%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : PUZ001-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:21:02 AM UTC 2026
% Result : Unsatisfiable 3.13s 1.90s
% Output : Refutation 3.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 15
% Syntax : Number of formulae : 31 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 49 ( 10 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 106 ( 20 ~; 18 |; 0 &; 68 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 20 ( 0 ^; 20 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
thf(killed_decl,type,
killed: $i > $i > $o ).
thf(aunt_agatha_decl,type,
aunt_agatha: $i ).
thf(lives_at_dreadsbury_decl,type,
lives_at_dreadsbury: $i > $o ).
thf(someone_decl,type,
someone: $i ).
thf(butler_decl,type,
butler: $i ).
thf(charles_decl,type,
charles: $i ).
thf(hates_decl,type,
hates: $i > $i > $o ).
thf(richer_decl,type,
richer: $i > $i > $o ).
thf(every_one_but_decl,type,
every_one_but: $i > $i ).
thf(13,axiom,
! [A: $i] :
( ( A @ ( butler @ hates ) )
| ~ ( A @ ( aunt_agatha @ hates ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',butler_and_agatha_hate_the_same_people) ).
thf(37,plain,
! [A: $i] :
( ( A @ ( butler @ hates ) )
| ~ ( A @ ( aunt_agatha @ hates ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(4,axiom,
aunt_agatha @ lives_at_dreadsbury,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',agatha_lives_at_mansion) ).
thf(20,plain,
aunt_agatha @ lives_at_dreadsbury,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(15,axiom,
aunt_agatha != butler,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',agatha_is_not_the_butler) ).
thf(41,plain,
aunt_agatha != butler,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ ( aunt_agatha @ hates ) )
| ( A = butler ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',agatha_likes_only_butler) ).
thf(32,plain,
! [A: $i] :
( ( A @ ( aunt_agatha @ hates ) )
| ( A = butler ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(6,axiom,
charles @ lives_at_dreadsbury,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',charles_lives_at_mansion) ).
thf(22,plain,
charles @ lives_at_dreadsbury,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(14,axiom,
! [A: $i] :
~ ( A @ every_one_but @ ( A @ hates ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',noone_hates_everyone) ).
thf(39,plain,
! [A: $i] :
~ ( A @ every_one_but @ ( A @ hates ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ ( butler @ hates ) )
| ( aunt_agatha @ ( A @ richer ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',butler_hates_poor_people) ).
thf(35,plain,
! [A: $i] :
( ( A @ ( butler @ hates ) )
| ( aunt_agatha @ ( A @ richer ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(2,axiom,
someone @ lives_at_dreadsbury,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',someone_in_mansion) ).
thf(18,plain,
someone @ lives_at_dreadsbury,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1,negated_conjecture,
~ ( aunt_agatha @ ( aunt_agatha @ killed ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_agatha_killed_herself) ).
thf(16,plain,
~ ( aunt_agatha @ ( aunt_agatha @ killed ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ richer ) )
| ~ ( B @ ( A @ killed ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',killer_poorer_than_victim) ).
thf(28,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ richer ) )
| ~ ( B @ ( A @ killed ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(5,axiom,
butler @ lives_at_dreadsbury,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',butler_lives_at_mansion) ).
thf(21,plain,
butler @ lives_at_dreadsbury,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ hates ) )
| ~ ( B @ ( A @ killed ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',killer_hates_victim) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ hates ) )
| ~ ( B @ ( A @ killed ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(7,axiom,
! [A: $i] :
( ( A = charles )
| ( A = butler )
| ( A = aunt_agatha )
| ~ ( A @ lives_at_dreadsbury ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',noone_else_lives_at_mansion) ).
thf(23,plain,
! [A: $i] :
( ( A = charles )
| ( A = butler )
| ( A = aunt_agatha )
| ~ ( A @ lives_at_dreadsbury ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(10,axiom,
! [A: $i] :
( ~ ( A @ ( charles @ hates ) )
| ~ ( A @ ( aunt_agatha @ hates ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',charles_and_agatha_hate_different_people) ).
thf(30,plain,
! [A: $i] :
( ~ ( A @ ( charles @ hates ) )
| ~ ( A @ ( aunt_agatha @ hates ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(3,axiom,
aunt_agatha @ ( someone @ killed ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',someone_killed_agatha) ).
thf(19,plain,
aunt_agatha @ ( someone @ killed ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(44,plain,
$false,
inference(e,[status(thm)],[37,20,41,32,22,39,35,18,16,28,21,26,23,30,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ001-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.15/0.41 % Computer : n018.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sat Sep 26 05:04:36 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.69/0.72 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.92/0.82 % [INFO] Parsing done (105ms).
% 0.92/0.83 % [INFO] Running in sequential loop mode.
% 1.63/1.22 % [INFO] eprover registered as external prover.
% 1.63/1.22 % [INFO] Scanning for conjecture ...
% 1.80/1.31 % [INFO] Found a conjecture (or negated_conjecture) and 14 axioms. Running axiom selection ...
% 1.80/1.34 % [INFO] Axiom selection finished. Selected 14 axioms (removed 0 axioms).
% 1.80/1.36 % [INFO] Problem is propositional (TPTP CNF).
% 1.80/1.37 % [INFO] Type checking passed.
% 1.80/1.37 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 3.13/1.90 % External prover 'e' found a proof!
% 3.13/1.90 % [INFO] Killing All external provers ...
% 3.13/1.90 % Time passed: 1400ms (effective reasoning time: 1067ms)
% 3.13/1.90 % Axioms used in derivation (14): butler_hates_poor_people, charles_and_agatha_hate_different_people, noone_else_lives_at_mansion, charles_lives_at_mansion, killer_hates_victim, agatha_is_not_the_butler, killer_poorer_than_victim, someone_killed_agatha, butler_and_agatha_hate_the_same_people, butler_lives_at_mansion, someone_in_mansion, noone_hates_everyone, agatha_lives_at_mansion, agatha_likes_only_butler
% 3.13/1.90 % No. of inferences in proof: 31
% 3.13/1.90 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1400 ms resp. 1067 ms w/o parsing
% 3.13/1.95 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.13/1.95 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------