TSTP Solution File: PUZ001-2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : PUZ001-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 : Sun Sep 18 14:10:45 EDT 2022
% Result : Unsatisfiable 0.14s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : PUZ001-2 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n004.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Sep 2 18:11:34 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.14/0.40 % SZS status Unsatisfiable
% 0.14/0.40 % SZS output start Proof
% 0.14/0.40 tff(hates_type, type, (
% 0.14/0.40 hates: ( $i * $i ) > $o)).
% 0.14/0.40 tff(aunt_agatha_type, type, (
% 0.14/0.40 aunt_agatha: $i)).
% 0.14/0.40 tff(charles_type, type, (
% 0.14/0.40 charles: $i)).
% 0.14/0.40 tff(someone_type, type, (
% 0.14/0.40 someone: $i)).
% 0.14/0.40 tff(killed_type, type, (
% 0.14/0.40 killed: ( $i * $i ) > $o)).
% 0.14/0.40 tff(butler_type, type, (
% 0.14/0.40 butler: $i)).
% 0.14/0.40 tff(every_one_but_type, type, (
% 0.14/0.40 every_one_but: $i > $i)).
% 0.14/0.40 tff(richer_type, type, (
% 0.14/0.40 richer: ( $i * $i ) > $o)).
% 0.14/0.40 tff(lives_at_dreadsbury_type, type, (
% 0.14/0.40 lives_at_dreadsbury: $i > $o)).
% 0.14/0.40 tff(1,assumption,(someone = aunt_agatha), introduced(assumption)).
% 0.14/0.40 tff(2,plain,
% 0.14/0.40 (killed(someone, aunt_agatha) <=> killed(aunt_agatha, aunt_agatha)),
% 0.14/0.40 inference(monotonicity,[status(thm)],[1])).
% 0.14/0.40 tff(3,plain,
% 0.14/0.40 (killed(aunt_agatha, aunt_agatha) <=> killed(someone, aunt_agatha)),
% 0.14/0.40 inference(symmetry,[status(thm)],[2])).
% 0.14/0.40 tff(4,plain,
% 0.14/0.40 ((~killed(aunt_agatha, aunt_agatha)) <=> (~killed(someone, aunt_agatha))),
% 0.14/0.40 inference(monotonicity,[status(thm)],[3])).
% 0.14/0.40 tff(5,plain,
% 0.14/0.40 ((~killed(aunt_agatha, aunt_agatha)) <=> (~killed(aunt_agatha, aunt_agatha))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(6,axiom,(~killed(aunt_agatha, aunt_agatha)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_agatha_killed_herself')).
% 0.14/0.40 tff(7,plain,
% 0.14/0.40 (~killed(aunt_agatha, aunt_agatha)),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.14/0.40 tff(8,plain,
% 0.14/0.40 (~killed(someone, aunt_agatha)),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[7, 4])).
% 0.14/0.40 tff(9,plain,
% 0.14/0.40 (killed(someone, aunt_agatha) <=> killed(someone, aunt_agatha)),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(10,axiom,(killed(someone, aunt_agatha)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','someone_killed_agatha')).
% 0.14/0.40 tff(11,plain,
% 0.14/0.40 (killed(someone, aunt_agatha)),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.14/0.40 tff(12,plain,
% 0.14/0.40 ($false),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[11, 8])).
% 0.14/0.40 tff(13,plain,(~(someone = aunt_agatha)), inference(lemma,lemma(discharge,[]))).
% 0.14/0.40 tff(14,assumption,(someone = butler), introduced(assumption)).
% 0.14/0.40 tff(15,plain,
% 0.14/0.40 (butler = someone),
% 0.14/0.40 inference(symmetry,[status(thm)],[14])).
% 0.14/0.40 tff(16,plain,
% 0.14/0.40 (hates(butler, every_one_but(someone)) <=> hates(someone, every_one_but(someone))),
% 0.14/0.40 inference(monotonicity,[status(thm)],[15])).
% 0.14/0.40 tff(17,plain,
% 0.14/0.40 (hates(someone, every_one_but(someone)) <=> hates(butler, every_one_but(someone))),
% 0.14/0.40 inference(symmetry,[status(thm)],[16])).
% 0.14/0.40 tff(18,plain,
% 0.14/0.40 ((~hates(someone, every_one_but(someone))) <=> (~hates(butler, every_one_but(someone)))),
% 0.14/0.40 inference(monotonicity,[status(thm)],[17])).
% 0.14/0.40 tff(19,plain,
% 0.14/0.40 (^[Person: $i] : refl((~hates(Person, every_one_but(Person))) <=> (~hates(Person, every_one_but(Person))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(20,plain,
% 0.14/0.40 (![Person: $i] : (~hates(Person, every_one_but(Person))) <=> ![Person: $i] : (~hates(Person, every_one_but(Person)))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[19])).
% 0.14/0.40 tff(21,plain,
% 0.14/0.40 (![Person: $i] : (~hates(Person, every_one_but(Person))) <=> ![Person: $i] : (~hates(Person, every_one_but(Person)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(22,axiom,(![Person: $i] : (~hates(Person, every_one_but(Person)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','noone_hates_everyone')).
% 0.14/0.40 tff(23,plain,
% 0.14/0.40 (![Person: $i] : (~hates(Person, every_one_but(Person)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.14/0.40 tff(24,plain,(
% 0.14/0.40 ![Person: $i] : (~hates(Person, every_one_but(Person)))),
% 0.14/0.40 inference(skolemize,[status(sab)],[23])).
% 0.14/0.40 tff(25,plain,
% 0.14/0.40 (![Person: $i] : (~hates(Person, every_one_but(Person)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.14/0.40 tff(26,plain,
% 0.14/0.40 ((~![Person: $i] : (~hates(Person, every_one_but(Person)))) | (~hates(someone, every_one_but(someone)))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(27,plain,
% 0.14/0.40 (~hates(someone, every_one_but(someone))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.14/0.40 tff(28,plain,
% 0.14/0.40 (~hates(butler, every_one_but(someone))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[27, 18])).
% 0.14/0.40 tff(29,plain,
% 0.14/0.40 (^[Person: $i] : refl(((~hates(aunt_agatha, Person)) | hates(butler, Person)) <=> ((~hates(aunt_agatha, Person)) | hates(butler, Person)))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(30,plain,
% 0.14/0.40 (![Person: $i] : ((~hates(aunt_agatha, Person)) | hates(butler, Person)) <=> ![Person: $i] : ((~hates(aunt_agatha, Person)) | hates(butler, Person))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[29])).
% 0.14/0.40 tff(31,plain,
% 0.14/0.40 (![Person: $i] : ((~hates(aunt_agatha, Person)) | hates(butler, Person)) <=> ![Person: $i] : ((~hates(aunt_agatha, Person)) | hates(butler, Person))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(32,axiom,(![Person: $i] : ((~hates(aunt_agatha, Person)) | hates(butler, Person))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','butler_and_agatha_hate_the_same_people')).
% 0.14/0.40 tff(33,plain,
% 0.14/0.40 (![Person: $i] : ((~hates(aunt_agatha, Person)) | hates(butler, Person))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.14/0.40 tff(34,plain,(
% 0.14/0.40 ![Person: $i] : ((~hates(aunt_agatha, Person)) | hates(butler, Person))),
% 0.14/0.40 inference(skolemize,[status(sab)],[33])).
% 0.14/0.40 tff(35,plain,
% 0.14/0.40 (![Person: $i] : ((~hates(aunt_agatha, Person)) | hates(butler, Person))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.14/0.40 tff(36,plain,
% 0.14/0.40 (((~![Person: $i] : ((~hates(aunt_agatha, Person)) | hates(butler, Person))) | ((~hates(aunt_agatha, every_one_but(someone))) | hates(butler, every_one_but(someone)))) <=> ((~![Person: $i] : ((~hates(aunt_agatha, Person)) | hates(butler, Person))) | (~hates(aunt_agatha, every_one_but(someone))) | hates(butler, every_one_but(someone)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(37,plain,
% 0.14/0.40 ((~![Person: $i] : ((~hates(aunt_agatha, Person)) | hates(butler, Person))) | ((~hates(aunt_agatha, every_one_but(someone))) | hates(butler, every_one_but(someone)))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(38,plain,
% 0.14/0.40 ((~![Person: $i] : ((~hates(aunt_agatha, Person)) | hates(butler, Person))) | (~hates(aunt_agatha, every_one_but(someone))) | hates(butler, every_one_but(someone))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.14/0.40 tff(39,plain,
% 0.14/0.40 ((~hates(aunt_agatha, every_one_but(someone))) | hates(butler, every_one_but(someone))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[38, 35])).
% 0.14/0.40 tff(40,plain,
% 0.14/0.40 (~hates(aunt_agatha, every_one_but(someone))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[39, 28])).
% 0.14/0.40 tff(41,plain,
% 0.14/0.40 (^[Person: $i] : refl(((Person = butler) | hates(aunt_agatha, Person)) <=> ((Person = butler) | hates(aunt_agatha, Person)))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(42,plain,
% 0.14/0.40 (![Person: $i] : ((Person = butler) | hates(aunt_agatha, Person)) <=> ![Person: $i] : ((Person = butler) | hates(aunt_agatha, Person))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[41])).
% 0.14/0.40 tff(43,plain,
% 0.14/0.40 (![Person: $i] : ((Person = butler) | hates(aunt_agatha, Person)) <=> ![Person: $i] : ((Person = butler) | hates(aunt_agatha, Person))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(44,axiom,(![Person: $i] : ((Person = butler) | hates(aunt_agatha, Person))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','agatha_likes_only_butler')).
% 0.14/0.40 tff(45,plain,
% 0.14/0.40 (![Person: $i] : ((Person = butler) | hates(aunt_agatha, Person))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.14/0.40 tff(46,plain,(
% 0.14/0.40 ![Person: $i] : ((Person = butler) | hates(aunt_agatha, Person))),
% 0.14/0.40 inference(skolemize,[status(sab)],[45])).
% 0.14/0.40 tff(47,plain,
% 0.14/0.40 (![Person: $i] : ((Person = butler) | hates(aunt_agatha, Person))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.14/0.40 tff(48,plain,
% 0.14/0.40 (((~![Person: $i] : ((Person = butler) | hates(aunt_agatha, Person))) | ((every_one_but(someone) = butler) | hates(aunt_agatha, every_one_but(someone)))) <=> ((~![Person: $i] : ((Person = butler) | hates(aunt_agatha, Person))) | (every_one_but(someone) = butler) | hates(aunt_agatha, every_one_but(someone)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(49,plain,
% 0.14/0.40 ((~![Person: $i] : ((Person = butler) | hates(aunt_agatha, Person))) | ((every_one_but(someone) = butler) | hates(aunt_agatha, every_one_but(someone)))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(50,plain,
% 0.14/0.41 ((~![Person: $i] : ((Person = butler) | hates(aunt_agatha, Person))) | (every_one_but(someone) = butler) | hates(aunt_agatha, every_one_but(someone))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.14/0.41 tff(51,plain,
% 0.14/0.41 (every_one_but(someone) = butler),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[50, 47, 40])).
% 0.14/0.41 tff(52,plain,
% 0.14/0.41 (butler = every_one_but(someone)),
% 0.14/0.41 inference(symmetry,[status(thm)],[51])).
% 0.14/0.41 tff(53,plain,
% 0.14/0.41 (someone = every_one_but(someone)),
% 0.14/0.41 inference(transitivity,[status(thm)],[14, 52])).
% 0.14/0.41 tff(54,plain,
% 0.14/0.41 (hates(butler, someone) <=> hates(someone, every_one_but(someone))),
% 0.14/0.41 inference(monotonicity,[status(thm)],[15, 53])).
% 0.14/0.41 tff(55,plain,
% 0.14/0.41 (hates(someone, every_one_but(someone)) <=> hates(butler, someone)),
% 0.14/0.41 inference(symmetry,[status(thm)],[54])).
% 0.14/0.41 tff(56,plain,
% 0.14/0.41 ((~hates(someone, every_one_but(someone))) <=> (~hates(butler, someone))),
% 0.14/0.41 inference(monotonicity,[status(thm)],[55])).
% 0.14/0.41 tff(57,plain,
% 0.14/0.41 (~hates(butler, someone)),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[27, 56])).
% 0.14/0.41 tff(58,plain,
% 0.14/0.41 (^[Victim: $i, Killer: $i] : refl(((~killed(Killer, Victim)) | (~richer(Killer, Victim))) <=> ((~killed(Killer, Victim)) | (~richer(Killer, Victim))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(59,plain,
% 0.14/0.41 (![Victim: $i, Killer: $i] : ((~killed(Killer, Victim)) | (~richer(Killer, Victim))) <=> ![Victim: $i, Killer: $i] : ((~killed(Killer, Victim)) | (~richer(Killer, Victim)))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[58])).
% 0.14/0.41 tff(60,plain,
% 0.14/0.41 (![Victim: $i, Killer: $i] : ((~killed(Killer, Victim)) | (~richer(Killer, Victim))) <=> ![Victim: $i, Killer: $i] : ((~killed(Killer, Victim)) | (~richer(Killer, Victim)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(61,axiom,(![Victim: $i, Killer: $i] : ((~killed(Killer, Victim)) | (~richer(Killer, Victim)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','killer_poorer_than_victim')).
% 0.14/0.41 tff(62,plain,
% 0.14/0.41 (![Victim: $i, Killer: $i] : ((~killed(Killer, Victim)) | (~richer(Killer, Victim)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.14/0.41 tff(63,plain,(
% 0.14/0.41 ![Victim: $i, Killer: $i] : ((~killed(Killer, Victim)) | (~richer(Killer, Victim)))),
% 0.14/0.41 inference(skolemize,[status(sab)],[62])).
% 0.14/0.41 tff(64,plain,
% 0.14/0.41 (![Victim: $i, Killer: $i] : ((~killed(Killer, Victim)) | (~richer(Killer, Victim)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.14/0.41 tff(65,plain,
% 0.14/0.41 (((~![Victim: $i, Killer: $i] : ((~killed(Killer, Victim)) | (~richer(Killer, Victim)))) | ((~killed(someone, aunt_agatha)) | (~richer(someone, aunt_agatha)))) <=> ((~![Victim: $i, Killer: $i] : ((~killed(Killer, Victim)) | (~richer(Killer, Victim)))) | (~killed(someone, aunt_agatha)) | (~richer(someone, aunt_agatha)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(66,plain,
% 0.14/0.41 ((~![Victim: $i, Killer: $i] : ((~killed(Killer, Victim)) | (~richer(Killer, Victim)))) | ((~killed(someone, aunt_agatha)) | (~richer(someone, aunt_agatha)))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(67,plain,
% 0.14/0.41 ((~![Victim: $i, Killer: $i] : ((~killed(Killer, Victim)) | (~richer(Killer, Victim)))) | (~killed(someone, aunt_agatha)) | (~richer(someone, aunt_agatha))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.14/0.41 tff(68,plain,
% 0.14/0.41 (~richer(someone, aunt_agatha)),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[67, 11, 64])).
% 0.14/0.41 tff(69,plain,
% 0.14/0.41 (^[Person: $i] : refl((hates(butler, Person) | richer(Person, aunt_agatha)) <=> (hates(butler, Person) | richer(Person, aunt_agatha)))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(70,plain,
% 0.14/0.41 (![Person: $i] : (hates(butler, Person) | richer(Person, aunt_agatha)) <=> ![Person: $i] : (hates(butler, Person) | richer(Person, aunt_agatha))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[69])).
% 0.14/0.41 tff(71,plain,
% 0.14/0.41 (![Person: $i] : (hates(butler, Person) | richer(Person, aunt_agatha)) <=> ![Person: $i] : (hates(butler, Person) | richer(Person, aunt_agatha))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(72,plain,
% 0.14/0.41 (^[Person: $i] : rewrite((richer(Person, aunt_agatha) | hates(butler, Person)) <=> (hates(butler, Person) | richer(Person, aunt_agatha)))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(73,plain,
% 0.14/0.41 (![Person: $i] : (richer(Person, aunt_agatha) | hates(butler, Person)) <=> ![Person: $i] : (hates(butler, Person) | richer(Person, aunt_agatha))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[72])).
% 0.14/0.41 tff(74,axiom,(![Person: $i] : (richer(Person, aunt_agatha) | hates(butler, Person))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','butler_hates_poor_people')).
% 0.14/0.41 tff(75,plain,
% 0.14/0.41 (![Person: $i] : (hates(butler, Person) | richer(Person, aunt_agatha))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.14/0.41 tff(76,plain,
% 0.14/0.41 (![Person: $i] : (hates(butler, Person) | richer(Person, aunt_agatha))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.14/0.41 tff(77,plain,(
% 0.14/0.41 ![Person: $i] : (hates(butler, Person) | richer(Person, aunt_agatha))),
% 0.14/0.41 inference(skolemize,[status(sab)],[76])).
% 0.14/0.41 tff(78,plain,
% 0.14/0.41 (![Person: $i] : (hates(butler, Person) | richer(Person, aunt_agatha))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[77, 70])).
% 0.14/0.41 tff(79,plain,
% 0.14/0.41 (((~![Person: $i] : (hates(butler, Person) | richer(Person, aunt_agatha))) | (hates(butler, someone) | richer(someone, aunt_agatha))) <=> ((~![Person: $i] : (hates(butler, Person) | richer(Person, aunt_agatha))) | hates(butler, someone) | richer(someone, aunt_agatha))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(80,plain,
% 0.14/0.41 ((~![Person: $i] : (hates(butler, Person) | richer(Person, aunt_agatha))) | (hates(butler, someone) | richer(someone, aunt_agatha))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(81,plain,
% 0.14/0.41 ((~![Person: $i] : (hates(butler, Person) | richer(Person, aunt_agatha))) | hates(butler, someone) | richer(someone, aunt_agatha)),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.14/0.41 tff(82,plain,
% 0.14/0.41 (hates(butler, someone)),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[81, 78, 68])).
% 0.14/0.41 tff(83,plain,
% 0.14/0.41 ($false),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[82, 57])).
% 0.14/0.41 tff(84,plain,(~(someone = butler)), inference(lemma,lemma(discharge,[]))).
% 0.14/0.41 tff(85,plain,
% 0.14/0.41 (^[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))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(86,plain,
% 0.14/0.41 (![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)))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[85])).
% 0.14/0.41 tff(87,plain,
% 0.14/0.41 (![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)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(88,plain,
% 0.14/0.41 (^[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)))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(89,plain,
% 0.14/0.41 (![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)))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[88])).
% 0.20/0.41 tff(90,axiom,(![Person: $i] : ((((~lives_at_dreadsbury(Person)) | (Person = aunt_agatha)) | (Person = butler)) | (Person = charles))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','noone_else_lives_at_mansion')).
% 0.20/0.41 tff(91,plain,
% 0.20/0.41 (![Person: $i] : ((Person = charles) | (Person = butler) | (Person = aunt_agatha) | (~lives_at_dreadsbury(Person)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.20/0.41 tff(92,plain,
% 0.20/0.41 (![Person: $i] : ((Person = charles) | (Person = butler) | (Person = aunt_agatha) | (~lives_at_dreadsbury(Person)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[91, 87])).
% 0.20/0.41 tff(93,plain,(
% 0.20/0.41 ![Person: $i] : ((Person = charles) | (Person = butler) | (Person = aunt_agatha) | (~lives_at_dreadsbury(Person)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[92])).
% 0.20/0.41 tff(94,plain,
% 0.20/0.41 (![Person: $i] : ((Person = charles) | (Person = butler) | (Person = aunt_agatha) | (~lives_at_dreadsbury(Person)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[93, 86])).
% 0.20/0.41 tff(95,plain,
% 0.20/0.41 (lives_at_dreadsbury(someone) <=> lives_at_dreadsbury(someone)),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(96,axiom,(lives_at_dreadsbury(someone)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','someone_in_mansion')).
% 0.20/0.41 tff(97,plain,
% 0.20/0.41 (lives_at_dreadsbury(someone)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.20/0.41 tff(98,plain,
% 0.20/0.41 (((~![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)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(99,plain,
% 0.20/0.41 ((~![Person: $i] : ((Person = charles) | (Person = butler) | (Person = aunt_agatha) | (~lives_at_dreadsbury(Person)))) | ((someone = charles) | (someone = butler) | (someone = aunt_agatha) | (~lives_at_dreadsbury(someone)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(100,plain,
% 0.20/0.41 ((~![Person: $i] : ((Person = charles) | (Person = butler) | (Person = aunt_agatha) | (~lives_at_dreadsbury(Person)))) | (someone = charles) | (someone = butler) | (someone = aunt_agatha) | (~lives_at_dreadsbury(someone))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.20/0.41 tff(101,plain,
% 0.20/0.41 ((someone = charles) | (someone = butler) | (someone = aunt_agatha)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[100, 97, 94])).
% 0.20/0.41 tff(102,plain,
% 0.20/0.41 ((someone = charles) | (someone = aunt_agatha)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[101, 84])).
% 0.20/0.41 tff(103,plain,
% 0.20/0.41 (someone = charles),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[102, 13])).
% 0.20/0.41 tff(104,plain,
% 0.20/0.41 (charles = someone),
% 0.20/0.41 inference(symmetry,[status(thm)],[103])).
% 0.20/0.41 tff(105,plain,
% 0.20/0.41 (hates(charles, aunt_agatha) <=> hates(someone, aunt_agatha)),
% 0.20/0.41 inference(monotonicity,[status(thm)],[104])).
% 0.20/0.41 tff(106,plain,
% 0.20/0.41 (hates(someone, aunt_agatha) <=> hates(charles, aunt_agatha)),
% 0.20/0.41 inference(symmetry,[status(thm)],[105])).
% 0.20/0.41 tff(107,plain,
% 0.20/0.41 (^[Victim: $i, Killer: $i] : refl(((~killed(Killer, Victim)) | hates(Killer, Victim)) <=> ((~killed(Killer, Victim)) | hates(Killer, Victim)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(108,plain,
% 0.20/0.41 (![Victim: $i, Killer: $i] : ((~killed(Killer, Victim)) | hates(Killer, Victim)) <=> ![Victim: $i, Killer: $i] : ((~killed(Killer, Victim)) | hates(Killer, Victim))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[107])).
% 0.20/0.41 tff(109,plain,
% 0.20/0.41 (![Victim: $i, Killer: $i] : ((~killed(Killer, Victim)) | hates(Killer, Victim)) <=> ![Victim: $i, Killer: $i] : ((~killed(Killer, Victim)) | hates(Killer, Victim))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(110,axiom,(![Victim: $i, Killer: $i] : ((~killed(Killer, Victim)) | hates(Killer, Victim))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','killer_hates_victim')).
% 0.20/0.41 tff(111,plain,
% 0.20/0.41 (![Victim: $i, Killer: $i] : ((~killed(Killer, Victim)) | hates(Killer, Victim))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.20/0.41 tff(112,plain,(
% 0.20/0.41 ![Victim: $i, Killer: $i] : ((~killed(Killer, Victim)) | hates(Killer, Victim))),
% 0.20/0.41 inference(skolemize,[status(sab)],[111])).
% 0.20/0.41 tff(113,plain,
% 0.20/0.41 (![Victim: $i, Killer: $i] : ((~killed(Killer, Victim)) | hates(Killer, Victim))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.20/0.41 tff(114,plain,
% 0.20/0.41 (((~![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))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(115,plain,
% 0.20/0.41 ((~![Victim: $i, Killer: $i] : ((~killed(Killer, Victim)) | hates(Killer, Victim))) | ((~killed(someone, aunt_agatha)) | hates(someone, aunt_agatha))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(116,plain,
% 0.20/0.41 ((~![Victim: $i, Killer: $i] : ((~killed(Killer, Victim)) | hates(Killer, Victim))) | (~killed(someone, aunt_agatha)) | hates(someone, aunt_agatha)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.20/0.41 tff(117,plain,
% 0.20/0.41 (hates(someone, aunt_agatha)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[116, 11, 113])).
% 0.20/0.41 tff(118,plain,
% 0.20/0.41 (hates(charles, aunt_agatha)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[117, 106])).
% 0.20/0.41 tff(119,plain,
% 0.20/0.41 (^[Person: $i] : refl(((~hates(aunt_agatha, Person)) | (~hates(charles, Person))) <=> ((~hates(aunt_agatha, Person)) | (~hates(charles, Person))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(120,plain,
% 0.20/0.41 (![Person: $i] : ((~hates(aunt_agatha, Person)) | (~hates(charles, Person))) <=> ![Person: $i] : ((~hates(aunt_agatha, Person)) | (~hates(charles, Person)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[119])).
% 0.20/0.41 tff(121,plain,
% 0.20/0.41 (![Person: $i] : ((~hates(aunt_agatha, Person)) | (~hates(charles, Person))) <=> ![Person: $i] : ((~hates(aunt_agatha, Person)) | (~hates(charles, Person)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(122,axiom,(![Person: $i] : ((~hates(aunt_agatha, Person)) | (~hates(charles, Person)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','charles_and_agatha_hate_different_people')).
% 0.20/0.41 tff(123,plain,
% 0.20/0.41 (![Person: $i] : ((~hates(aunt_agatha, Person)) | (~hates(charles, Person)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.20/0.41 tff(124,plain,(
% 0.20/0.41 ![Person: $i] : ((~hates(aunt_agatha, Person)) | (~hates(charles, Person)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[123])).
% 0.20/0.41 tff(125,plain,
% 0.20/0.41 (![Person: $i] : ((~hates(aunt_agatha, Person)) | (~hates(charles, Person)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[124, 120])).
% 0.20/0.41 tff(126,plain,
% 0.20/0.41 (((~![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)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(127,plain,
% 0.20/0.41 ((~![Person: $i] : ((~hates(aunt_agatha, Person)) | (~hates(charles, Person)))) | ((~hates(aunt_agatha, aunt_agatha)) | (~hates(charles, aunt_agatha)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(128,plain,
% 0.20/0.41 ((~![Person: $i] : ((~hates(aunt_agatha, Person)) | (~hates(charles, Person)))) | (~hates(aunt_agatha, aunt_agatha)) | (~hates(charles, aunt_agatha))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.20/0.41 tff(129,plain,
% 0.20/0.41 ((~hates(aunt_agatha, aunt_agatha)) | (~hates(charles, aunt_agatha))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[128, 125])).
% 0.20/0.41 tff(130,plain,
% 0.20/0.41 (~hates(aunt_agatha, aunt_agatha)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[129, 118])).
% 0.20/0.41 tff(131,plain,
% 0.20/0.41 ((~(aunt_agatha = butler)) <=> (~(aunt_agatha = butler))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(132,axiom,(~(aunt_agatha = butler)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','agatha_is_not_the_butler')).
% 0.20/0.41 tff(133,plain,
% 0.20/0.41 (~(aunt_agatha = butler)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.20/0.42 tff(134,plain,
% 0.20/0.42 (((~![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))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(135,plain,
% 0.20/0.42 ((~![Person: $i] : ((Person = butler) | hates(aunt_agatha, Person))) | ((aunt_agatha = butler) | hates(aunt_agatha, aunt_agatha))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(136,plain,
% 0.20/0.42 ((~![Person: $i] : ((Person = butler) | hates(aunt_agatha, Person))) | (aunt_agatha = butler) | hates(aunt_agatha, aunt_agatha)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.20/0.42 tff(137,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[136, 47, 133, 130])).
% 0.20/0.42 % SZS output end Proof
%------------------------------------------------------------------------------