'paul'\|)), inference(symmetry,[status(thm)],[658])). tff(660,plain, ((~(mary = lucy)) <=> (~(X!0 = \|'paul'\|))), inference(monotonicity,[status(thm)],[659])). tff(661,plain, (~(X!0 = \|'paul'\|)), inference(modus_ponens,[status(thm)],[89, 660])). tff(662,plain, (X!0 = \|'fred'\|), inference(unit_resolution,[status(thm)],[184, 661, 94, 656])). tff(663,plain, ($false), inference(unit_resolution,[status(thm)],[662, 651])). tff(664,plain,((~(paul = \|'alice'\|)) \| (~(lucy = X!0)) \| (X!0 = \|'mary'\|) \| (alice = \|'mary'\|) \| (mary = \|'fred'\|) \| (mary = \|'mary'\|)), inference(lemma,lemma(discharge,[]))). tff(665,plain, (~(paul = \|'alice'\|)), inference(unit_resolution,[status(thm)],[664, 586, 20, 581, 24, 576])). tff(666,plain, (paul = \|'fred'\|), inference(unit_resolution,[status(thm)],[176, 665, 626, 22])). tff(667,plain, (\|'fred'\| = paul), inference(symmetry,[status(thm)],[666])). tff(668,plain, ((X!0 = \|'fred'\|) <=> (lucy = paul)), inference(monotonicity,[status(thm)],[31, 667])). tff(669,plain, ((X!0 = \|'fred'\|) <=> (paul = lucy)), inference(transitivity,[status(thm)],[668, 25])). tff(670,plain, ((paul = lucy) <=> (X!0 = \|'fred'\|)), inference(symmetry,[status(thm)],[669])). tff(671,plain, ((~(paul = lucy)) <=> (~(X!0 = \|'fred'\|))), inference(monotonicity,[status(thm)],[670])). tff(672,plain, (~(X!0 = \|'fred'\|)), inference(modus_ponens,[status(thm)],[106, 671])). tff(673,plain, ((alice = \|'fred'\|) <=> (alice = paul)), inference(monotonicity,[status(thm)],[667])). tff(674,plain, ((alice = \|'fred'\|) <=> (paul = alice)), inference(transitivity,[status(thm)],[673, 30])). tff(675,plain, ((paul = alice) <=> (alice = \|'fred'\|)), inference(symmetry,[status(thm)],[674])). tff(676,plain, ((~(paul = alice)) <=> (~(alice = \|'fred'\|))), inference(monotonicity,[status(thm)],[675])). tff(677,plain, (~(alice = \|'fred'\|)), inference(modus_ponens,[status(thm)],[165, 676])). tff(678,assumption,(X!0 = \|'paul'\|), introduced(assumption)). tff(679,plain, (\|'paul'\| = X!0), inference(symmetry,[status(thm)],[678])). tff(680,plain, (\|'paul'\| = lucy), inference(transitivity,[status(thm)],[679, 31])). tff(681,plain, ((mary = \|'paul'\|) <=> (mary = lucy)), inference(monotonicity,[status(thm)],[680])). tff(682,plain, ((mary = lucy) <=> (mary = \|'paul'\|)), inference(symmetry,[status(thm)],[681])). tff(683,plain, ((~(mary = lucy)) <=> (~(mary = \|'paul'\|))), inference(monotonicity,[status(thm)],[682])). tff(684,plain, (~(mary = \|'paul'\|)), inference(modus_ponens,[status(thm)],[89, 683])). tff(685,plain, (mary = \|'alice'\|), inference(unit_resolution,[status(thm)],[306, 684, 24, 594])). tff(686,plain, (\|'alice'\| = mary), inference(symmetry,[status(thm)],[685])). tff(687,plain, ((alice = \|'alice'\|) <=> (alice = mary)), inference(monotonicity,[status(thm)],[686])). tff(688,plain, ((alice = \|'alice'\|) <=> (mary = alice)), inference(transitivity,[status(thm)],[687, 23])). tff(689,plain, ((mary = alice) <=> (alice = \|'alice'\|)), inference(symmetry,[status(thm)],[688])). tff(690,plain, ((~(mary = alice)) <=> (~(alice = \|'alice'\|))), inference(monotonicity,[status(thm)],[689])). tff(691,plain, (~(alice = \|'alice'\|)), inference(modus_ponens,[status(thm)],[80, 690])). tff(692,assumption,(~(alice = \|'fred'\|)), introduced(assumption)). tff(693,plain, ((alice = \|'paul'\|) <=> (alice = lucy)), inference(monotonicity,[status(thm)],[680])). tff(694,plain, ((alice = lucy) <=> (alice = \|'paul'\|)), inference(symmetry,[status(thm)],[693])). tff(695,plain, ((~(alice = lucy)) <=> (~(alice = \|'paul'\|))), inference(monotonicity,[status(thm)],[694])). tff(696,plain, (~(alice = \|'paul'\|)), inference(modus_ponens,[status(thm)],[146, 695])). tff(697,plain, (alice = \|'alice'\|), inference(unit_resolution,[status(thm)],[157, 696, 92, 692])). tff(698,plain, ($false), inference(unit_resolution,[status(thm)],[697, 691])). tff(699,plain,((~(X!0 = \|'paul'\|)) \| (alice = \|'mary'\|) \| (alice = \|'fred'\|) \| (mary = \|'fred'\|) \| (mary = \|'mary'\|) \| (~(lucy = X!0))), inference(lemma,lemma(discharge,[]))). tff(700,plain, (~(X!0 = \|'paul'\|)), inference(unit_resolution,[status(thm)],[699, 581, 677, 24, 576, 20])). tff(701,plain, (X!0 = \|'alice'\|), inference(unit_resolution,[status(thm)],[184, 700, 586, 672])). tff(702,plain, (\|'alice'\| = X!0), inference(symmetry,[status(thm)],[701])). tff(703,plain, (\|'alice'\| = lucy), inference(transitivity,[status(thm)],[702, 31])). tff(704,plain, ((mary = \|'alice'\|) <=> (mary = lucy)), inference(monotonicity,[status(thm)],[703])). tff(705,plain, ((mary = lucy) <=> (mary = \|'alice'\|)), inference(symmetry,[status(thm)],[704])). tff(706,plain, ((~(mary = lucy)) <=> (~(mary = \|'alice'\|))), inference(monotonicity,[status(thm)],[705])). tff(707,plain, (~(mary = \|'alice'\|)), inference(modus_ponens,[status(thm)],[89, 706])). tff(708,plain, (mary = \|'paul'\|), inference(unit_resolution,[status(thm)],[306, 707, 24, 576])). tff(709,plain, (\|'paul'\| = mary), inference(symmetry,[status(thm)],[708])). tff(710,plain, ((alice = \|'paul'\|) <=> (alice = mary)), inference(monotonicity,[status(thm)],[709])). tff(711,plain, ((alice = \|'paul'\|) <=> (mary = alice)), inference(transitivity,[status(thm)],[710, 23])). tff(712,plain, ((mary = alice) <=> (alice = \|'paul'\|)), inference(symmetry,[status(thm)],[711])). tff(713,plain, ((~(mary = alice)) <=> (~(alice = \|'paul'\|))), inference(monotonicity,[status(thm)],[712])). tff(714,plain, (~(alice = \|'paul'\|)), inference(modus_ponens,[status(thm)],[80, 713])). tff(715,plain, ((alice = \|'alice'\|) <=> (alice = lucy)), inference(monotonicity,[status(thm)],[703])). tff(716,plain, ((alice = lucy) <=> (alice = \|'alice'\|)), inference(symmetry,[status(thm)],[715])). tff(717,plain, ((~(alice = lucy)) <=> (~(alice = \|'alice'\|))), inference(monotonicity,[status(thm)],[716])). tff(718,plain, (~(alice = \|'alice'\|)), inference(modus_ponens,[status(thm)],[146, 717])). tff(719,plain, (alice = \|'paul'\|), inference(unit_resolution,[status(thm)],[157, 718, 581, 677])). tff(720,plain, ($false), inference(unit_resolution,[status(thm)],[719, 714])). tff(721,plain,((mary = \|'fred'\|) \| (~(lucy = X!0)) \| (paul = \|'mary'\|)), inference(lemma,lemma(discharge,[]))). tff(722,plain, (mary = \|'fred'\|), inference(unit_resolution,[status(thm)],[721, 22, 20])). tff(723,plain, (\|'fred'\| = mary), inference(symmetry,[status(thm)],[722])). tff(724,plain, ((alice = \|'fred'\|) <=> (alice = mary)), inference(monotonicity,[status(thm)],[723])). tff(725,plain, ((alice = \|'fred'\|) <=> (mary = alice)), inference(transitivity,[status(thm)],[724, 23])). tff(726,plain, ((mary = alice) <=> (alice = \|'fred'\|)), inference(symmetry,[status(thm)],[725])). tff(727,plain, ((~(mary = alice)) <=> (~(alice = \|'fred'\|))), inference(monotonicity,[status(thm)],[726])). tff(728,plain, (~(alice = \|'fred'\|)), inference(modus_ponens,[status(thm)],[80, 727])). tff(729,plain, ((paul = \|'fred'\|) <=> (paul = mary)), inference(monotonicity,[status(thm)],[723])). tff(730,plain, ((paul = \|'fred'\|) <=> (mary = paul)), inference(transitivity,[status(thm)],[729, 26])). tff(731,plain, ((mary = paul) <=> (paul = \|'fred'\|)), inference(symmetry,[status(thm)],[730])). tff(732,plain, ((~(mary = paul)) <=> (~(paul = \|'fred'\|))), inference(monotonicity,[status(thm)],[731])). tff(733,plain, (~(paul = \|'fred'\|)), inference(modus_ponens,[status(thm)],[324, 732])). tff(734,plain, (\|'mary'\| = lucy), inference(transitivity,[status(thm)],[2, 31])). tff(735,plain, ((alice = \|'mary'\|) <=> (alice = lucy)), inference(monotonicity,[status(thm)],[734])). tff(736,plain, ((alice = lucy) <=> (alice = \|'mary'\|)), inference(symmetry,[status(thm)],[735])). tff(737,plain, ((~(alice = lucy)) <=> (~(alice = \|'mary'\|))), inference(monotonicity,[status(thm)],[736])). tff(738,plain, (~(alice = \|'mary'\|)), inference(modus_ponens,[status(thm)],[146, 737])). tff(739,plain, (alice = \|'paul'\|), inference(unit_resolution,[status(thm)],[157, 738, 29, 728])). tff(740,plain, (\|'paul'\| = alice), inference(symmetry,[status(thm)],[739])). tff(741,plain, ((paul = \|'paul'\|) <=> (paul = alice)), inference(monotonicity,[status(thm)],[740])). tff(742,plain, ((paul = alice) <=> (paul = \|'paul'\|)), inference(symmetry,[status(thm)],[741])). tff(743,plain, ((~(paul = alice)) <=> (~(paul = \|'paul'\|))), inference(monotonicity,[status(thm)],[742])). tff(744,plain, (~(paul = \|'paul'\|)), inference(modus_ponens,[status(thm)],[165, 743])). tff(745,plain, (paul = \|'alice'\|), inference(unit_resolution,[status(thm)],[176, 744, 733, 22])). tff(746,plain, (\|'alice'\| = paul), inference(symmetry,[status(thm)],[745])). tff(747,plain, ((fred = \|'alice'\|) <=> (fred = paul)), inference(monotonicity,[status(thm)],[746])). tff(748,plain, ((fred = \|'alice'\|) <=> (paul = fred)), inference(transitivity,[status(thm)],[747, 96])). tff(749,plain, ((paul = fred) <=> (fred = \|'alice'\|)), inference(symmetry,[status(thm)],[748])). tff(750,plain, ((~(paul = fred)) <=> (~(fred = \|'alice'\|))), inference(monotonicity,[status(thm)],[749])). tff(751,plain, (~(fred = \|'alice'\|)), inference(modus_ponens,[status(thm)],[139, 750])). tff(752,plain, ((fred = \|'mary'\|) <=> (fred = lucy)), inference(monotonicity,[status(thm)],[734])). tff(753,plain, ((fred = lucy) <=> (fred = \|'mary'\|)), inference(symmetry,[status(thm)],[752])). tff(754,plain, ((~(fred = lucy)) <=> (~(fred = \|'mary'\|))), inference(monotonicity,[status(thm)],[753])). tff(755,plain, (~(fred = \|'mary'\|)), inference(modus_ponens,[status(thm)],[113, 754])). tff(756,plain, ((fred = \|'fred'\|) <=> (fred = mary)), inference(monotonicity,[status(thm)],[723])). tff(757,plain, ((fred = \|'fred'\|) <=> (mary = fred)), inference(transitivity,[status(thm)],[756, 19])). tff(758,plain, ((mary = fred) <=> (fred = \|'fred'\|)), inference(symmetry,[status(thm)],[757])). tff(759,plain, ((~(mary = fred)) <=> (~(fred = \|'fred'\|))), inference(monotonicity,[status(thm)],[758])). tff(760,plain, (~(fred = \|'fred'\|)), inference(modus_ponens,[status(thm)],[316, 759])). tff(761,plain, ((fred = \|'paul'\|) <=> (fred = alice)), inference(monotonicity,[status(thm)],[740])). tff(762,plain, ((fred = alice) <=> (fred = \|'paul'\|)), inference(symmetry,[status(thm)],[761])). tff(763,plain, ((~(fred = alice)) <=> (~(fred = \|'paul'\|))), inference(monotonicity,[status(thm)],[762])). tff(764,plain, (~(fred = \|'paul'\|)), inference(modus_ponens,[status(thm)],[214, 763])). tff(765,plain, (fred = \|'alice'\|), inference(unit_resolution,[status(thm)],[131, 764, 760, 755])). tff(766,plain, ($false), inference(unit_resolution,[status(thm)],[765, 751])). tff(767,plain,((~(X!0 = \|'mary'\|)) \| (paul = \|'mary'\|) \| (alice = \|'alice'\|) \| (~(lucy = X!0))), inference(lemma,lemma(discharge,[]))). tff(768,plain, (~(X!0 = \|'mary'\|)), inference(unit_resolution,[status(thm)],[767, 29, 22, 20])). tff(769,assumption,(alice = \|'paul'\|), introduced(assumption)). tff(770,plain, (\|'paul'\| = alice), inference(symmetry,[status(thm)],[769])). tff(771,plain, ((paul = \|'paul'\|) <=> (paul = alice)), inference(monotonicity,[status(thm)],[770])). tff(772,plain, ((paul = alice) <=> (paul = \|'paul'\|)), inference(symmetry,[status(thm)],[771])). tff(773,plain, ((~(paul = alice)) <=> (~(paul = \|'paul'\|))), inference(monotonicity,[status(thm)],[772])). tff(774,plain, (~(paul = \|'paul'\|)), inference(modus_ponens,[status(thm)],[165, 773])). tff(775,plain, (paul = \|'alice'\|), inference(unit_resolution,[status(thm)],[176, 774, 733, 22])). tff(776,plain, (\|'alice'\| = paul), inference(symmetry,[status(thm)],[775])). tff(777,plain, ((X!0 = \|'alice'\|) <=> (lucy = paul)), inference(monotonicity,[status(thm)],[31, 776])). tff(778,plain, ((X!0 = \|'alice'\|) <=> (paul = lucy)), inference(transitivity,[status(thm)],[777, 25])). tff(779,plain, ((paul = lucy) <=> (X!0 = \|'alice'\|)), inference(symmetry,[status(thm)],[778])). tff(780,plain, ((~(paul = lucy)) <=> (~(X!0 = \|'alice'\|))), inference(monotonicity,[status(thm)],[779])). tff(781,plain, (~(X!0 = \|'alice'\|)), inference(modus_ponens,[status(thm)],[106, 780])). tff(782,plain, ((X!0 = \|'fred'\|) <=> (lucy = mary)), inference(monotonicity,[status(thm)],[31, 723])). tff(783,plain, ((X!0 = \|'fred'\|) <=> (mary = lucy)), inference(transitivity,[status(thm)],[782, 82])). tff(784,plain, ((mary = lucy) <=> (X!0 = \|'fred'\|)), inference(symmetry,[status(thm)],[783])). tff(785,plain, ((~(mary = lucy)) <=> (~(X!0 = \|'fred'\|))), inference(monotonicity,[status(thm)],[784])). tff(786,plain, (~(X!0 = \|'fred'\|)), inference(modus_ponens,[status(thm)],[89, 785])). tff(787,plain, ((X!0 = \|'paul'\|) <=> (lucy = alice)), inference(monotonicity,[status(thm)],[31, 770])). tff(788,plain, ((X!0 = \|'paul'\|) <=> (alice = lucy)), inference(transitivity,[status(thm)],[787, 91])). tff(789,plain, ((alice = lucy) <=> (X!0 = \|'paul'\|)), inference(symmetry,[status(thm)],[788])). tff(790,plain, ((~(alice = lucy)) <=> (~(X!0 = \|'paul'\|))), inference(monotonicity,[status(thm)],[789])). tff(791,plain, (~(X!0 = \|'paul'\|)), inference(modus_ponens,[status(thm)],[146, 790])). tff(792,plain, (X!0 = \|'alice'\|), inference(unit_resolution,[status(thm)],[184, 791, 94, 786])). tff(793,plain, ($false), inference(unit_resolution,[status(thm)],[792, 781])). tff(794,plain,((~(alice = \|'paul'\|)) \| (~(lucy = X!0)) \| (X!0 = \|'mary'\|) \| (paul = \|'mary'\|)), inference(lemma,lemma(discharge,[]))). tff(795,plain, (~(alice = \|'paul'\|)), inference(unit_resolution,[status(thm)],[794, 768, 20, 22])). tff(796,plain, (alice = \|'mary'\|), inference(unit_resolution,[status(thm)],[157, 795, 29, 728])). tff(797,plain, (\|'mary'\| = alice), inference(symmetry,[status(thm)],[796])). tff(798,plain, ((fred = \|'mary'\|) <=> (fred = alice)), inference(monotonicity,[status(thm)],[797])). tff(799,plain, ((fred = alice) <=> (fred = \|'mary'\|)), inference(symmetry,[status(thm)],[798])). tff(800,plain, ((~(fred = alice)) <=> (~(fred = \|'mary'\|))), inference(monotonicity,[status(thm)],[799])). tff(801,plain, (~(fred = \|'mary'\|)), inference(modus_ponens,[status(thm)],[214, 800])). tff(802,assumption,(~(fred = \|'fred'\|)), introduced(assumption)). tff(803,plain, ((fred = \|'paul'\|) <=> (fred = paul)), inference(monotonicity,[status(thm)],[588])). tff(804,plain, ((fred = \|'paul'\|) <=> (paul = fred)), inference(transitivity,[status(thm)],[803, 96])). tff(805,plain, ((paul = fred) <=> (fred = \|'paul'\|)), inference(symmetry,[status(thm)],[804])). tff(806,plain, ((~(paul = fred)) <=> (~(fred = \|'paul'\|))), inference(monotonicity,[status(thm)],[805])). tff(807,plain, (~(fred = \|'paul'\|)), inference(modus_ponens,[status(thm)],[139, 806])). tff(808,plain, (fred = \|'alice'\|), inference(unit_resolution,[status(thm)],[131, 807, 802, 27])). tff(809,plain, (\|'alice'\| = fred), inference(symmetry,[status(thm)],[808])). tff(810,plain, ((X!0 = \|'alice'\|) <=> (lucy = fred)), inference(monotonicity,[status(thm)],[31, 809])). tff(811,plain, ((X!0 = \|'alice'\|) <=> (fred = lucy)), inference(transitivity,[status(thm)],[810, 21])). tff(812,plain, ((fred = lucy) <=> (X!0 = \|'alice'\|)), inference(symmetry,[status(thm)],[811])). tff(813,plain, ((~(fred = lucy)) <=> (~(X!0 = \|'alice'\|))), inference(monotonicity,[status(thm)],[812])). tff(814,plain, (~(X!0 = \|'alice'\|)), inference(modus_ponens,[status(thm)],[113, 813])). tff(815,assumption,(~(X!0 = \|'fred'\|)), introduced(assumption)). tff(816,plain, (X!0 = \|'alice'\|), inference(unit_resolution,[status(thm)],[184, 617, 94, 815])). tff(817,plain, ($false), inference(unit_resolution,[status(thm)],[816, 814])). tff(818,plain,((~(paul = \|'paul'\|)) \| (~(lucy = X!0)) \| (X!0 = \|'mary'\|) \| (X!0 = \|'fred'\|) \| (fred = \|'fred'\|) \| (fred = \|'mary'\|)), inference(lemma,lemma(discharge,[]))). tff(819,plain, (~(paul = \|'paul'\|)), inference(unit_resolution,[status(thm)],[818, 768, 20, 786, 760, 801])). tff(820,plain, (paul = \|'alice'\|), inference(unit_resolution,[status(thm)],[176, 819, 733, 22])). tff(821,plain, (\|'alice'\| = paul), inference(symmetry,[status(thm)],[820])). tff(822,plain, ((fred = \|'alice'\|) <=> (fred = paul)), inference(monotonicity,[status(thm)],[821])). tff(823,plain, ((fred = \|'alice'\|) <=> (paul = fred)), inference(transitivity,[status(thm)],[822, 96])). tff(824,plain, ((paul = fred) <=> (fred = \|'alice'\|)), inference(symmetry,[status(thm)],[823])). tff(825,plain, ((~(paul = fred)) <=> (~(fred = \|'alice'\|))), inference(monotonicity,[status(thm)],[824])). tff(826,plain, (~(fred = \|'alice'\|)), inference(modus_ponens,[status(thm)],[139, 825])). tff(827,plain, (fred = \|'paul'\|), inference(unit_resolution,[status(thm)],[131, 826, 760, 801])). tff(828,plain, (\|'paul'\| = fred), inference(symmetry,[status(thm)],[827])). tff(829,plain, ((X!0 = \|'paul'\|) <=> (lucy = fred)), inference(monotonicity,[status(thm)],[31, 828])). tff(830,plain, ((X!0 = \|'paul'\|) <=> (fred = lucy)), inference(transitivity,[status(thm)],[829, 21])). tff(831,plain, ((fred = lucy) <=> (X!0 = \|'paul'\|)), inference(symmetry,[status(thm)],[830])). tff(832,plain, ((~(fred = lucy)) <=> (~(X!0 = \|'paul'\|))), inference(monotonicity,[status(thm)],[831])). tff(833,plain, (~(X!0 = \|'paul'\|)), inference(modus_ponens,[status(thm)],[113, 832])). tff(834,plain, ((X!0 = \|'alice'\|) <=> (lucy = paul)), inference(monotonicity,[status(thm)],[31, 821])). tff(835,plain, ((X!0 = \|'alice'\|) <=> (paul = lucy)), inference(transitivity,[status(thm)],[834, 25])). tff(836,plain, ((paul = lucy) <=> (X!0 = \|'alice'\|)), inference(symmetry,[status(thm)],[835])). tff(837,plain, ((~(paul = lucy)) <=> (~(X!0 = \|'alice'\|))), inference(monotonicity,[status(thm)],[836])). tff(838,plain, (~(X!0 = \|'alice'\|)), inference(modus_ponens,[status(thm)],[106, 837])). tff(839,plain, (X!0 = \|'paul'\|), inference(unit_resolution,[status(thm)],[184, 838, 768, 786])). tff(840,plain, ($false), inference(unit_resolution,[status(thm)],[839, 833])). tff(841,plain,((alice = \|'alice'\|) \| (~(lucy = X!0)) \| (paul = \|'mary'\|)), inference(lemma,lemma(discharge,[]))). tff(842,plain, (alice = \|'alice'\|), inference(unit_resolution,[status(thm)],[841, 22, 20])). tff(843,plain, (\|'alice'\| = alice), inference(symmetry,[status(thm)],[842])). tff(844,plain, ((fred = \|'alice'\|) <=> (fred = alice)), inference(monotonicity,[status(thm)],[843])). tff(845,plain, ((fred = alice) <=> (fred = \|'alice'\|)), inference(symmetry,[status(thm)],[844])). tff(846,plain, ((~(fred = alice)) <=> (~(fred = \|'alice'\|))), inference(monotonicity,[status(thm)],[845])). tff(847,plain, (~(fred = \|'alice'\|)), inference(modus_ponens,[status(thm)],[214, 846])). tff(848,plain, ((paul = \|'alice'\|) <=> (paul = alice)), inference(monotonicity,[status(thm)],[843])). tff(849,plain, ((paul = alice) <=> (paul = \|'alice'\|)), inference(symmetry,[status(thm)],[848])). tff(850,plain, ((~(paul = alice)) <=> (~(paul = \|'alice'\|))), inference(monotonicity,[status(thm)],[849])). tff(851,plain, (~(paul = \|'alice'\|)), inference(modus_ponens,[status(thm)],[165, 850])). tff(852,plain, (paul = \|'paul'\|), inference(unit_resolution,[status(thm)],[176, 851, 733, 22])). tff(853,plain, (\|'paul'\| = paul), inference(symmetry,[status(thm)],[852])). tff(854,plain, ((fred = \|'paul'\|) <=> (fred = paul)), inference(monotonicity,[status(thm)],[853])). tff(855,plain, ((fred = \|'paul'\|) <=> (paul = fred)), inference(transitivity,[status(thm)],[854, 96])). tff(856,plain, ((paul = fred) <=> (fred = \|'paul'\|)), inference(symmetry,[status(thm)],[855])). tff(857,plain, ((~(paul = fred)) <=> (~(fred = \|'paul'\|))), inference(monotonicity,[status(thm)],[856])). tff(858,plain, (~(fred = \|'paul'\|)), inference(modus_ponens,[status(thm)],[139, 857])). tff(859,plain, (fred = \|'mary'\|), inference(unit_resolution,[status(thm)],[131, 858, 760, 847])). tff(860,plain, (\|'mary'\| = fred), inference(symmetry,[status(thm)],[859])). tff(861,plain, ((X!0 = \|'mary'\|) <=> (lucy = fred)), inference(monotonicity,[status(thm)],[31, 860])). tff(862,plain, ((X!0 = \|'mary'\|) <=> (fred = lucy)), inference(transitivity,[status(thm)],[861, 21])). tff(863,plain, ((fred = lucy) <=> (X!0 = \|'mary'\|)), inference(symmetry,[status(thm)],[862])). tff(864,plain, ((~(fred = lucy)) <=> (~(X!0 = \|'mary'\|))), inference(monotonicity,[status(thm)],[863])). tff(865,plain, (~(X!0 = \|'mary'\|)), inference(modus_ponens,[status(thm)],[113, 864])). tff(866,plain, ((X!0 = \|'alice'\|) <=> (lucy = alice)), inference(monotonicity,[status(thm)],[31, 843])). tff(867,plain, ((X!0 = \|'alice'\|) <=> (alice = lucy)), inference(transitivity,[status(thm)],[866, 91])). tff(868,plain, ((alice = lucy) <=> (X!0 = \|'alice'\|)), inference(symmetry,[status(thm)],[867])). tff(869,plain, ((~(alice = lucy)) <=> (~(X!0 = \|'alice'\|))), inference(monotonicity,[status(thm)],[868])). tff(870,plain, (~(X!0 = \|'alice'\|)), inference(modus_ponens,[status(thm)],[146, 869])). tff(871,plain, ((X!0 = \|'paul'\|) <=> (lucy = paul)), inference(monotonicity,[status(thm)],[31, 853])). tff(872,plain, ((X!0 = \|'paul'\|) <=> (paul = lucy)), inference(transitivity,[status(thm)],[871, 25])). tff(873,plain, ((paul = lucy) <=> (X!0 = \|'paul'\|)), inference(symmetry,[status(thm)],[872])). tff(874,plain, ((~(paul = lucy)) <=> (~(X!0 = \|'paul'\|))), inference(monotonicity,[status(thm)],[873])). tff(875,plain, (~(X!0 = \|'paul'\|)), inference(modus_ponens,[status(thm)],[106, 874])). tff(876,plain, (X!0 = \|'mary'\|), inference(unit_resolution,[status(thm)],[184, 875, 870, 786])). tff(877,plain, ($false), inference(unit_resolution,[status(thm)],[876, 865])). tff(878,plain,((paul = \|'mary'\|) \| (~(lucy = X!0))), inference(lemma,lemma(discharge,[]))). tff(879,plain, (paul = \|'mary'\|), inference(unit_resolution,[status(thm)],[878, 20])). tff(880,plain, (\|'mary'\| = paul), inference(symmetry,[status(thm)],[879])). tff(881,plain, ((mary = \|'mary'\|) <=> (mary = paul)), inference(monotonicity,[status(thm)],[880])). tff(882,plain, ((mary = paul) <=> (mary = \|'mary'\|)), inference(symmetry,[status(thm)],[881])). tff(883,plain, ((~(mary = paul)) <=> (~(mary = \|'mary'\|))), inference(monotonicity,[status(thm)],[882])). tff(884,plain, (~(mary = \|'mary'\|)), inference(modus_ponens,[status(thm)],[324, 883])). tff(885,plain, ((mary = \|'fred'\|) <=> (mary = lucy)), inference(monotonicity,[status(thm)],[100])). tff(886,plain, ((mary = lucy) <=> (mary = \|'fred'\|)), inference(symmetry,[status(thm)],[885])). tff(887,plain, ((~(mary = lucy)) <=> (~(mary = \|'fred'\|))), inference(monotonicity,[status(thm)],[886])). tff(888,plain, (~(mary = \|'fred'\|)), inference(modus_ponens,[status(thm)],[89, 887])). tff(889,plain, ((alice = \|'mary'\|) <=> (alice = paul)), inference(monotonicity,[status(thm)],[880])). tff(890,plain, ((alice = \|'mary'\|) <=> (paul = alice)), inference(transitivity,[status(thm)],[889, 30])). tff(891,plain, ((paul = alice) <=> (alice = \|'mary'\|)), inference(symmetry,[status(thm)],[890])). tff(892,plain, ((~(paul = alice)) <=> (~(alice = \|'mary'\|))), inference(monotonicity,[status(thm)],[891])). tff(893,plain, (~(alice = \|'mary'\|)), inference(modus_ponens,[status(thm)],[165, 892])). tff(894,plain, ((fred = \|'mary'\|) <=> (fred = paul)), inference(monotonicity,[status(thm)],[880])). tff(895,plain, ((fred = \|'mary'\|) <=> (paul = fred)), inference(transitivity,[status(thm)],[894, 96])). tff(896,plain, ((paul = fred) <=> (fred = \|'mary'\|)), inference(symmetry,[status(thm)],[895])). tff(897,plain, ((~(paul = fred)) <=> (~(fred = \|'mary'\|))), inference(monotonicity,[status(thm)],[896])). tff(898,plain, (~(fred = \|'mary'\|)), inference(modus_ponens,[status(thm)],[139, 897])). tff(899,plain, ((mary = \|'paul'\|) <=> (mary = alice)), inference(monotonicity,[status(thm)],[770])). tff(900,plain, ((mary = alice) <=> (mary = \|'paul'\|)), inference(symmetry,[status(thm)],[899])). tff(901,plain, ((~(mary = alice)) <=> (~(mary = \|'paul'\|))), inference(monotonicity,[status(thm)],[900])). tff(902,plain, (~(mary = \|'paul'\|)), inference(modus_ponens,[status(thm)],[80, 901])). tff(903,plain, (mary = \|'alice'\|), inference(unit_resolution,[status(thm)],[306, 902, 24, 594])). tff(904,plain, (\|'alice'\| = mary), inference(symmetry,[status(thm)],[903])). tff(905,plain, ((fred = \|'alice'\|) <=> (fred = mary)), inference(monotonicity,[status(thm)],[904])). tff(906,plain, ((fred = \|'alice'\|) <=> (mary = fred)), inference(transitivity,[status(thm)],[905, 19])). tff(907,plain, ((mary = fred) <=> (fred = \|'alice'\|)), inference(symmetry,[status(thm)],[906])). tff(908,plain, ((~(mary = fred)) <=> (~(fred = \|'alice'\|))), inference(monotonicity,[status(thm)],[907])). tff(909,plain, (~(fred = \|'alice'\|)), inference(modus_ponens,[status(thm)],[316, 908])). tff(910,plain, ((fred = \|'paul'\|) <=> (fred = alice)), inference(monotonicity,[status(thm)],[770])). tff(911,plain, ((fred = alice) <=> (fred = \|'paul'\|)), inference(symmetry,[status(thm)],[910])). tff(912,plain, ((~(fred = alice)) <=> (~(fred = \|'paul'\|))), inference(monotonicity,[status(thm)],[911])). tff(913,plain, (~(fred = \|'paul'\|)), inference(modus_ponens,[status(thm)],[214, 912])). tff(914,plain, (fred = \|'alice'\|), inference(unit_resolution,[status(thm)],[131, 913, 27, 802])). tff(915,plain, ($false), inference(unit_resolution,[status(thm)],[914, 909])). tff(916,plain,((~(alice = \|'paul'\|)) \| (fred = \|'mary'\|) \| (fred = \|'fred'\|) \| (mary = \|'fred'\|) \| (mary = \|'mary'\|)), inference(lemma,lemma(discharge,[]))). tff(917,plain, (~(alice = \|'paul'\|)), inference(unit_resolution,[status(thm)],[916, 114, 898, 888, 884])). tff(918,plain, (alice = \|'alice'\|), inference(unit_resolution,[status(thm)],[157, 917, 893, 147])). tff(919,plain, (\|'alice'\| = alice), inference(symmetry,[status(thm)],[918])). tff(920,plain, ((mary = \|'alice'\|) <=> (mary = alice)), inference(monotonicity,[status(thm)],[919])). tff(921,plain, ((mary = alice) <=> (mary = \|'alice'\|)), inference(symmetry,[status(thm)],[920])). tff(922,plain, ((~(mary = alice)) <=> (~(mary = \|'alice'\|))), inference(monotonicity,[status(thm)],[921])). tff(923,plain, (~(mary = \|'alice'\|)), inference(modus_ponens,[status(thm)],[80, 922])). tff(924,plain, (mary = \|'paul'\|), inference(unit_resolution,[status(thm)],[306, 923, 888, 884])). tff(925,plain, (\|'paul'\| = mary), inference(symmetry,[status(thm)],[924])). tff(926,plain, ((fred = \|'paul'\|) <=> (fred = mary)), inference(monotonicity,[status(thm)],[925])). tff(927,plain, ((fred = \|'paul'\|) <=> (mary = fred)), inference(transitivity,[status(thm)],[926, 19])). tff(928,plain, ((mary = fred) <=> (fred = \|'paul'\|)), inference(symmetry,[status(thm)],[927])). tff(929,plain, ((~(mary = fred)) <=> (~(fred = \|'paul'\|))), inference(monotonicity,[status(thm)],[928])). tff(930,plain, (~(fred = \|'paul'\|)), inference(modus_ponens,[status(thm)],[316, 929])). tff(931,plain, ((fred = \|'alice'\|) <=> (fred = alice)), inference(monotonicity,[status(thm)],[919])). tff(932,plain, ((fred = alice) <=> (fred = \|'alice'\|)), inference(symmetry,[status(thm)],[931])). tff(933,plain, ((~(fred = alice)) <=> (~(fred = \|'alice'\|))), inference(monotonicity,[status(thm)],[932])). tff(934,plain, (~(fred = \|'alice'\|)), inference(modus_ponens,[status(thm)],[214, 933])). tff(935,plain, (fred = \|'paul'\|), inference(unit_resolution,[status(thm)],[131, 934, 898, 114])). tff(936,plain, ($false), inference(unit_resolution,[status(thm)],[935, 930])). tff(937,plain,((~(X!0 = \|'fred'\|)) \| (~(lucy = X!0))), inference(lemma,lemma(discharge,[]))). tff(938,plain, (~(X!0 = \|'fred'\|)), inference(unit_resolution,[status(thm)],[937, 20])). tff(939,plain, ((X!0 = \|'mary'\|) <=> (lucy = paul)), inference(monotonicity,[status(thm)],[31, 880])). tff(940,plain, ((X!0 = \|'mary'\|) <=> (paul = lucy)), inference(transitivity,[status(thm)],[939, 25])). tff(941,plain, ((paul = lucy) <=> (X!0 = \|'mary'\|)), inference(symmetry,[status(thm)],[940])). tff(942,plain, ((~(paul = lucy)) <=> (~(X!0 = \|'mary'\|))), inference(monotonicity,[status(thm)],[941])). tff(943,plain, (~(X!0 = \|'mary'\|)), inference(modus_ponens,[status(thm)],[106, 942])). tff(944,assumption,(X!0 = \|'alice'\|), introduced(assumption)). tff(945,plain, (\|'alice'\| = X!0), inference(symmetry,[status(thm)],[944])). tff(946,plain, (\|'alice'\| = lucy), inference(transitivity,[status(thm)],[945, 31])). tff(947,plain, ((mary = \|'alice'\|) <=> (mary = lucy)), inference(monotonicity,[status(thm)],[946])). tff(948,plain, ((mary = lucy) <=> (mary = \|'alice'\|)), inference(symmetry,[status(thm)],[947])). tff(949,plain, ((~(mary = lucy)) <=> (~(mary = \|'alice'\|))), inference(monotonicity,[status(thm)],[948])). tff(950,plain, (~(mary = \|'alice'\|)), inference(modus_ponens,[status(thm)],[89, 949])). tff(951,plain, ((fred = \|'alice'\|) <=> (fred = lucy)), inference(monotonicity,[status(thm)],[946])). tff(952,plain, ((fred = lucy) <=> (fred = \|'alice'\|)), inference(symmetry,[status(thm)],[951])). tff(953,plain, ((~(fred = lucy)) <=> (~(fred = \|'alice'\|))), inference(monotonicity,[status(thm)],[952])). tff(954,plain, (~(fred = \|'alice'\|)), inference(modus_ponens,[status(thm)],[113, 953])). tff(955,plain, ((mary = \|'fred'\|) <=> (mary = fred)), inference(monotonicity,[status(thm)],[254])). tff(956,plain, ((mary = fred) <=> (mary = \|'fred'\|)), inference(symmetry,[status(thm)],[955])). tff(957,plain, ((~(mary = fred)) <=> (~(mary = \|'fred'\|))), inference(monotonicity,[status(thm)],[956])). tff(958,plain, (~(mary = \|'fred'\|)), inference(modus_ponens,[status(thm)],[316, 957])). tff(959,plain, (mary = \|'paul'\|), inference(unit_resolution,[status(thm)],[306, 958, 28, 594])). tff(960,plain, (\|'paul'\| = mary), inference(symmetry,[status(thm)],[959])). tff(961,plain, ((alice = \|'paul'\|) <=> (alice = mary)), inference(monotonicity,[status(thm)],[960])). tff(962,plain, ((alice = \|'paul'\|) <=> (mary = alice)), inference(transitivity,[status(thm)],[961, 23])). tff(963,plain, ((mary = alice) <=> (alice = \|'paul'\|)), inference(symmetry,[status(thm)],[962])). tff(964,plain, ((~(mary = alice)) <=> (~(alice = \|'paul'\|))), inference(monotonicity,[status(thm)],[963])). tff(965,plain, (~(alice = \|'paul'\|)), inference(modus_ponens,[status(thm)],[80, 964])). tff(966,plain, (alice = \|'paul'\|), inference(unit_resolution,[status(thm)],[157, 270, 92, 29])). tff(967,plain, ($false), inference(unit_resolution,[status(thm)],[966, 965])). tff(968,plain,((~(fred = \|'fred'\|)) \| (alice = \|'mary'\|) \| (alice = \|'alice'\|) \| (mary = \|'alice'\|) \| (mary = \|'mary'\|)), inference(lemma,lemma(discharge,[]))). tff(969,plain, (~(fred = \|'fred'\|)), inference(unit_resolution,[status(thm)],[968, 950, 29, 893, 884])). tff(970,plain, (fred = \|'paul'\|), inference(unit_resolution,[status(thm)],[131, 969, 898, 954])). tff(971,plain, (\|'paul'\| = fred), inference(symmetry,[status(thm)],[970])). tff(972,plain, ((mary = \|'paul'\|) <=> (mary = fred)), inference(monotonicity,[status(thm)],[971])). tff(973,plain, ((mary = fred) <=> (mary = \|'paul'\|)), inference(symmetry,[status(thm)],[972])). tff(974,plain, ((~(mary = fred)) <=> (~(mary = \|'paul'\|))), inference(monotonicity,[status(thm)],[973])). tff(975,plain, (~(mary = \|'paul'\|)), inference(modus_ponens,[status(thm)],[316, 974])). tff(976,plain, (mary = \|'fred'\|), inference(unit_resolution,[status(thm)],[306, 975, 950, 884])). tff(977,plain, (\|'fred'\| = mary), inference(symmetry,[status(thm)],[976])). tff(978,plain, ((alice = \|'fred'\|) <=> (alice = mary)), inference(monotonicity,[status(thm)],[977])). tff(979,plain, ((alice = \|'fred'\|) <=> (mary = alice)), inference(transitivity,[status(thm)],[978, 23])). tff(980,plain, ((mary = alice) <=> (alice = \|'fred'\|)), inference(symmetry,[status(thm)],[979])). tff(981,plain, ((~(mary = alice)) <=> (~(alice = \|'fred'\|))), inference(monotonicity,[status(thm)],[980])). tff(982,plain, (~(alice = \|'fred'\|)), inference(modus_ponens,[status(thm)],[80, 981])). tff(983,plain, ((alice = \|'paul'\|) <=> (alice = fred)), inference(monotonicity,[status(thm)],[971])). tff(984,plain, ((alice = \|'paul'\|) <=> (fred = alice)), inference(transitivity,[status(thm)],[983, 93])). tff(985,plain, ((fred = alice) <=> (alice = \|'paul'\|)), inference(symmetry,[status(thm)],[984])). tff(986,plain, ((~(fred = alice)) <=> (~(alice = \|'paul'\|))), inference(monotonicity,[status(thm)],[985])). tff(987,plain, (~(alice = \|'paul'\|)), inference(modus_ponens,[status(thm)],[214, 986])). tff(988,plain, (alice = \|'fred'\|), inference(unit_resolution,[status(thm)],[157, 987, 893, 29])). tff(989,plain, ($false), inference(unit_resolution,[status(thm)],[988, 982])). tff(990,plain,((~(X!0 = \|'alice'\|)) \| (alice = \|'alice'\|) \| (~(lucy = X!0))), inference(lemma,lemma(discharge,[]))). tff(991,plain, (~(X!0 = \|'alice'\|)), inference(unit_resolution,[status(thm)],[990, 29, 20])). tff(992,plain, (X!0 = \|'paul'\|), inference(unit_resolution,[status(thm)],[184, 991, 943, 938])). tff(993,plain, (\|'paul'\| = X!0), inference(symmetry,[status(thm)],[992])). tff(994,plain, (\|'paul'\| = lucy), inference(transitivity,[status(thm)],[993, 31])). tff(995,plain, ((mary = \|'paul'\|) <=> (mary = lucy)), inference(monotonicity,[status(thm)],[994])). tff(996,plain, ((mary = lucy) <=> (mary = \|'paul'\|)), inference(symmetry,[status(thm)],[995])). tff(997,plain, ((~(mary = lucy)) <=> (~(mary = \|'paul'\|))), inference(monotonicity,[status(thm)],[996])). tff(998,plain, (~(mary = \|'paul'\|)), inference(modus_ponens,[status(thm)],[89, 997])). tff(999,plain, ((alice = \|'paul'\|) <=> (alice = lucy)), inference(monotonicity,[status(thm)],[994])). tff(1000,plain, ((alice = lucy) <=> (alice = \|'paul'\|)), inference(symmetry,[status(thm)],[999])). tff(1001,plain, ((~(alice = lucy)) <=> (~(alice = \|'paul'\|))), inference(monotonicity,[status(thm)],[1000])). tff(1002,plain, (~(alice = \|'paul'\|)), inference(modus_ponens,[status(thm)],[146, 1001])). tff(1003,plain, (alice = \|'fred'\|), inference(unit_resolution,[status(thm)],[157, 1002, 893, 29])). tff(1004,plain, (\|'fred'\| = alice), inference(symmetry,[status(thm)],[1003])). tff(1005,plain, ((mary = \|'fred'\|) <=> (mary = alice)), inference(monotonicity,[status(thm)],[1004])). tff(1006,plain, ((mary = alice) <=> (mary = \|'fred'\|)), inference(symmetry,[status(thm)],[1005])). tff(1007,plain, ((~(mary = alice)) <=> (~(mary = \|'fred'\|))), inference(monotonicity,[status(thm)],[1006])). tff(1008,plain, (~(mary = \|'fred'\|)), inference(modus_ponens,[status(thm)],[80, 1007])). tff(1009,plain, (mary = \|'alice'\|), inference(unit_resolution,[status(thm)],[306, 1008, 998, 884])). tff(1010,plain, (\|'alice'\| = mary), inference(symmetry,[status(thm)],[1009])). tff(1011,plain, ((fred = \|'alice'\|) <=> (fred = mary)), inference(monotonicity,[status(thm)],[1010])). tff(1012,plain, ((fred = \|'alice'\|) <=> (mary = fred)), inference(transitivity,[status(thm)],[1011, 19])). tff(1013,plain, ((mary = fred) <=> (fred = \|'alice'\|)), inference(symmetry,[status(thm)],[1012])). tff(1014,plain, ((~(mary = fred)) <=> (~(fred = \|'alice'\|))), inference(monotonicity,[status(thm)],[1013])). tff(1015,plain, (~(fred = \|'alice'\|)), inference(modus_ponens,[status(thm)],[316, 1014])). tff(1016,plain, ((fred = \|'paul'\|) <=> (fred = lucy)), inference(monotonicity,[status(thm)],[994])). tff(1017,plain, ((fred = lucy) <=> (fred = \|'paul'\|)), inference(symmetry,[status(thm)],[1016])). tff(1018,plain, ((~(fred = lucy)) <=> (~(fred = \|'paul'\|))), inference(monotonicity,[status(thm)],[1017])). tff(1019,plain, (~(fred = \|'paul'\|)), inference(modus_ponens,[status(thm)],[113, 1018])). tff(1020,plain, ((fred = \|'fred'\|) <=> (fred = alice)), inference(monotonicity,[status(thm)],[1004])). tff(1021,plain, ((fred = alice) <=> (fred = \|'fred'\|)), inference(symmetry,[status(thm)],[1020])). tff(1022,plain, ((~(fred = alice)) <=> (~(fred = \|'fred'\|))), inference(monotonicity,[status(thm)],[1021])). tff(1023,plain, (~(fred = \|'fred'\|)), inference(modus_ponens,[status(thm)],[214, 1022])). tff(1024,plain, (fred = \|'alice'\|), inference(unit_resolution,[status(thm)],[131, 1023, 898, 1019])). tff(1025,plain, ($false), inference(unit_resolution,[status(thm)],[1024, 1015])). tff(1026,plain,((alice = \|'alice'\|) \| (~(lucy = X!0))), inference(lemma,lemma(discharge,[]))). tff(1027,plain, (alice = \|'alice'\|), inference(unit_resolution,[status(thm)],[1026, 20])). tff(1028,plain, (\|'alice'\| = alice), inference(symmetry,[status(thm)],[1027])). tff(1029,plain, ((mary = \|'alice'\|) <=> (mary = alice)), inference(monotonicity,[status(thm)],[1028])). tff(1030,plain, ((mary = alice) <=> (mary = \|'alice'\|)), inference(symmetry,[status(thm)],[1029])). tff(1031,plain, ((~(mary = alice)) <=> (~(mary = \|'alice'\|))), inference(monotonicity,[status(thm)],[1030])). tff(1032,plain, (~(mary = \|'alice'\|)), inference(modus_ponens,[status(thm)],[80, 1031])). tff(1033,plain, ((X!0 = \|'alice'\|) <=> (lucy = alice)), inference(monotonicity,[status(thm)],[31, 1028])). tff(1034,plain, ((X!0 = \|'alice'\|) <=> (alice = lucy)), inference(transitivity,[status(thm)],[1033, 91])). tff(1035,plain, ((alice = lucy) <=> (X!0 = \|'alice'\|)), inference(symmetry,[status(thm)],[1034])). tff(1036,plain, ((~(alice = lucy)) <=> (~(X!0 = \|'alice'\|))), inference(monotonicity,[status(thm)],[1035])). tff(1037,plain, (~(X!0 = \|'alice'\|)), inference(modus_ponens,[status(thm)],[146, 1036])). tff(1038,plain, (X!0 = \|'paul'\|), inference(unit_resolution,[status(thm)],[184, 1037, 943, 938])). tff(1039,plain, (\|'paul'\| = X!0), inference(symmetry,[status(thm)],[1038])). tff(1040,plain, (\|'paul'\| = lucy), inference(transitivity,[status(thm)],[1039, 31])). tff(1041,plain, ((mary = \|'paul'\|) <=> (mary = lucy)), inference(monotonicity,[status(thm)],[1040])). tff(1042,plain, ((mary = lucy) <=> (mary = \|'paul'\|)), inference(symmetry,[status(thm)],[1041])). tff(1043,plain, ((~(mary = lucy)) <=> (~(mary = \|'paul'\|))), inference(monotonicity,[status(thm)],[1042])). tff(1044,plain, (~(mary = \|'paul'\|)), inference(modus_ponens,[status(thm)],[89, 1043])). tff(1045,plain, (mary = \|'fred'\|), inference(unit_resolution,[status(thm)],[306, 1044, 1032, 884])). tff(1046,plain, (\|'fred'\| = mary), inference(symmetry,[status(thm)],[1045])). tff(1047,plain, ((fred = \|'fred'\|) <=> (fred = mary)), inference(monotonicity,[status(thm)],[1046])). tff(1048,plain, ((fred = \|'fred'\|) <=> (mary = fred)), inference(transitivity,[status(thm)],[1047, 19])). tff(1049,plain, ((mary = fred) <=> (fred = \|'fred'\|)), inference(symmetry,[status(thm)],[1048])). tff(1050,plain, ((~(mary = fred)) <=> (~(fred = \|'fred'\|))), inference(monotonicity,[status(thm)],[1049])). tff(1051,plain, (~(fred = \|'fred'\|)), inference(modus_ponens,[status(thm)],[316, 1050])). tff(1052,plain, ((fred = \|'alice'\|) <=> (fred = alice)), inference(monotonicity,[status(thm)],[1028])). tff(1053,plain, ((fred = alice) <=> (fred = \|'alice'\|)), inference(symmetry,[status(thm)],[1052])). tff(1054,plain, ((~(fred = alice)) <=> (~(fred = \|'alice'\|))), inference(monotonicity,[status(thm)],[1053])). tff(1055,plain, (~(fred = \|'alice'\|)), inference(modus_ponens,[status(thm)],[214, 1054])). tff(1056,plain, ((fred = \|'paul'\|) <=> (fred = lucy)), inference(monotonicity,[status(thm)],[1040])). tff(1057,plain, ((fred = lucy) <=> (fred = \|'paul'\|)), inference(symmetry,[status(thm)],[1056])). tff(1058,plain, ((~(fred = lucy)) <=> (~(fred = \|'paul'\|))), inference(monotonicity,[status(thm)],[1057])). tff(1059,plain, (~(fred = \|'paul'\|)), inference(modus_ponens,[status(thm)],[113, 1058])). tff(1060,plain, (fred = \|'fred'\|), inference(unit_resolution,[status(thm)],[131, 1059, 898, 1055])). tff(1061,plain, ($false), inference(unit_resolution,[status(thm)],[1060, 1051])). tff(1062,plain,(~(lucy = X!0)), inference(lemma,lemma(discharge,[]))). tff(1063,plain, (~(lucy = \|'mary'\|)), inference(modus_ponens,[status(thm)],[1062, 18])). tff(1064,assumption,(~like(lucy, lucy)), introduced(assumption)). tff(1065,plain, (^[X: $i, Y: $i] : refl(((X = Y) \| like(Y, lucy) \| like(X, lucy)) <=> ((X = Y) \| like(Y, lucy) \| like(X, lucy)))), inference(bind,[status(th)],[])). tff(1066,plain, (![X: $i, Y: $i] : ((X = Y) \| like(Y, lucy) \| like(X, lucy)) <=> ![X: $i, Y: $i] : ((X = Y) \| like(Y, lucy) \| like(X, lucy))), inference(quant_intro,[status(thm)],[1065])). tff(1067,plain, (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~like(X, lucy)) & (~like(Y, lucy))) <=> (~(like(Y, lucy) \| like(X, lucy)))), ((~((~like(X, lucy)) & (~like(Y, lucy)))) <=> (~(~(like(Y, lucy) \| like(X, lucy)))))), rewrite((~(~(like(Y, lucy) \| like(X, lucy)))) <=> (like(Y, lucy) \| like(X, lucy))), ((~((~like(X, lucy)) & (~like(Y, lucy)))) <=> (like(Y, lucy) \| like(X, lucy)))), (((~((~like(X, lucy)) & (~like(Y, lucy)))) \| (X = Y)) <=> ((like(Y, lucy) \| like(X, lucy)) \| (X = Y)))), rewrite(((like(Y, lucy) \| like(X, lucy)) \| (X = Y)) <=> ((X = Y) \| like(Y, lucy) \| like(X, lucy))), (((~((~like(X, lucy)) & (~like(Y, lucy)))) \| (X = Y)) <=> ((X = Y) \| like(Y, lucy) \| like(X, lucy))))), inference(bind,[status(th)],[])). tff(1068,plain, (![X: $i, Y: $i] : ((~((~like(X, lucy)) & (~like(Y, lucy)))) \| (X = Y)) <=> ![X: $i, Y: $i] : ((X = Y) \| like(Y, lucy) \| like(X, lucy))), inference(quant_intro,[status(thm)],[1067])). tff(1069,plain, (![X: $i, Y: $i] : ((~((~like(X, lucy)) & (~like(Y, lucy)))) \| (X = Y)) <=> ![X: $i, Y: $i] : ((~((~like(X, lucy)) & (~like(Y, lucy)))) \| (X = Y))), inference(rewrite,[status(thm)],[])). tff(1070,plain, (![X: $i, Y: $i] : ((~((~like(X, lucy)) & (~like(Y, lucy)))) \| (X = Y))), inference(and_elim,[status(thm)],[10])). tff(1071,plain, (![X: $i, Y: $i] : ((~((~like(X, lucy)) & (~like(Y, lucy)))) \| (X = Y))), inference(modus_ponens,[status(thm)],[1070, 1069])). tff(1072,plain,( ![X: $i, Y: $i] : ((~((~like(X, lucy)) & (~like(Y, lucy)))) \| (X = Y))), inference(skolemize,[status(sab)],[1071])). tff(1073,plain, (![X: $i, Y: $i] : ((X = Y) \| like(Y, lucy) \| like(X, lucy))), inference(modus_ponens,[status(thm)],[1072, 1068])). tff(1074,plain, (![X: $i, Y: $i] : ((X = Y) \| like(Y, lucy) \| like(X, lucy))), inference(modus_ponens,[status(thm)],[1073, 1066])). tff(1075,plain, (((~![X: $i, Y: $i] : ((X = Y) \| like(Y, lucy) \| like(X, lucy))) \| ((lucy = \|'mary'\|) \| like(\|'mary'\|, lucy) \| like(lucy, lucy))) <=> ((~![X: $i, Y: $i] : ((X = Y) \| like(Y, lucy) \| like(X, lucy))) \| (lucy = \|'mary'\|) \| like(\|'mary'\|, lucy) \| like(lucy, lucy))), inference(rewrite,[status(thm)],[])). tff(1076,plain, ((~![X: $i, Y: $i] : ((X = Y) \| like(Y, lucy) \| like(X, lucy))) \| ((lucy = \|'mary'\|) \| like(\|'mary'\|, lucy) \| like(lucy, lucy))), inference(quant_inst,[status(thm)],[])). tff(1077,plain, ((~![X: $i, Y: $i] : ((X = Y) \| like(Y, lucy) \| like(X, lucy))) \| (lucy = \|'mary'\|) \| like(\|'mary'\|, lucy) \| like(lucy, lucy)), inference(modus_ponens,[status(thm)],[1076, 1075])). tff(1078,plain, ((lucy = \|'mary'\|) \| like(\|'mary'\|, lucy)), inference(unit_resolution,[status(thm)],[1077, 1074, 1064])). tff(1079,plain, ($false), inference(unit_resolution,[status(thm)],[1078, 15, 1063])). tff(1080,plain,(like(lucy, lucy) \| (~(X!0 = \|'mary'\|))), inference(lemma,lemma(discharge,[]))). tff(1081,plain, (like(lucy, lucy)), inference(unit_resolution,[status(thm)],[1080, 1])). tff(1082,plain, (?[X: $i] : ((~room(X)) & (~happy(X)) & (~tall(X))) <=> ?[X: $i] : ((~room(X)) & (~happy(X)) & (~tall(X)))), inference(rewrite,[status(thm)],[])). tff(1083,plain, (?[X: $i] : ((~room(X)) & (~happy(X)) & (~tall(X)))), inference(and_elim,[status(thm)],[10])). tff(1084,plain, (?[X: $i] : ((~room(X)) & (~happy(X)) & (~tall(X)))), inference(modus_ponens,[status(thm)],[1083, 1082])). tff(1085,plain,( (~room(X!3)) & (~happy(X!3)) & (~tall(X!3))), inference(skolemize,[status(sab)],[1084])). tff(1086,plain, (~happy(X!3)), inference(and_elim,[status(thm)],[1085])). tff(1087,plain, (((~creative(X!3)) \| (~happy(X!3)) \| (~tourist(X!3))) \| happy(X!3)), inference(tautology,[status(thm)],[])). tff(1088,plain, ((~creative(X!3)) \| (~happy(X!3)) \| (~tourist(X!3))), inference(unit_resolution,[status(thm)],[1087, 1086])). tff(1089,assumption,(~((X!4 = \|'alice'\|) \| (X!4 = \|'fred'\|) \| (X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|) \| (~room(X!4)))), introduced(assumption)). tff(1090,plain, (((X!4 = \|'alice'\|) \| (X!4 = \|'fred'\|) \| (X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|) \| (~room(X!4))) \| room(X!4)), inference(tautology,[status(thm)],[])). tff(1091,plain, (room(X!4)), inference(unit_resolution,[status(thm)],[1090, 1089])). tff(1092,plain, (((X!4 = \|'alice'\|) \| (X!4 = \|'fred'\|) \| (X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|) \| (~room(X!4))) \| (~(X!4 = \|'mary'\|))), inference(tautology,[status(thm)],[])). tff(1093,plain, (~(X!4 = \|'mary'\|)), inference(unit_resolution,[status(thm)],[1092, 1089])). tff(1094,plain, (((X!4 = \|'alice'\|) \| (X!4 = \|'fred'\|) \| (X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|) \| (~room(X!4))) \| (~(X!4 = \|'paul'\|))), inference(tautology,[status(thm)],[])). tff(1095,plain, (~(X!4 = \|'paul'\|)), inference(unit_resolution,[status(thm)],[1094, 1089])). tff(1096,plain, (((X!4 = \|'alice'\|) \| (X!4 = \|'fred'\|) \| (X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|) \| (~room(X!4))) \| (~(X!4 = \|'fred'\|))), inference(tautology,[status(thm)],[])). tff(1097,plain, (~(X!4 = \|'fred'\|)), inference(unit_resolution,[status(thm)],[1096, 1089])). tff(1098,plain, (((X!4 = \|'alice'\|) \| (X!4 = \|'fred'\|) \| (X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|) \| (~room(X!4))) \| (~(X!4 = \|'alice'\|))), inference(tautology,[status(thm)],[])). tff(1099,plain, (~(X!4 = \|'alice'\|)), inference(unit_resolution,[status(thm)],[1098, 1089])). tff(1100,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(1101,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(1102,plain, ((~![X: $i] : ((X = \|'alice'\|) \| (X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| (X!4 = \|'alice'\|) \| (X!4 = \|'fred'\|) \| (X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|) \| (~room(X!4))), inference(modus_ponens,[status(thm)],[1101, 1100])). tff(1103,plain, ($false), inference(unit_resolution,[status(thm)],[1102, 121, 1099, 1097, 1095, 1093, 1091])). tff(1104,plain,((X!4 = \|'alice'\|) \| (X!4 = \|'fred'\|) \| (X!4 = \|'paul'\|) \| (X!4 = \|'mary'\|) \| (~room(X!4))), inference(lemma,lemma(discharge,[]))). tff(1105,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] : ((~like(X, Y)) \| (~((~creative(X)) \| (~happy(X)) \| (~tourist(X)))) \| (~like(lucy, 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] : ((~like(X, Y)) \| (~((~creative(X)) \| (~happy(X)) \| (~tourist(X)))) \| (~like(lucy, Y))))), inference(rewrite,[status(thm)],[])). tff(1106,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] : ((~like(X, Y)) \| (~((~creative(X)) \| (~happy(X)) \| (~tourist(X)))) \| (~like(lucy, 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] : ((~like(X, Y)) \| (~((~creative(X)) \| (~happy(X)) \| (~tourist(X)))) \| (~like(lucy, Y))))), inference(rewrite,[status(thm)],[])). tff(1107,plain, (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((creative(X) & happy(X) & tourist(X)) <=> (~((~creative(X)) \| (~happy(X)) \| (~tourist(X))))), ((~(creative(X) & happy(X) & tourist(X))) <=> (~(~((~creative(X)) \| (~happy(X)) \| (~tourist(X))))))), rewrite((~(~((~creative(X)) \| (~happy(X)) \| (~tourist(X))))) <=> ((~creative(X)) \| (~happy(X)) \| (~tourist(X)))), ((~(creative(X) & happy(X) & tourist(X))) <=> ((~creative(X)) \| (~happy(X)) \| (~tourist(X))))), (((~(creative(X) & happy(X) & tourist(X))) & like(lucy, Y) & like(X, Y)) <=> (((~creative(X)) \| (~happy(X)) \| (~tourist(X))) & like(lucy, Y) & like(X, Y)))), rewrite((((~creative(X)) \| (~happy(X)) \| (~tourist(X))) & like(lucy, Y) & like(X, Y)) <=> (~((~like(X, Y)) \| (~((~creative(X)) \| (~happy(X)) \| (~tourist(X)))) \| (~like(lucy, Y))))), (((~(creative(X) & happy(X) & tourist(X))) & like(lucy, Y) & like(X, Y)) <=> (~((~like(X, Y)) \| (~((~creative(X)) \| (~happy(X)) \| (~tourist(X)))) \| (~like(lucy, Y)))))), ((~((~(creative(X) & happy(X) & tourist(X))) & like(lucy, Y) & like(X, Y))) <=> (~(~((~like(X, Y)) \| (~((~creative(X)) \| (~happy(X)) \| (~tourist(X)))) \| (~like(lucy, Y))))))), rewrite((~(~((~like(X, Y)) \| (~((~creative(X)) \| (~happy(X)) \| (~tourist(X)))) \| (~like(lucy, Y))))) <=> ((~like(X, Y)) \| (~((~creative(X)) \| (~happy(X)) \| (~tourist(X)))) \| (~like(lucy, Y)))), ((~((~(creative(X) & happy(X) & tourist(X))) & like(lucy, Y) & like(X, Y))) <=> ((~like(X, Y)) \| (~((~creative(X)) \| (~happy(X)) \| (~tourist(X)))) \| (~like(lucy, Y)))))), inference(bind,[status(th)],[])). tff(1108,plain, (![X: $i, Y: $i] : (~((~(creative(X) & happy(X) & tourist(X))) & like(lucy, Y) & like(X, Y))) <=> ![X: $i, Y: $i] : ((~like(X, Y)) \| (~((~creative(X)) \| (~happy(X)) \| (~tourist(X)))) \| (~like(lucy, Y)))), inference(quant_intro,[status(thm)],[1107])). tff(1109,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(1110,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] : (~((~(creative(X) & happy(X) & tourist(X))) & like(lucy, Y) & like(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] : ((~like(X, Y)) \| (~((~creative(X)) \| (~happy(X)) \| (~tourist(X)))) \| (~like(lucy, Y))))), inference(monotonicity,[status(thm)],[1109, 1108])). tff(1111,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] : (~((~(creative(X) & happy(X) & tourist(X))) & like(lucy, Y) & like(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] : ((~like(X, Y)) \| (~((~creative(X)) \| (~happy(X)) \| (~tourist(X)))) \| (~like(lucy, Y))))), inference(transitivity,[status(thm)],[1110, 1106])). tff(1112,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] : (~((~(creative(X) & happy(X) & tourist(X))) & like(lucy, Y) & like(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] : (~((~(creative(X) & happy(X) & tourist(X))) & like(lucy, Y) & like(X, Y))))), inference(rewrite,[status(thm)],[])). tff(1113,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] : (~((~(creative(X) & happy(X) & tourist(X))) & like(lucy, Y) & like(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] : (~((~(creative(X) & happy(X) & tourist(X))) & like(lucy, Y) & like(X, Y))))), inference(monotonicity,[status(thm)],[1109])). tff(1114,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] : (~((~(creative(X) & happy(X) & tourist(X))) & like(lucy, Y) & like(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] : (~((~(creative(X) & happy(X) & tourist(X))) & like(lucy, Y) & like(X, Y))))), inference(transitivity,[status(thm)],[1113, 1112])). tff(1115,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] : ((~(creative(X) & happy(X) & tourist(X))) & like(lucy, Y) & like(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] : ((~(creative(X) & happy(X) & tourist(X))) & like(lucy, Y) & like(X, Y)))), inference(rewrite,[status(thm)],[])). tff(1116,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] : ((~(creative(X) & happy(X) & tourist(X))) & like(lucy, Y) & like(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] : ((~(creative(X) & happy(X) & tourist(X))) & like(lucy, Y) & like(X, Y))))), inference(monotonicity,[status(thm)],[1115])). tff(1117,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] : ((~(creative(X) & happy(X) & tourist(X))) & like(lucy, Y) & like(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] : ((~(creative(X) & happy(X) & tourist(X))) & like(lucy, Y) & like(X, Y))))), inference(rewrite,[status(thm)],[])). tff(1118,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] : ((~(creative(X) & happy(X) & tourist(X))) & like(lucy, Y) & like(X, Y)))), inference(or_elim,[status(thm)],[9])). tff(1119,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] : ((~(creative(X) & happy(X) & tourist(X))) & like(lucy, Y) & like(X, Y)))), inference(modus_ponens,[status(thm)],[1118, 1116])). tff(1120,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] : ((~(creative(X) & happy(X) & tourist(X))) & like(lucy, Y) & like(X, Y)))), inference(modus_ponens,[status(thm)],[1119, 1117])). tff(1121,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] : ((~(creative(X) & happy(X) & tourist(X))) & like(lucy, Y) & like(X, Y)))), inference(modus_ponens,[status(thm)],[1120, 1116])). 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 (not (and (creative X) (happy X) (tourist X))) (like lucy Y) (like X Y)))) (refl (~ (not a!1) (not a!1)))))) (a!8 (exists ((X $i) (Y $i)) (and (not (and (creative X) (happy X) (tourist X))) (like lucy Y) (like X Y)))) (a!9 (forall ((X $i) (Y $i)) (let ((a!1 (and (not (and (creative X) (happy X) (tourist X))) (like lucy Y) (like 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(deborah)&room(matthew)&room(charlene)&room(margaret)&(![X]:(room(X)=>(X='deborah'\|X='matthew'\|X='charlene'\|X='margaret')))& ((![X]:(room(X)=>(((~(tall(X)&tourist(X)))=>(~like(X,marie))))))& (((?[X]:(room(X)&~like(X,marie)))&(![X,Y]:((~like(X,marie)&~like(Y,marie))=>(X=Y)))))& (?[X,Y]:((like(X,marie))&(Y!=matthew)&(client(X,Y))))& (((?[X]:(~room(X)&~happy(X)&~tall(X)))&(![X,Y]:((~happy(X)&~tall(X)&~happy(Y)&~tall(Y))=>(X=Y))))))	room(deborah)&room(matthew)&room(charlene)&room(margaret)&(![X]:(room(X)=>(X='deborah'\|X='matthew'\|X='charlene'\|X='margaret')))& (?[X,Y]:((~(creative(X)&happy(X)&tourist(X)))&(like(marie,Y))&(like(X,Y))))	contradiction	neutral	neutral
Carmela is the only person in the room. "Someone outside the room who is not creative, not rich is richer than Dale" if "someone who is liked by Eric is a client of someone who is not Carmela". Carmela is not creative or does enjoy mountain biking or both. Felicia is richer than Carmela. Carmela who is liked by Angela, does enjoy mountain biking. Eric and Carmela like each other. Carmela likes Eric or is not happy, not creative, not rich or both. Someone outside the room who is not creative, not rich is richer than Dale.	It is not the case that 'Carmela who is richer than Felicia, is not a happy creative person'.	entailment	% SZS status Unsatisfiable % SZS output start Proof tff(tptp_fun__mary__type, type, ( tptp_fun__mary_: $i)). tff(tptp_fun_X_1_type, type, ( tptp_fun_X_1: $i)). tff(room_type, type, ( room: $i > $o)). tff(person_type, type, ( person: $i > $o)). tff(mary_type, type, ( mary: $i)). tff(happy_type, type, ( happy: $i > $o)). tff(creative_type, type, ( creative: $i > $o)). tff(richer_type, type, ( richer: ( $i * $i ) > $o)). tff(lucy_type, type, ( lucy: $i)). tff(rich_type, type, ( rich: $i > $o)). tff(fred_type, type, ( fred: $i)). tff(like_type, type, ( like: ( $i * $i ) > $o)). tff(susan_type, type, ( susan: $i)). tff(predb_type, type, ( predb: $i > $o)). tff(john_type, type, ( john: $i)). tff(client_type, type, ( client: ( $i * $i ) > $o)). tff(alice_type, type, ( alice: $i)). tff(paul_type, type, ( paul: $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, Y: $i] : ((like(X, susan) & (~(Y = mary))) & client(X, Y)) => ?[X: $i] : ((~room(X)) => (((~creative(X)) & (~rich(X))) => richer(fred, X)))) & ((~creative(mary)) \| predb(mary))) & richer(mary, lucy)) & (like(mary, john) & predb(mary))) & (like(susan, mary) & like(mary, susan))) & (like(susan, mary) \| (((~happy(mary)) & (~creative(mary))) & (~rich(mary))))) & ?[X: $i] : ((~room(X)) => (((~creative(X)) & (~rich(X))) => richer(fred, X))))) => ((room(mary) & ![X: $i] : (room(X) => (X = \|'mary'\|))) & (~(richer(lucy, mary) & (~((happy(mary) & creative(mary)) & person(mary)))))))) <=> (~((~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ((~?[X: $i, Y: $i] : (like(X, susan) & (~(Y = mary)) & client(X, Y))) \| ?[X: $i] : (room(X) \| richer(fred, X) \| (~((~creative(X)) & (~rich(X)))))) & ((~creative(mary)) \| predb(mary)) & richer(mary, lucy) & like(mary, john) & predb(mary) & like(susan, mary) & like(mary, susan) & (like(susan, mary) \| ((~happy(mary)) & (~creative(mary)) & (~rich(mary)))) & ?[X: $i] : (room(X) \| richer(fred, X) \| (~((~creative(X)) & (~rich(X))))))) \| (room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~(richer(lucy, mary) & (~(happy(mary) & creative(mary) & person(mary))))))))), inference(rewrite,[status(thm)],[])). tff(5,axiom,(~(((room(mary) & ![X: $i] : (room(X) => (X = \|'mary'\|))) & (((((((?[X: $i, Y: $i] : ((like(X, susan) & (~(Y = mary))) & client(X, Y)) => ?[X: $i] : ((~room(X)) => (((~creative(X)) & (~rich(X))) => richer(fred, X)))) & ((~creative(mary)) \| predb(mary))) & richer(mary, lucy)) & (like(mary, john) & predb(mary))) & (like(susan, mary) & like(mary, susan))) & (like(susan, mary) \| (((~happy(mary)) & (~creative(mary))) & (~rich(mary))))) & ?[X: $i] : ((~room(X)) => (((~creative(X)) & (~rich(X))) => richer(fred, X))))) => ((room(mary) & ![X: $i] : (room(X) => (X = \|'mary'\|))) & (~(richer(lucy, mary) & (~((happy(mary) & creative(mary)) & person(mary)))))))), file('/mnt/tmpfs//2084215998316892255514477.p','negated')). tff(6,plain, (~((~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ((~?[X: $i, Y: $i] : (like(X, susan) & (~(Y = mary)) & client(X, Y))) \| ?[X: $i] : (room(X) \| richer(fred, X) \| (~((~creative(X)) & (~rich(X)))))) & ((~creative(mary)) \| predb(mary)) & richer(mary, lucy) & like(mary, john) & predb(mary) & like(susan, mary) & like(mary, susan) & (like(susan, mary) \| ((~happy(mary)) & (~creative(mary)) & (~rich(mary)))) & ?[X: $i] : (room(X) \| richer(fred, X) \| (~((~creative(X)) & (~rich(X))))))) \| (room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~(richer(lucy, mary) & (~(happy(mary) & creative(mary) & person(mary)))))))), inference(modus_ponens,[status(thm)],[5, 4])). tff(7,plain, (room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & ((~?[X: $i, Y: $i] : (like(X, susan) & (~(Y = mary)) & client(X, Y))) \| ?[X: $i] : (room(X) \| richer(fred, X) \| (~((~creative(X)) & (~rich(X)))))) & ((~creative(mary)) \| predb(mary)) & richer(mary, lucy) & like(mary, john) & predb(mary) & like(susan, mary) & like(mary, susan) & (like(susan, mary) \| ((~happy(mary)) & (~creative(mary)) & (~rich(mary)))) & ?[X: $i] : (room(X) \| richer(fred, X) \| (~((~creative(X)) & (~rich(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, (\|'mary'\| = mary), inference(symmetry,[status(thm)],[18])). tff(20,plain, (richer(lucy, \|'mary'\|) <=> richer(lucy, mary)), inference(monotonicity,[status(thm)],[19])). tff(21,plain, (richer(lucy, mary) <=> richer(lucy, \|'mary'\|)), inference(symmetry,[status(thm)],[20])). tff(22,assumption,(richer(lucy, mary)), introduced(assumption)). tff(23,plain, (richer(lucy, \|'mary'\|)), inference(modus_ponens,[status(thm)],[22, 21])). tff(24,plain, ((lucy = mary) <=> (mary = lucy)), inference(commutativity,[status(thm)],[])). tff(25,plain, ((lucy = \|'mary'\|) <=> (lucy = mary)), inference(monotonicity,[status(thm)],[19])). tff(26,plain, ((lucy = \|'mary'\|) <=> (mary = lucy)), inference(transitivity,[status(thm)],[25, 24])). tff(27,plain, ((mary = lucy) <=> (lucy = \|'mary'\|)), inference(symmetry,[status(thm)],[26])). tff(28,plain, ((~(mary = lucy)) <=> (~(lucy = \|'mary'\|))), inference(monotonicity,[status(thm)],[27])). tff(29,plain, ((~(mary = lucy)) <=> (~(mary = lucy))), inference(rewrite,[status(thm)],[])). tff(30,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//2084215998316892255514477.p','b14')). 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))) & (~(lucy = alice))) & (~(lucy = john))), 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))) & (~(lucy = fred))) & (~(lucy = alice))), 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))) & (~(lucy = paul))) & (~(lucy = fred))), 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))) & (~(lucy = mary))) & (~(lucy = paul))), 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))) & (~(susan = lucy))) & (~(lucy = mary))), 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))) & (~(susan = john))) & (~(susan = lucy))), 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))) & (~(susan = alice))) & (~(susan = john))), 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))) & (~(susan = fred))) & (~(susan = alice))), 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))), 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))), 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))), 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))), 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))), 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))), 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))), 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))), 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))), 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))), 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))), 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))), 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))), 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))), 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))), 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))), 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))), 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))), 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))), 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))), 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))), 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))), 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))), 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))), 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))), 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))), inference(and_elim,[status(thm)],[63])). tff(65,plain, (((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))), inference(and_elim,[status(thm)],[64])). tff(66,plain, ((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))), inference(and_elim,[status(thm)],[65])). tff(67,plain, (~(mary = lucy)), inference(and_elim,[status(thm)],[66])). tff(68,plain, (~(mary = lucy)), inference(modus_ponens,[status(thm)],[67, 29])). tff(69,plain, (~(lucy = \|'mary'\|)), inference(modus_ponens,[status(thm)],[68, 28])). tff(70,plain, (richer(\|'mary'\|, lucy) <=> richer(mary, lucy)), inference(monotonicity,[status(thm)],[19])). tff(71,plain, (richer(mary, lucy) <=> richer(\|'mary'\|, lucy)), inference(symmetry,[status(thm)],[70])). tff(72,plain, (richer(mary, lucy) <=> richer(mary, lucy)), inference(rewrite,[status(thm)],[])). tff(73,plain, (richer(mary, lucy)), inference(and_elim,[status(thm)],[7])). tff(74,plain, (richer(mary, lucy)), inference(modus_ponens,[status(thm)],[73, 72])). tff(75,plain, (richer(\|'mary'\|, lucy)), inference(modus_ponens,[status(thm)],[74, 71])). tff(76,plain, (![X: $i, Y: $i] : ((X = Y) \| (~richer(Y, X)) \| (~richer(X, Y))) <=> ![X: $i, Y: $i] : ((X = Y) \| (~richer(Y, X)) \| (~richer(X, Y)))), inference(rewrite,[status(thm)],[])). tff(77,plain, (![X: $i, Y: $i] : ((X = Y) \| (~richer(Y, X)) \| (~richer(X, Y))) <=> ![X: $i, Y: $i] : ((X = Y) \| (~richer(Y, X)) \| (~richer(X, Y)))), inference(rewrite,[status(thm)],[])). tff(78,plain, (^[X: $i, Y: $i] : trans(monotonicity(rewrite((richer(X, Y) => (~richer(Y, X))) <=> ((~richer(Y, X)) \| (~richer(X, Y)))), (((~(X = Y)) => (richer(X, Y) => (~richer(Y, X)))) <=> ((~(X = Y)) => ((~richer(Y, X)) \| (~richer(X, Y)))))), rewrite(((~(X = Y)) => ((~richer(Y, X)) \| (~richer(X, Y)))) <=> ((X = Y) \| (~richer(Y, X)) \| (~richer(X, Y)))), (((~(X = Y)) => (richer(X, Y) => (~richer(Y, X)))) <=> ((X = Y) \| (~richer(Y, X)) \| (~richer(X, Y)))))), inference(bind,[status(th)],[])). tff(79,plain, (![X: $i, Y: $i] : ((~(X = Y)) => (richer(X, Y) => (~richer(Y, X)))) <=> ![X: $i, Y: $i] : ((X = Y) \| (~richer(Y, X)) \| (~richer(X, Y)))), inference(quant_intro,[status(thm)],[78])). tff(80,axiom,(![X: $i, Y: $i] : ((~(X = Y)) => (richer(X, Y) => (~richer(Y, X))))), file('/mnt/tmpfs//2084215998316892255514477.p','b7')). tff(81,plain, (![X: $i, Y: $i] : ((X = Y) \| (~richer(Y, X)) \| (~richer(X, Y)))), inference(modus_ponens,[status(thm)],[80, 79])). tff(82,plain, (![X: $i, Y: $i] : ((X = Y) \| (~richer(Y, X)) \| (~richer(X, Y)))), inference(modus_ponens,[status(thm)],[81, 77])). tff(83,plain,( ![X: $i, Y: $i] : ((X = Y) \| (~richer(Y, X)) \| (~richer(X, Y)))), inference(skolemize,[status(sab)],[82])). tff(84,plain, (![X: $i, Y: $i] : ((X = Y) \| (~richer(Y, X)) \| (~richer(X, Y)))), inference(modus_ponens,[status(thm)],[83, 76])). tff(85,plain, (((~![X: $i, Y: $i] : ((X = Y) \| (~richer(Y, X)) \| (~richer(X, Y)))) \| ((lucy = \|'mary'\|) \| (~richer(\|'mary'\|, lucy)) \| (~richer(lucy, \|'mary'\|)))) <=> ((~![X: $i, Y: $i] : ((X = Y) \| (~richer(Y, X)) \| (~richer(X, Y)))) \| (lucy = \|'mary'\|) \| (~richer(\|'mary'\|, lucy)) \| (~richer(lucy, \|'mary'\|)))), inference(rewrite,[status(thm)],[])). tff(86,plain, ((~![X: $i, Y: $i] : ((X = Y) \| (~richer(Y, X)) \| (~richer(X, Y)))) \| ((lucy = \|'mary'\|) \| (~richer(\|'mary'\|, lucy)) \| (~richer(lucy, \|'mary'\|)))), inference(quant_inst,[status(thm)],[])). tff(87,plain, ((~![X: $i, Y: $i] : ((X = Y) \| (~richer(Y, X)) \| (~richer(X, Y)))) \| (lucy = \|'mary'\|) \| (~richer(\|'mary'\|, lucy)) \| (~richer(lucy, \|'mary'\|))), inference(modus_ponens,[status(thm)],[86, 85])). tff(88,plain, ((lucy = \|'mary'\|) \| (~richer(\|'mary'\|, lucy)) \| (~richer(lucy, \|'mary'\|))), inference(unit_resolution,[status(thm)],[87, 84])). tff(89,plain, ($false), inference(unit_resolution,[status(thm)],[88, 75, 69, 23])). tff(90,plain,(~richer(lucy, mary)), inference(lemma,lemma(discharge,[]))). tff(91,plain, (((~richer(lucy, mary)) \| (~((~creative(mary)) \| (~happy(mary)) \| (~person(mary))))) \| richer(lucy, mary)), inference(tautology,[status(thm)],[])). tff(92,plain, ((~richer(lucy, mary)) \| (~((~creative(mary)) \| (~happy(mary)) \| (~person(mary))))), inference(unit_resolution,[status(thm)],[91, 90])). tff(93,plain, (((~room(mary)) \| (~((~room(X!1)) \| (X!1 = \|'mary'\|))) \| (richer(lucy, mary) & (~(happy(mary) & creative(mary) & person(mary))))) <=> ((~room(mary)) \| (~((~room(X!1)) \| (X!1 = \|'mary'\|))) \| (~((~richer(lucy, mary)) \| (~((~creative(mary)) \| (~happy(mary)) \| (~person(mary)))))))), inference(rewrite,[status(thm)],[])). tff(94,plain, ((room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~(richer(lucy, mary) & (~(happy(mary) & creative(mary) & person(mary)))))) <=> (room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~(richer(lucy, mary) & (~(happy(mary) & creative(mary) & person(mary))))))), inference(rewrite,[status(thm)],[])). tff(95,plain, ((~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~(richer(lucy, mary) & (~(happy(mary) & creative(mary) & person(mary))))))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~(richer(lucy, mary) & (~(happy(mary) & creative(mary) & person(mary)))))))), inference(monotonicity,[status(thm)],[94])). tff(96,plain, ((~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~(richer(lucy, mary) & (~(happy(mary) & creative(mary) & person(mary))))))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~(richer(lucy, mary) & (~(happy(mary) & creative(mary) & person(mary)))))))), inference(rewrite,[status(thm)],[])). tff(97,plain, (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~(richer(lucy, mary) & (~(happy(mary) & creative(mary) & person(mary))))))), inference(or_elim,[status(thm)],[6])). tff(98,plain, (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~(richer(lucy, mary) & (~(happy(mary) & creative(mary) & person(mary))))))), inference(modus_ponens,[status(thm)],[97, 95])). tff(99,plain, (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~(richer(lucy, mary) & (~(happy(mary) & creative(mary) & person(mary))))))), inference(modus_ponens,[status(thm)],[98, 96])). tff(100,plain, (~(room(mary) & ![X: $i] : ((~room(X)) \| (X = \|'mary'\|)) & (~(richer(lucy, mary) & (~(happy(mary) & creative(mary) & person(mary))))))), inference(modus_ponens,[status(thm)],[99, 95])). unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary))))) (a!2 (forall ((X $i)) (or (not (room X)) (= X \|'mary'\|)))) (a!3 (not (or (not (room X!1)) (= X!1 \|'mary'\|)))) (a!4 (and (richer lucy mary) (not (and (happy mary) (creative mary) (person mary)))))) (let ((a!5 (~ (not (and (room mary) a!2 (not a!4))) (or (not (room mary)) a!3 a!4)))) (nnf-neg a!1 (sk (~ (not a!2) a!3)) (refl (~ a!4 a!4)) a!5)))	room(carmela)&(![X]:(room(X)=>(X='carmela')))& (((?[X,Y]:((like(X,eric))&(Y!=carmela)&(client(X,Y))))=>(?[X]:(~room(X)=>(((~creative(X)&~rich(X))=>(richer(dale,X)))))))& (((~creative(carmela))\|(does_enjoy_mountain_biking(carmela))))& (richer(carmela,felicia))& ((like(carmela,angela))&(does_enjoy_mountain_biking(carmela)))& ((like(eric,carmela) & like(carmela,eric)))& (((like(eric,carmela))\|(~happy(carmela)&~creative(carmela)&~rich(carmela))))& (?[X]:(~room(X)=>(((~creative(X)&~rich(X))=>(richer(dale,X)))))))	room(carmela)&(![X]:(room(X)=>(X='carmela')))& (~((richer(felicia,carmela))&(~(happy(carmela)&creative(carmela)&person(carmela)))))	entailment	entailment	contradiction
Jason, Tiffany, Patricia are the only persons in the room. Jason and Tiffany are respectively quiet and tall unless Tiffany is the tallest in the room. Jason is the least quiet in the room if Tiffany neither collects action figures nor hates Joseph. Someone who does not collect action figures hate someone who does not practice zumba if Jason is the least tall in the room and vice versa. Tiffany and Patricia do not hate Jean unless someone in the room is not Patricia. Jason and Tiffany hate Joseph. It is not the case that 'Tiffany does not hate Jean and is not hated by Jean'. Patricia is the least tall in the room. Jason practices zumba. Tiffany neither is not quiet, not tall nor is not a tall european. Only one person outside the room is not a quiet european. Someone who practices zumba hate someone who is not hated by Jean. Tiffany who is not Patricia, does not practice zumba.	Tiffany is a tall quiet person or is a creative quiet person or both.	entailment	% SZS status Unsatisfiable % SZS output start Proof tff(quiet_type, type, ( quiet: $i > $o)). tff(tptp_fun_X_4_type, type, ( tptp_fun_X_4: $i)). tff(european_type, type, ( european: $i > $o)). tff(paul_type, type, ( paul: $i)). tff(person_type, type, ( person: $i > $o)). tff(tall_type, type, ( tall: $i > $o)). tff(creative_type, type, ( creative: $i > $o)). tff(room_type, type, ( room: $i > $o)). tff(tptp_fun_X_7_type, type, ( tptp_fun_X_7: $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(predb_type, type, ( predb: $i > $o)). tff(fred_type, type, ( fred: $i)). tff(hate_type, type, ( hate: ( $i * $i ) > $o)). tff(susan_type, type, ( susan: $i)). tff(mary_type, type, ( mary: $i)). tff(taller_type, type, ( taller: ( $i * $i ) > $o)). tff(alice_type, type, ( alice: $i)). tff(predc_type, type, ( predc: $i > $o)). tff(quieter_type, type, ( quieter: ( $i * $i ) > $o)). tff(1,assumption,(~european(X!4)), introduced(assumption)). tff(2,plain, (((~european(X!4)) \| (~quiet(X!4))) \| european(X!4)), inference(tautology,[status(thm)],[])). tff(3,plain, ((~european(X!4)) \| (~quiet(X!4))), inference(unit_resolution,[status(thm)],[2, 1])). tff(4,assumption,(~((X!7 = \|'fred'\|) \| (X!7 = \|'paul'\|) \| (X!7 = \|'mary'\|) \| (~room(X!7)))), introduced(assumption)). tff(5,plain, (((X!7 = \|'fred'\|) \| (X!7 = \|'paul'\|) \| (X!7 = \|'mary'\|) \| (~room(X!7))) \| room(X!7)), inference(tautology,[status(thm)],[])). tff(6,plain, (room(X!7)), inference(unit_resolution,[status(thm)],[5, 4])). tff(7,plain, (((X!7 = \|'fred'\|) \| (X!7 = \|'paul'\|) \| (X!7 = \|'mary'\|) \| (~room(X!7))) \| (~(X!7 = \|'mary'\|))), inference(tautology,[status(thm)],[])). tff(8,plain, (~(X!7 = \|'mary'\|)), inference(unit_resolution,[status(thm)],[7, 4])). tff(9,plain, (((X!7 = \|'fred'\|) \| (X!7 = \|'paul'\|) \| (X!7 = \|'mary'\|) \| (~room(X!7))) \| (~(X!7 = \|'paul'\|))), inference(tautology,[status(thm)],[])). tff(10,plain, (~(X!7 = \|'paul'\|)), inference(unit_resolution,[status(thm)],[9, 4])). tff(11,plain, (((X!7 = \|'fred'\|) \| (X!7 = \|'paul'\|) \| (X!7 = \|'mary'\|) \| (~room(X!7))) \| (~(X!7 = \|'fred'\|))), inference(tautology,[status(thm)],[])). tff(12,plain, (~(X!7 = \|'fred'\|)), inference(unit_resolution,[status(thm)],[11, 4])). tff(13,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(14,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)],[13])). tff(15,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(16,plain, ((~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)))) & (((((((((((((~![X: $i] : taller(X, paul)) => (quiet(mary) & tall(paul))) & ((~(predc(paul) \| hate(alice, paul))) => ![X: $i] : quieter(mary, X))) & (![X: $i] : taller(mary, X) <=> ?[X: $i, Y: $i] : (((~predc(X)) & (~predb(Y))) & hate(X, Y)))) & ((~?[X: $i] : (room(X) => (~(X = fred)))) => ((~hate(susan, paul)) & (~hate(susan, fred))))) & (hate(alice, mary) & hate(alice, paul))) & (~((~hate(susan, paul)) & (~hate(paul, susan))))) & ![X: $i] : taller(fred, X)) & predb(mary)) & (~(((~quiet(paul)) & (~tall(paul))) \| (~(tall(paul) & european(paul)))))) & (?[X: $i] : ((~room(X)) & (~(quiet(X) & european(X)))) & ![X: $i, Y: $i] : (((~(quiet(X) & european(X))) & (~(quiet(Y) & european(Y)))) => (X = Y)))) & ?[X: $i, Y: $i] : ((predb(X) & (~hate(Y, susan))) & hate(X, Y))) & ((~(paul = fred)) & (~predb(paul))))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)))) & (((tall(paul) & quiet(paul)) & person(paul)) \| ((creative(paul) & quiet(paul)) & person(paul)))))) <=> (~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (![X: $i] : taller(X, paul) \| (quiet(mary) & tall(paul))) & (predc(paul) \| hate(alice, paul) \| ![X: $i] : quieter(mary, X)) & (![X: $i] : taller(mary, X) <=> ?[X: $i, Y: $i] : ((~predc(X)) & (~predb(Y)) & hate(X, Y))) & (((~hate(susan, paul)) & (~hate(susan, fred))) \| ?[X: $i] : ((~room(X)) \| (~(X = fred)))) & hate(alice, mary) & hate(alice, paul) & (~((~hate(susan, paul)) & (~hate(paul, susan)))) & ![X: $i] : taller(fred, X) & predb(mary) & (~(((~quiet(paul)) & (~tall(paul))) \| (~(tall(paul) & european(paul))))) & ?[X: $i] : ((~room(X)) & (~(quiet(X) & european(X)))) & ![X: $i, Y: $i] : ((~((~(quiet(X) & european(X))) & (~(quiet(Y) & european(Y))))) \| (X = Y)) & ?[X: $i, Y: $i] : (predb(X) & (~hate(Y, susan)) & hate(X, Y)) & (~(paul = fred)) & (~predb(paul)))) \| (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((tall(paul) & quiet(paul) & person(paul)) \| (creative(paul) & quiet(paul) & person(paul))))))), inference(rewrite,[status(thm)],[])). tff(17,axiom,(~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)))) & (((((((((((((~![X: $i] : taller(X, paul)) => (quiet(mary) & tall(paul))) & ((~(predc(paul) \| hate(alice, paul))) => ![X: $i] : quieter(mary, X))) & (![X: $i] : taller(mary, X) <=> ?[X: $i, Y: $i] : (((~predc(X)) & (~predb(Y))) & hate(X, Y)))) & ((~?[X: $i] : (room(X) => (~(X = fred)))) => ((~hate(susan, paul)) & (~hate(susan, fred))))) & (hate(alice, mary) & hate(alice, paul))) & (~((~hate(susan, paul)) & (~hate(paul, susan))))) & ![X: $i] : taller(fred, X)) & predb(mary)) & (~(((~quiet(paul)) & (~tall(paul))) \| (~(tall(paul) & european(paul)))))) & (?[X: $i] : ((~room(X)) & (~(quiet(X) & european(X)))) & ![X: $i, Y: $i] : (((~(quiet(X) & european(X))) & (~(quiet(Y) & european(Y)))) => (X = Y)))) & ?[X: $i, Y: $i] : ((predb(X) & (~hate(Y, susan))) & hate(X, Y))) & ((~(paul = fred)) & (~predb(paul))))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = \|'mary'\|) \| (X = \|'paul'\|)) \| (X = \|'fred'\|)))) & (((tall(paul) & quiet(paul)) & person(paul)) \| ((creative(paul) & quiet(paul)) & person(paul)))))), file('/mnt/tmpfs//8158747558240201689806759.p','negated')). tff(18,plain, (~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (![X: $i] : taller(X, paul) \| (quiet(mary) & tall(paul))) & (predc(paul) \| hate(alice, paul) \| ![X: $i] : quieter(mary, X)) & (![X: $i] : taller(mary, X) <=> ?[X: $i, Y: $i] : ((~predc(X)) & (~predb(Y)) & hate(X, Y))) & (((~hate(susan, paul)) & (~hate(susan, fred))) \| ?[X: $i] : ((~room(X)) \| (~(X = fred)))) & hate(alice, mary) & hate(alice, paul) & (~((~hate(susan, paul)) & (~hate(paul, susan)))) & ![X: $i] : taller(fred, X) & predb(mary) & (~(((~quiet(paul)) & (~tall(paul))) \| (~(tall(paul) & european(paul))))) & ?[X: $i] : ((~room(X)) & (~(quiet(X) & european(X)))) & ![X: $i, Y: $i] : ((~((~(quiet(X) & european(X))) & (~(quiet(Y) & european(Y))))) \| (X = Y)) & ?[X: $i, Y: $i] : (predb(X) & (~hate(Y, susan)) & hate(X, Y)) & (~(paul = fred)) & (~predb(paul)))) \| (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((tall(paul) & quiet(paul) & person(paul)) \| (creative(paul) & quiet(paul) & person(paul)))))), inference(modus_ponens,[status(thm)],[17, 16])). tff(19,plain, (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & (![X: $i] : taller(X, paul) \| (quiet(mary) & tall(paul))) & (predc(paul) \| hate(alice, paul) \| ![X: $i] : quieter(mary, X)) & (![X: $i] : taller(mary, X) <=> ?[X: $i, Y: $i] : ((~predc(X)) & (~predb(Y)) & hate(X, Y))) & (((~hate(susan, paul)) & (~hate(susan, fred))) \| ?[X: $i] : ((~room(X)) \| (~(X = fred)))) & hate(alice, mary) & hate(alice, paul) & (~((~hate(susan, paul)) & (~hate(paul, susan)))) & ![X: $i] : taller(fred, X) & predb(mary) & (~(((~quiet(paul)) & (~tall(paul))) \| (~(tall(paul) & european(paul))))) & ?[X: $i] : ((~room(X)) & (~(quiet(X) & european(X)))) & ![X: $i, Y: $i] : ((~((~(quiet(X) & european(X))) & (~(quiet(Y) & european(Y))))) \| (X = Y)) & ?[X: $i, Y: $i] : (predb(X) & (~hate(Y, susan)) & hate(X, Y)) & (~(paul = fred)) & (~predb(paul))), inference(or_elim,[status(thm)],[18])). tff(20,plain, (![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))), inference(and_elim,[status(thm)],[19])). tff(21,plain, (![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))), inference(modus_ponens,[status(thm)],[20, 15])). tff(22,plain,( ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))), inference(skolemize,[status(sab)],[21])). tff(23,plain, (![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))), inference(modus_ponens,[status(thm)],[22, 14])). tff(24,plain, (((~![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| ((X!7 = \|'fred'\|) \| (X!7 = \|'paul'\|) \| (X!7 = \|'mary'\|) \| (~room(X!7)))) <=> ((~![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| (X!7 = \|'fred'\|) \| (X!7 = \|'paul'\|) \| (X!7 = \|'mary'\|) \| (~room(X!7)))), inference(rewrite,[status(thm)],[])). tff(25,plain, ((~![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| ((X!7 = \|'fred'\|) \| (X!7 = \|'paul'\|) \| (X!7 = \|'mary'\|) \| (~room(X!7)))), inference(quant_inst,[status(thm)],[])). tff(26,plain, ((~![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X)))) \| (X!7 = \|'fred'\|) \| (X!7 = \|'paul'\|) \| (X!7 = \|'mary'\|) \| (~room(X!7))), inference(modus_ponens,[status(thm)],[25, 24])). tff(27,plain, ($false), inference(unit_resolution,[status(thm)],[26, 23, 12, 10, 8, 6])). tff(28,plain,((X!7 = \|'fred'\|) \| (X!7 = \|'paul'\|) \| (X!7 = \|'mary'\|) \| (~room(X!7))), inference(lemma,lemma(discharge,[]))). tff(29,plain, (room(fred) <=> room(fred)), inference(rewrite,[status(thm)],[])). tff(30,plain, (room(fred)), inference(and_elim,[status(thm)],[19])). tff(31,plain, (room(fred)), inference(modus_ponens,[status(thm)],[30, 29])). tff(32,plain, (room(paul) <=> room(paul)), inference(rewrite,[status(thm)],[])). tff(33,plain, (room(paul)), inference(and_elim,[status(thm)],[19])). tff(34,plain, (room(paul)), inference(modus_ponens,[status(thm)],[33, 32])). tff(35,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(36,plain, (room(mary)), inference(and_elim,[status(thm)],[19])). tff(37,plain, (room(mary)), inference(modus_ponens,[status(thm)],[36, 35])). tff(38,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!7 = \|'fred'\|) \| (X!7 = \|'paul'\|) \| (X!7 = \|'mary'\|) \| (~room(X!7)))) \| (~((~((~quiet(paul)) \| (~tall(paul)) \| (~person(paul)))) \| (~((~quiet(paul)) \| (~person(paul)) \| (~creative(paul))))))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!7 = \|'fred'\|) \| (X!7 = \|'paul'\|) \| (X!7 = \|'mary'\|) \| (~room(X!7)))) \| (~((~((~quiet(paul)) \| (~tall(paul)) \| (~person(paul)))) \| (~((~quiet(paul)) \| (~person(paul)) \| (~creative(paul)))))))), inference(rewrite,[status(thm)],[])). tff(39,plain, ((~((tall(paul) & quiet(paul) & person(paul)) \| (creative(paul) & quiet(paul) & person(paul)))) <=> (~((~((~quiet(paul)) \| (~tall(paul)) \| (~person(paul)))) \| (~((~quiet(paul)) \| (~person(paul)) \| (~creative(paul))))))), inference(rewrite,[status(thm)],[])). tff(40,plain, ((~((X!7 = \|'fred'\|) \| (X!7 = \|'paul'\|) \| (X!7 = \|'mary'\|) \| (~room(X!7)))) <=> (~((X!7 = \|'fred'\|) \| (X!7 = \|'paul'\|) \| (X!7 = \|'mary'\|) \| (~room(X!7))))), inference(rewrite,[status(thm)],[])). tff(41,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!7 = \|'fred'\|) \| (X!7 = \|'paul'\|) \| (X!7 = \|'mary'\|) \| (~room(X!7)))) \| (~((tall(paul) & quiet(paul) & person(paul)) \| (creative(paul) & quiet(paul) & person(paul))))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!7 = \|'fred'\|) \| (X!7 = \|'paul'\|) \| (X!7 = \|'mary'\|) \| (~room(X!7)))) \| (~((~((~quiet(paul)) \| (~tall(paul)) \| (~person(paul)))) \| (~((~quiet(paul)) \| (~person(paul)) \| (~creative(paul)))))))), inference(monotonicity,[status(thm)],[40, 39])). tff(42,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!7 = \|'fred'\|) \| (X!7 = \|'paul'\|) \| (X!7 = \|'mary'\|) \| (~room(X!7)))) \| (~((tall(paul) & quiet(paul) & person(paul)) \| (creative(paul) & quiet(paul) & person(paul))))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!7 = \|'fred'\|) \| (X!7 = \|'paul'\|) \| (X!7 = \|'mary'\|) \| (~room(X!7)))) \| (~((~((~quiet(paul)) \| (~tall(paul)) \| (~person(paul)))) \| (~((~quiet(paul)) \| (~person(paul)) \| (~creative(paul)))))))), inference(transitivity,[status(thm)],[41, 38])). tff(43,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!7 = \|'fred'\|) \| (X!7 = \|'paul'\|) \| (X!7 = \|'mary'\|) \| (~room(X!7)))) \| (~((tall(paul) & quiet(paul) & person(paul)) \| (creative(paul) & quiet(paul) & person(paul))))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!7 = \|'fred'\|) \| (X!7 = \|'paul'\|) \| (X!7 = \|'mary'\|) \| (~room(X!7)))) \| (~((tall(paul) & quiet(paul) & person(paul)) \| (creative(paul) & quiet(paul) & person(paul)))))), inference(rewrite,[status(thm)],[])). tff(44,plain, ((~((tall(paul) & quiet(paul) & person(paul)) \| (creative(paul) & quiet(paul) & person(paul)))) <=> (~((tall(paul) & quiet(paul) & person(paul)) \| (creative(paul) & quiet(paul) & person(paul))))), inference(rewrite,[status(thm)],[])). tff(45,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!7 = \|'fred'\|) \| (X!7 = \|'paul'\|) \| (X!7 = \|'mary'\|) \| (~room(X!7)))) \| (~((tall(paul) & quiet(paul) & person(paul)) \| (creative(paul) & quiet(paul) & person(paul))))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!7 = \|'fred'\|) \| (X!7 = \|'paul'\|) \| (X!7 = \|'mary'\|) \| (~room(X!7)))) \| (~((tall(paul) & quiet(paul) & person(paul)) \| (creative(paul) & quiet(paul) & person(paul)))))), inference(monotonicity,[status(thm)],[40, 44])). tff(46,plain, (((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!7 = \|'fred'\|) \| (X!7 = \|'paul'\|) \| (X!7 = \|'mary'\|) \| (~room(X!7)))) \| (~((tall(paul) & quiet(paul) & person(paul)) \| (creative(paul) & quiet(paul) & person(paul))))) <=> ((~room(mary)) \| (~room(paul)) \| (~room(fred)) \| (~((X!7 = \|'fred'\|) \| (X!7 = \|'paul'\|) \| (X!7 = \|'mary'\|) \| (~room(X!7)))) \| (~((tall(paul) & quiet(paul) & person(paul)) \| (creative(paul) & quiet(paul) & person(paul)))))), inference(transitivity,[status(thm)],[45, 43])). tff(47,plain, ((room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((tall(paul) & quiet(paul) & person(paul)) \| (creative(paul) & quiet(paul) & person(paul)))) <=> (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((tall(paul) & quiet(paul) & person(paul)) \| (creative(paul) & quiet(paul) & person(paul))))), inference(rewrite,[status(thm)],[])). tff(48,plain, ((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((tall(paul) & quiet(paul) & person(paul)) \| (creative(paul) & quiet(paul) & person(paul))))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((tall(paul) & quiet(paul) & person(paul)) \| (creative(paul) & quiet(paul) & person(paul)))))), inference(monotonicity,[status(thm)],[47])). tff(49,plain, ((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((tall(paul) & quiet(paul) & person(paul)) \| (creative(paul) & quiet(paul) & person(paul))))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((tall(paul) & quiet(paul) & person(paul)) \| (creative(paul) & quiet(paul) & person(paul)))))), inference(rewrite,[status(thm)],[])). tff(50,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((tall(paul) & quiet(paul) & person(paul)) \| (creative(paul) & quiet(paul) & person(paul))))), inference(or_elim,[status(thm)],[18])). tff(51,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((tall(paul) & quiet(paul) & person(paul)) \| (creative(paul) & quiet(paul) & person(paul))))), inference(modus_ponens,[status(thm)],[50, 48])). tff(52,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((tall(paul) & quiet(paul) & person(paul)) \| (creative(paul) & quiet(paul) & person(paul))))), inference(modus_ponens,[status(thm)],[51, 49])). tff(53,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = \|'fred'\|) \| (X = \|'paul'\|) \| (X = \|'mary'\|) \| (~room(X))) & ((tall(paul) & quiet(paul) & person(paul)) \| (creative(paul) & quiet(paul) & person(paul))))), inference(modus_ponens,[status(thm)],[52, 48])). 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!7 \|'fred'\|) (= X!7 \|'paul'\|) (= X!7 \|'mary'\|) (not (room X!7))))) (a!6 (or (and (tall paul) (quiet paul) (person paul)) (and (creative paul) (quiet paul) (person paul))))) (let ((a!7 (~ (not (and (room mary) (room paul) (room fred) a!4 a!6)) (or (not (room mary)) (not (room paul)) (not (room fred)) a!5 (not a!6))))) (nnf-neg a!1 a!2 a!3 (sk (~ (not a!4) a!5)) (refl (~ (not a!6) (not a!6))) a!7)))	room(jason)&room(tiffany)&room(patricia)&(![X]:(room(X)=>(X='jason'\|X='tiffany'\|X='patricia')))& ((~(![X]:(taller(X,tiffany)))=>((quiet(jason))&(tall(tiffany))))& ((~((collects_action_figures(tiffany))\|(hate(joseph,tiffany))))=>(![X]:(quieter(jason,X))))& ((![X]:(taller(jason,X)))<=>(?[X,Y]:((does_not_collect_action_figures(X))&(does_not_practice_zumba(Y))&(hate(X,Y)))))& (~(?[X]:(room(X)=>(X!=patricia)))=>(~hate(jean,tiffany)&~hate(jean,patricia)))& (hate(joseph,jason)&hate(joseph,tiffany))& (~((~hate(jean,tiffany))&(~hate(tiffany,jean))))& (![X]:(taller(patricia,X)))& (practices_zumba(jason))& (~((~quiet(tiffany)&~tall(tiffany))\|(~(tall(tiffany)&european(tiffany)))))& (((?[X]:(~room(X)&~(quiet(X)&european(X))))&(![X,Y]:((~(quiet(X)&european(X))&~(quiet(Y)&european(Y)))=>(X=Y)))))& (?[X,Y]:((practices_zumba(X))&(~hate(Y,jean))&(hate(X,Y))))& ((tiffany!=patricia)&(does_not_practice_zumba(tiffany))))	room(jason)&room(tiffany)&room(patricia)&(![X]:(room(X)=>(X='jason'\|X='tiffany'\|X='patricia')))& (((tall(tiffany)&quiet(tiffany)&person(tiffany))\|(creative(tiffany)&quiet(tiffany)&person(tiffany))))	neutral	entailment	entailment
At least one of the following is true:. -Lidia is not rich and does not play the drums. -Lidia either likes Douglas or plays the drums.	Lidia who plays the drums, likes Douglas.	contradiction	-	room(lidia)&room(ruth)&room(juan)&(![X]:(room(X)=>(X='lidia'\|X='ruth'\|X='juan')))& ((((~rich(lidia))&(does_not_play_the_drums(lidia)))\| ((((like(douglas,lidia))\|(plays_the_drums(lidia)))&(~((like(douglas,lidia))\|(plays_the_drums(lidia))))))))	room(lidia)&room(ruth)&room(juan)&(![X]:(room(X)=>(X='lidia'\|X='ruth'\|X='juan')))& ((plays_the_drums(lidia))&(like(douglas,lidia)))	contradiction	neutral	contradiction