%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PUZ001-2 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:23:06 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : PUZ001-2 : TPTP v9.0.0. Released v1.0.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 02:39:05 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Unsatisfiable
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(hates_type, type, (
% 0.12/0.37 hates: ( $i * $i ) > $o)).
% 0.12/0.37 tff(aunt_agatha_type, type, (
% 0.12/0.37 aunt_agatha: $i)).
% 0.12/0.37 tff(charles_type, type, (
% 0.12/0.37 charles: $i)).
% 0.12/0.37 tff(someone_type, type, (
% 0.12/0.37 someone: $i)).
% 0.12/0.37 tff(killed_type, type, (
% 0.12/0.37 killed: ( $i * $i ) > $o)).
% 0.12/0.37 tff(butler_type, type, (
% 0.12/0.37 butler: $i)).
% 0.12/0.37 tff(every_one_but_type, type, (
% 0.12/0.37 every_one_but: $i > $i)).
% 0.12/0.37 tff(richer_type, type, (
% 0.12/0.37 richer: ( $i * $i ) > $o)).
% 0.12/0.37 tff(lives_at_dreadsbury_type, type, (
% 0.12/0.37 lives_at_dreadsbury: $i > $o)).
% 0.12/0.37 tff(1,assumption,(someone = aunt_agatha), introduced(assumption)).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 (killed(someone, aunt_agatha) <=> killed(aunt_agatha, aunt_agatha)),
% 0.12/0.37 inference(monotonicity,[status(thm)],[1])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 (killed(aunt_agatha, aunt_agatha) <=> killed(someone, aunt_agatha)),
% 0.12/0.37 inference(symmetry,[status(thm)],[2])).
% 0.12/0.37 tff(4,plain,
% 0.12/0.37 ((~killed(aunt_agatha, aunt_agatha)) <=> (~killed(someone, aunt_agatha))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[3])).
% 0.12/0.37 tff(5,plain,
% 0.12/0.37 ((~killed(aunt_agatha, aunt_agatha)) <=> (~killed(aunt_agatha, aunt_agatha))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(6,axiom,(~killed(aunt_agatha, aunt_agatha)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_agatha_killed_herself')).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 (~killed(aunt_agatha, aunt_agatha)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 (~killed(someone, aunt_agatha)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[7, 4])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 (killed(someone, aunt_agatha) <=> killed(someone, aunt_agatha)),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(10,axiom,(killed(someone, aunt_agatha)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','someone_killed_agatha')).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 (killed(someone, aunt_agatha)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[11, 8])).
% 0.12/0.37 tff(13,plain,(~(someone = aunt_agatha)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.37 tff(14,plain,
% 0.12/0.37 (^[Person: $i] : refl((~hates(Person, every_one_but(Person))) <=> (~hates(Person, every_one_but(Person))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(15,plain,
% 0.12/0.37 (![Person: $i] : (~hates(Person, every_one_but(Person))) <=> ![Person: $i] : (~hates(Person, every_one_but(Person)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[14])).
% 0.12/0.37 tff(16,plain,
% 0.12/0.37 (![Person: $i] : (~hates(Person, every_one_but(Person))) <=> ![Person: $i] : (~hates(Person, every_one_but(Person)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(17,axiom,(![Person: $i] : (~hates(Person, every_one_but(Person)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','noone_hates_everyone')).
% 0.12/0.37 tff(18,plain,
% 0.12/0.37 (![Person: $i] : (~hates(Person, every_one_but(Person)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.12/0.37 tff(19,plain,(
% 0.12/0.37 ![Person: $i] : (~hates(Person, every_one_but(Person)))),
% 0.12/0.37 inference(skolemize,[status(sab)],[18])).
% 0.12/0.37 tff(20,plain,
% 0.12/0.37 (![Person: $i] : (~hates(Person, every_one_but(Person)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.12/0.37 tff(21,plain,
% 0.12/0.37 ((~![Person: $i] : (~hates(Person, every_one_but(Person)))) | (~hates(butler, every_one_but(butler)))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(22,plain,
% 0.12/0.37 (~hates(butler, every_one_but(butler))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.12/0.37 tff(23,plain,
% 0.12/0.37 (^[Person: $i] : refl(((~hates(aunt_agatha, Person)) | hates(butler, Person)) <=> ((~hates(aunt_agatha, Person)) | hates(butler, Person)))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(24,plain,
% 0.12/0.37 (![Person: $i] : ((~hates(aunt_agatha, Person)) | hates(butler, Person)) <=> ![Person: $i] : ((~hates(aunt_agatha, Person)) | hates(butler, Person))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[23])).
% 0.12/0.37 tff(25,plain,
% 0.12/0.37 (![Person: $i] : ((~hates(aunt_agatha, Person)) | hates(butler, Person)) <=> ![Person: $i] : ((~hates(aunt_agatha, Person)) | hates(butler, Person))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(26,axiom,(![Person: $i] : ((~hates(aunt_agatha, Person)) | hates(butler, Person))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','butler_and_agatha_hate_the_same_people')).
% 0.12/0.37 tff(27,plain,
% 0.12/0.37 (![Person: $i] : ((~hates(aunt_agatha, Person)) | hates(butler, Person))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.12/0.37 tff(28,plain,(
% 0.12/0.37 ![Person: $i] : ((~hates(aunt_agatha, Person)) | hates(butler, Person))),
% 0.12/0.37 inference(skolemize,[status(sab)],[27])).
% 0.12/0.37 tff(29,plain,
% 0.12/0.37 (![Person: $i] : ((~hates(aunt_agatha, Person)) | hates(butler, Person))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.12/0.37 tff(30,plain,
% 0.12/0.37 (((~![Person: $i] : ((~hates(aunt_agatha, Person)) | hates(butler, Person))) | ((~hates(aunt_agatha, every_one_but(butler))) | hates(butler, every_one_but(butler)))) <=> ((~![Person: $i] : ((~hates(aunt_agatha, Person)) | hates(butler, Person))) | (~hates(aunt_agatha, every_one_but(butler))) | hates(butler, every_one_but(butler)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(31,plain,
% 0.12/0.37 ((~![Person: $i] : ((~hates(aunt_agatha, Person)) | hates(butler, Person))) | ((~hates(aunt_agatha, every_one_but(butler))) | hates(butler, every_one_but(butler)))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(32,plain,
% 0.12/0.37 ((~![Person: $i] : ((~hates(aunt_agatha, Person)) | hates(butler, Person))) | (~hates(aunt_agatha, every_one_but(butler))) | hates(butler, every_one_but(butler))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.12/0.37 tff(33,plain,
% 0.12/0.37 (~hates(aunt_agatha, every_one_but(butler))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[32, 29, 22])).
% 0.12/0.37 tff(34,plain,
% 0.12/0.37 (^[Person: $i] : refl(((Person = butler) | hates(aunt_agatha, Person)) <=> ((Person = butler) | hates(aunt_agatha, Person)))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(35,plain,
% 0.12/0.37 (![Person: $i] : ((Person = butler) | hates(aunt_agatha, Person)) <=> ![Person: $i] : ((Person = butler) | hates(aunt_agatha, Person))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[34])).
% 0.12/0.37 tff(36,plain,
% 0.12/0.37 (![Person: $i] : ((Person = butler) | hates(aunt_agatha, Person)) <=> ![Person: $i] : ((Person = butler) | hates(aunt_agatha, Person))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(37,axiom,(![Person: $i] : ((Person = butler) | hates(aunt_agatha, Person))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','agatha_likes_only_butler')).
% 0.12/0.37 tff(38,plain,
% 0.12/0.37 (![Person: $i] : ((Person = butler) | hates(aunt_agatha, Person))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.12/0.37 tff(39,plain,(
% 0.12/0.37 ![Person: $i] : ((Person = butler) | hates(aunt_agatha, Person))),
% 0.12/0.37 inference(skolemize,[status(sab)],[38])).
% 0.12/0.37 tff(40,plain,
% 0.12/0.37 (![Person: $i] : ((Person = butler) | hates(aunt_agatha, Person))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.12/0.37 tff(41,plain,
% 0.12/0.37 (((~![Person: $i] : ((Person = butler) | hates(aunt_agatha, Person))) | ((every_one_but(butler) = butler) | hates(aunt_agatha, every_one_but(butler)))) <=> ((~![Person: $i] : ((Person = butler) | hates(aunt_agatha, Person))) | (every_one_but(butler) = butler) | hates(aunt_agatha, every_one_but(butler)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(42,plain,
% 0.12/0.37 ((~![Person: $i] : ((Person = butler) | hates(aunt_agatha, Person))) | ((every_one_but(butler) = butler) | hates(aunt_agatha, every_one_but(butler)))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(43,plain,
% 0.12/0.37 ((~![Person: $i] : ((Person = butler) | hates(aunt_agatha, Person))) | (every_one_but(butler) = butler) | hates(aunt_agatha, every_one_but(butler))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.12/0.37 tff(44,plain,
% 0.12/0.37 (every_one_but(butler) = butler),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[43, 40, 33])).
% 0.12/0.37 tff(45,plain,
% 0.12/0.37 (butler = every_one_but(butler)),
% 0.12/0.37 inference(symmetry,[status(thm)],[44])).
% 0.12/0.37 tff(46,assumption,(someone = butler), introduced(assumption)).
% 0.12/0.37 tff(47,plain,
% 0.12/0.37 (someone = every_one_but(butler)),
% 0.12/0.37 inference(transitivity,[status(thm)],[46, 45])).
% 0.12/0.37 tff(48,plain,
% 0.12/0.37 (killed(someone, aunt_agatha) <=> killed(every_one_but(butler), aunt_agatha)),
% 0.12/0.37 inference(monotonicity,[status(thm)],[47])).
% 0.12/0.37 tff(49,plain,
% 0.12/0.37 (killed(every_one_but(butler), aunt_agatha) <=> killed(someone, aunt_agatha)),
% 0.12/0.37 inference(symmetry,[status(thm)],[48])).
% 0.12/0.37 tff(50,plain,
% 0.12/0.37 ((~killed(every_one_but(butler), aunt_agatha)) <=> (~killed(someone, aunt_agatha))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[49])).
% 0.12/0.37 tff(51,plain,
% 0.12/0.37 (^[Person: $i] : refl((hates(butler, Person) | richer(Person, aunt_agatha)) <=> (hates(butler, Person) | richer(Person, aunt_agatha)))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(52,plain,
% 0.12/0.37 (![Person: $i] : (hates(butler, Person) | richer(Person, aunt_agatha)) <=> ![Person: $i] : (hates(butler, Person) | richer(Person, aunt_agatha))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[51])).
% 0.12/0.37 tff(53,plain,
% 0.12/0.37 (![Person: $i] : (hates(butler, Person) | richer(Person, aunt_agatha)) <=> ![Person: $i] : (hates(butler, Person) | richer(Person, aunt_agatha))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(54,plain,
% 0.12/0.37 (^[Person: $i] : rewrite((richer(Person, aunt_agatha) | hates(butler, Person)) <=> (hates(butler, Person) | richer(Person, aunt_agatha)))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(55,plain,
% 0.12/0.37 (![Person: $i] : (richer(Person, aunt_agatha) | hates(butler, Person)) <=> ![Person: $i] : (hates(butler, Person) | richer(Person, aunt_agatha))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[54])).
% 0.12/0.37 tff(56,axiom,(![Person: $i] : (richer(Person, aunt_agatha) | hates(butler, Person))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','butler_hates_poor_people')).
% 0.12/0.37 tff(57,plain,
% 0.12/0.37 (![Person: $i] : (hates(butler, Person) | richer(Person, aunt_agatha))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.12/0.37 tff(58,plain,
% 0.12/0.37 (![Person: $i] : (hates(butler, Person) | richer(Person, aunt_agatha))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.12/0.37 tff(59,plain,(
% 0.12/0.37 ![Person: $i] : (hates(butler, Person) | richer(Person, aunt_agatha))),
% 0.12/0.37 inference(skolemize,[status(sab)],[58])).
% 0.12/0.37 tff(60,plain,
% 0.12/0.37 (![Person: $i] : (hates(butler, Person) | richer(Person, aunt_agatha))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.12/0.37 tff(61,plain,
% 0.12/0.37 (((~![Person: $i] : (hates(butler, Person) | richer(Person, aunt_agatha))) | (hates(butler, every_one_but(butler)) | richer(every_one_but(butler), aunt_agatha))) <=> ((~![Person: $i] : (hates(butler, Person) | richer(Person, aunt_agatha))) | hates(butler, every_one_but(butler)) | richer(every_one_but(butler), aunt_agatha))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(62,plain,
% 0.12/0.37 ((~![Person: $i] : (hates(butler, Person) | richer(Person, aunt_agatha))) | (hates(butler, every_one_but(butler)) | richer(every_one_but(butler), aunt_agatha))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(63,plain,
% 0.12/0.37 ((~![Person: $i] : (hates(butler, Person) | richer(Person, aunt_agatha))) | hates(butler, every_one_but(butler)) | richer(every_one_but(butler), aunt_agatha)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.12/0.37 tff(64,plain,
% 0.12/0.37 (richer(every_one_but(butler), aunt_agatha)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[63, 60, 22])).
% 0.12/0.37 tff(65,plain,
% 0.12/0.37 (^[Victim: $i, Killer: $i] : refl(((~killed(Killer, Victim)) | (~richer(Killer, Victim))) <=> ((~killed(Killer, Victim)) | (~richer(Killer, Victim))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(66,plain,
% 0.12/0.37 (![Victim: $i, Killer: $i] : ((~killed(Killer, Victim)) | (~richer(Killer, Victim))) <=> ![Victim: $i, Killer: $i] : ((~killed(Killer, Victim)) | (~richer(Killer, Victim)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[65])).
% 0.12/0.37 tff(67,plain,
% 0.12/0.37 (![Victim: $i, Killer: $i] : ((~killed(Killer, Victim)) | (~richer(Killer, Victim))) <=> ![Victim: $i, Killer: $i] : ((~killed(Killer, Victim)) | (~richer(Killer, Victim)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(68,axiom,(![Victim: $i, Killer: $i] : ((~killed(Killer, Victim)) | (~richer(Killer, Victim)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','killer_poorer_than_victim')).
% 0.12/0.37 tff(69,plain,
% 0.12/0.37 (![Victim: $i, Killer: $i] : ((~killed(Killer, Victim)) | (~richer(Killer, Victim)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.12/0.37 tff(70,plain,(
% 0.12/0.37 ![Victim: $i, Killer: $i] : ((~killed(Killer, Victim)) | (~richer(Killer, Victim)))),
% 0.12/0.37 inference(skolemize,[status(sab)],[69])).
% 0.12/0.37 tff(71,plain,
% 0.12/0.38 (![Victim: $i, Killer: $i] : ((~killed(Killer, Victim)) | (~richer(Killer, Victim)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.12/0.38 tff(72,plain,
% 0.12/0.38 (((~![Victim: $i, Killer: $i] : ((~killed(Killer, Victim)) | (~richer(Killer, Victim)))) | ((~killed(every_one_but(butler), aunt_agatha)) | (~richer(every_one_but(butler), aunt_agatha)))) <=> ((~![Victim: $i, Killer: $i] : ((~killed(Killer, Victim)) | (~richer(Killer, Victim)))) | (~killed(every_one_but(butler), aunt_agatha)) | (~richer(every_one_but(butler), aunt_agatha)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(73,plain,
% 0.12/0.38 ((~![Victim: $i, Killer: $i] : ((~killed(Killer, Victim)) | (~richer(Killer, Victim)))) | ((~killed(every_one_but(butler), aunt_agatha)) | (~richer(every_one_but(butler), aunt_agatha)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(74,plain,
% 0.12/0.38 ((~![Victim: $i, Killer: $i] : ((~killed(Killer, Victim)) | (~richer(Killer, Victim)))) | (~killed(every_one_but(butler), aunt_agatha)) | (~richer(every_one_but(butler), aunt_agatha))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.12/0.38 tff(75,plain,
% 0.12/0.38 (~killed(every_one_but(butler), aunt_agatha)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[74, 71, 64])).
% 0.12/0.38 tff(76,plain,
% 0.12/0.38 (~killed(someone, aunt_agatha)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[75, 50])).
% 0.12/0.38 tff(77,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[11, 76])).
% 0.12/0.38 tff(78,plain,(~(someone = butler)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(79,plain,
% 0.12/0.38 (^[Person: $i] : refl(((Person = charles) | (Person = butler) | (Person = aunt_agatha) | (~lives_at_dreadsbury(Person))) <=> ((Person = charles) | (Person = butler) | (Person = aunt_agatha) | (~lives_at_dreadsbury(Person))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(80,plain,
% 0.12/0.38 (![Person: $i] : ((Person = charles) | (Person = butler) | (Person = aunt_agatha) | (~lives_at_dreadsbury(Person))) <=> ![Person: $i] : ((Person = charles) | (Person = butler) | (Person = aunt_agatha) | (~lives_at_dreadsbury(Person)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[79])).
% 0.12/0.38 tff(81,plain,
% 0.12/0.38 (![Person: $i] : ((Person = charles) | (Person = butler) | (Person = aunt_agatha) | (~lives_at_dreadsbury(Person))) <=> ![Person: $i] : ((Person = charles) | (Person = butler) | (Person = aunt_agatha) | (~lives_at_dreadsbury(Person)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(82,plain,
% 0.12/0.38 (^[Person: $i] : trans(monotonicity(rewrite((((~lives_at_dreadsbury(Person)) | (Person = aunt_agatha)) | (Person = butler)) <=> ((Person = butler) | (Person = aunt_agatha) | (~lives_at_dreadsbury(Person)))), (((((~lives_at_dreadsbury(Person)) | (Person = aunt_agatha)) | (Person = butler)) | (Person = charles)) <=> (((Person = butler) | (Person = aunt_agatha) | (~lives_at_dreadsbury(Person))) | (Person = charles)))), rewrite((((Person = butler) | (Person = aunt_agatha) | (~lives_at_dreadsbury(Person))) | (Person = charles)) <=> ((Person = charles) | (Person = butler) | (Person = aunt_agatha) | (~lives_at_dreadsbury(Person)))), (((((~lives_at_dreadsbury(Person)) | (Person = aunt_agatha)) | (Person = butler)) | (Person = charles)) <=> ((Person = charles) | (Person = butler) | (Person = aunt_agatha) | (~lives_at_dreadsbury(Person)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(83,plain,
% 0.12/0.38 (![Person: $i] : ((((~lives_at_dreadsbury(Person)) | (Person = aunt_agatha)) | (Person = butler)) | (Person = charles)) <=> ![Person: $i] : ((Person = charles) | (Person = butler) | (Person = aunt_agatha) | (~lives_at_dreadsbury(Person)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[82])).
% 0.12/0.38 tff(84,axiom,(![Person: $i] : ((((~lives_at_dreadsbury(Person)) | (Person = aunt_agatha)) | (Person = butler)) | (Person = charles))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','noone_else_lives_at_mansion')).
% 0.12/0.38 tff(85,plain,
% 0.12/0.38 (![Person: $i] : ((Person = charles) | (Person = butler) | (Person = aunt_agatha) | (~lives_at_dreadsbury(Person)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.12/0.38 tff(86,plain,
% 0.12/0.38 (![Person: $i] : ((Person = charles) | (Person = butler) | (Person = aunt_agatha) | (~lives_at_dreadsbury(Person)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[85, 81])).
% 0.12/0.38 tff(87,plain,(
% 0.12/0.38 ![Person: $i] : ((Person = charles) | (Person = butler) | (Person = aunt_agatha) | (~lives_at_dreadsbury(Person)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[86])).
% 0.12/0.38 tff(88,plain,
% 0.12/0.38 (![Person: $i] : ((Person = charles) | (Person = butler) | (Person = aunt_agatha) | (~lives_at_dreadsbury(Person)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[87, 80])).
% 0.12/0.38 tff(89,plain,
% 0.12/0.38 (lives_at_dreadsbury(someone) <=> lives_at_dreadsbury(someone)),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(90,axiom,(lives_at_dreadsbury(someone)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','someone_in_mansion')).
% 0.12/0.38 tff(91,plain,
% 0.12/0.38 (lives_at_dreadsbury(someone)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.12/0.38 tff(92,plain,
% 0.12/0.38 (((~![Person: $i] : ((Person = charles) | (Person = butler) | (Person = aunt_agatha) | (~lives_at_dreadsbury(Person)))) | ((someone = charles) | (someone = butler) | (someone = aunt_agatha) | (~lives_at_dreadsbury(someone)))) <=> ((~![Person: $i] : ((Person = charles) | (Person = butler) | (Person = aunt_agatha) | (~lives_at_dreadsbury(Person)))) | (someone = charles) | (someone = butler) | (someone = aunt_agatha) | (~lives_at_dreadsbury(someone)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(93,plain,
% 0.12/0.38 ((~![Person: $i] : ((Person = charles) | (Person = butler) | (Person = aunt_agatha) | (~lives_at_dreadsbury(Person)))) | ((someone = charles) | (someone = butler) | (someone = aunt_agatha) | (~lives_at_dreadsbury(someone)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(94,plain,
% 0.12/0.38 ((~![Person: $i] : ((Person = charles) | (Person = butler) | (Person = aunt_agatha) | (~lives_at_dreadsbury(Person)))) | (someone = charles) | (someone = butler) | (someone = aunt_agatha) | (~lives_at_dreadsbury(someone))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.12/0.38 tff(95,plain,
% 0.12/0.38 ((someone = charles) | (someone = butler) | (someone = aunt_agatha)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[94, 91, 88])).
% 0.12/0.38 tff(96,plain,
% 0.12/0.38 ((someone = charles) | (someone = aunt_agatha)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[95, 78])).
% 0.12/0.38 tff(97,plain,
% 0.12/0.38 (someone = charles),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[96, 13])).
% 0.12/0.38 tff(98,plain,
% 0.12/0.38 (charles = someone),
% 0.12/0.38 inference(symmetry,[status(thm)],[97])).
% 0.12/0.38 tff(99,plain,
% 0.12/0.38 (hates(charles, aunt_agatha) <=> hates(someone, aunt_agatha)),
% 0.12/0.38 inference(monotonicity,[status(thm)],[98])).
% 0.12/0.38 tff(100,plain,
% 0.12/0.38 (hates(someone, aunt_agatha) <=> hates(charles, aunt_agatha)),
% 0.12/0.38 inference(symmetry,[status(thm)],[99])).
% 0.12/0.38 tff(101,plain,
% 0.12/0.38 (^[Victim: $i, Killer: $i] : refl(((~killed(Killer, Victim)) | hates(Killer, Victim)) <=> ((~killed(Killer, Victim)) | hates(Killer, Victim)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(102,plain,
% 0.12/0.38 (![Victim: $i, Killer: $i] : ((~killed(Killer, Victim)) | hates(Killer, Victim)) <=> ![Victim: $i, Killer: $i] : ((~killed(Killer, Victim)) | hates(Killer, Victim))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[101])).
% 0.12/0.38 tff(103,plain,
% 0.12/0.38 (![Victim: $i, Killer: $i] : ((~killed(Killer, Victim)) | hates(Killer, Victim)) <=> ![Victim: $i, Killer: $i] : ((~killed(Killer, Victim)) | hates(Killer, Victim))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(104,axiom,(![Victim: $i, Killer: $i] : ((~killed(Killer, Victim)) | hates(Killer, Victim))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','killer_hates_victim')).
% 0.12/0.38 tff(105,plain,
% 0.12/0.38 (![Victim: $i, Killer: $i] : ((~killed(Killer, Victim)) | hates(Killer, Victim))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.12/0.38 tff(106,plain,(
% 0.12/0.38 ![Victim: $i, Killer: $i] : ((~killed(Killer, Victim)) | hates(Killer, Victim))),
% 0.12/0.38 inference(skolemize,[status(sab)],[105])).
% 0.12/0.38 tff(107,plain,
% 0.12/0.38 (![Victim: $i, Killer: $i] : ((~killed(Killer, Victim)) | hates(Killer, Victim))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[106, 102])).
% 0.12/0.38 tff(108,plain,
% 0.12/0.38 (((~![Victim: $i, Killer: $i] : ((~killed(Killer, Victim)) | hates(Killer, Victim))) | ((~killed(someone, aunt_agatha)) | hates(someone, aunt_agatha))) <=> ((~![Victim: $i, Killer: $i] : ((~killed(Killer, Victim)) | hates(Killer, Victim))) | (~killed(someone, aunt_agatha)) | hates(someone, aunt_agatha))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(109,plain,
% 0.12/0.38 ((~![Victim: $i, Killer: $i] : ((~killed(Killer, Victim)) | hates(Killer, Victim))) | ((~killed(someone, aunt_agatha)) | hates(someone, aunt_agatha))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(110,plain,
% 0.12/0.38 ((~![Victim: $i, Killer: $i] : ((~killed(Killer, Victim)) | hates(Killer, Victim))) | (~killed(someone, aunt_agatha)) | hates(someone, aunt_agatha)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.12/0.38 tff(111,plain,
% 0.12/0.38 (hates(someone, aunt_agatha)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[110, 11, 107])).
% 0.12/0.38 tff(112,plain,
% 0.12/0.38 (hates(charles, aunt_agatha)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[111, 100])).
% 0.12/0.38 tff(113,plain,
% 0.12/0.38 (^[Person: $i] : refl(((~hates(aunt_agatha, Person)) | (~hates(charles, Person))) <=> ((~hates(aunt_agatha, Person)) | (~hates(charles, Person))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(114,plain,
% 0.12/0.38 (![Person: $i] : ((~hates(aunt_agatha, Person)) | (~hates(charles, Person))) <=> ![Person: $i] : ((~hates(aunt_agatha, Person)) | (~hates(charles, Person)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[113])).
% 0.12/0.38 tff(115,plain,
% 0.12/0.38 (![Person: $i] : ((~hates(aunt_agatha, Person)) | (~hates(charles, Person))) <=> ![Person: $i] : ((~hates(aunt_agatha, Person)) | (~hates(charles, Person)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(116,axiom,(![Person: $i] : ((~hates(aunt_agatha, Person)) | (~hates(charles, Person)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','charles_and_agatha_hate_different_people')).
% 0.12/0.38 tff(117,plain,
% 0.12/0.38 (![Person: $i] : ((~hates(aunt_agatha, Person)) | (~hates(charles, Person)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.12/0.38 tff(118,plain,(
% 0.12/0.38 ![Person: $i] : ((~hates(aunt_agatha, Person)) | (~hates(charles, Person)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[117])).
% 0.12/0.38 tff(119,plain,
% 0.12/0.38 (![Person: $i] : ((~hates(aunt_agatha, Person)) | (~hates(charles, Person)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[118, 114])).
% 0.12/0.38 tff(120,plain,
% 0.12/0.38 (((~![Person: $i] : ((~hates(aunt_agatha, Person)) | (~hates(charles, Person)))) | ((~hates(aunt_agatha, aunt_agatha)) | (~hates(charles, aunt_agatha)))) <=> ((~![Person: $i] : ((~hates(aunt_agatha, Person)) | (~hates(charles, Person)))) | (~hates(aunt_agatha, aunt_agatha)) | (~hates(charles, aunt_agatha)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(121,plain,
% 0.12/0.38 ((~![Person: $i] : ((~hates(aunt_agatha, Person)) | (~hates(charles, Person)))) | ((~hates(aunt_agatha, aunt_agatha)) | (~hates(charles, aunt_agatha)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(122,plain,
% 0.12/0.38 ((~![Person: $i] : ((~hates(aunt_agatha, Person)) | (~hates(charles, Person)))) | (~hates(aunt_agatha, aunt_agatha)) | (~hates(charles, aunt_agatha))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.12/0.38 tff(123,plain,
% 0.12/0.38 ((~hates(aunt_agatha, aunt_agatha)) | (~hates(charles, aunt_agatha))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[122, 119])).
% 0.12/0.38 tff(124,plain,
% 0.12/0.38 (~hates(aunt_agatha, aunt_agatha)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[123, 112])).
% 0.12/0.38 tff(125,plain,
% 0.12/0.38 ((~(aunt_agatha = butler)) <=> (~(aunt_agatha = butler))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(126,axiom,(~(aunt_agatha = butler)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','agatha_is_not_the_butler')).
% 0.12/0.38 tff(127,plain,
% 0.12/0.38 (~(aunt_agatha = butler)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.12/0.38 tff(128,plain,
% 0.12/0.38 (((~![Person: $i] : ((Person = butler) | hates(aunt_agatha, Person))) | ((aunt_agatha = butler) | hates(aunt_agatha, aunt_agatha))) <=> ((~![Person: $i] : ((Person = butler) | hates(aunt_agatha, Person))) | (aunt_agatha = butler) | hates(aunt_agatha, aunt_agatha))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(129,plain,
% 0.12/0.38 ((~![Person: $i] : ((Person = butler) | hates(aunt_agatha, Person))) | ((aunt_agatha = butler) | hates(aunt_agatha, aunt_agatha))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(130,plain,
% 0.12/0.38 ((~![Person: $i] : ((Person = butler) | hates(aunt_agatha, Person))) | (aunt_agatha = butler) | hates(aunt_agatha, aunt_agatha)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.12/0.38 tff(131,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[130, 40, 127, 124])).
% 0.12/0.38 % SZS output end Proof
% 0.12/0.38 % E exiting
%------------------------------------------------------------------------------