TSTP Solution File: PUZ001-2 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : PUZ001-2 : TPTP v8.2.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n026.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 : Tue May 21 02:26:28 EDT 2024

% Result   : Unsatisfiable 3.49s 2.32s
% Output   : Refutation 3.50s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   40 (  17 unt;   9 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  :    8 (   8   >;   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_type,type,
    killed: $i > $i > $o ).

thf(aunt_agatha_type,type,
    aunt_agatha: $i ).

thf(lives_at_dreadsbury_type,type,
    lives_at_dreadsbury: $i > $o ).

thf(someone_type,type,
    someone: $i ).

thf(butler_type,type,
    butler: $i ).

thf(charles_type,type,
    charles: $i ).

thf(hates_type,type,
    hates: $i > $i > $o ).

thf(richer_type,type,
    richer: $i > $i > $o ).

thf(every_one_but_type,type,
    every_one_but: $i > $i ).

thf(13,axiom,
    ! [A: $i] :
      ( ~ ( hates @ aunt_agatha @ A )
      | ( hates @ butler @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',butler_and_agatha_hate_the_same_people) ).

thf(37,plain,
    ! [A: $i] :
      ( ~ ( hates @ aunt_agatha @ A )
      | ( hates @ butler @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(4,axiom,
    lives_at_dreadsbury @ aunt_agatha,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',agatha_lives_at_mansion) ).

thf(20,plain,
    lives_at_dreadsbury @ aunt_agatha,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(15,axiom,
    aunt_agatha != butler,
    file('/export/starexec/sandbox2/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 = butler )
      | ( hates @ aunt_agatha @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',agatha_likes_only_butler) ).

thf(32,plain,
    ! [A: $i] :
      ( ( A = butler )
      | ( hates @ aunt_agatha @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(6,axiom,
    lives_at_dreadsbury @ charles,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',charles_lives_at_mansion) ).

thf(22,plain,
    lives_at_dreadsbury @ charles,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(14,axiom,
    ! [A: $i] :
      ~ ( hates @ A @ ( every_one_but @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',noone_hates_everyone) ).

thf(39,plain,
    ! [A: $i] :
      ~ ( hates @ A @ ( every_one_but @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(12,axiom,
    ! [A: $i] :
      ( ( richer @ A @ aunt_agatha )
      | ( hates @ butler @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',butler_hates_poor_people) ).

thf(35,plain,
    ! [A: $i] :
      ( ( richer @ A @ aunt_agatha )
      | ( hates @ butler @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(2,axiom,
    lives_at_dreadsbury @ someone,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',someone_in_mansion) ).

thf(18,plain,
    lives_at_dreadsbury @ someone,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(1,negated_conjecture,
    ~ ( killed @ aunt_agatha @ aunt_agatha ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_agatha_killed_herself) ).

thf(16,plain,
    ~ ( killed @ aunt_agatha @ aunt_agatha ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(9,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( killed @ A @ B )
      | ~ ( richer @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',killer_poorer_than_victim) ).

thf(28,plain,
    ! [B: $i,A: $i] :
      ( ~ ( killed @ A @ B )
      | ~ ( richer @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(5,axiom,
    lives_at_dreadsbury @ butler,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',butler_lives_at_mansion) ).

thf(21,plain,
    lives_at_dreadsbury @ butler,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(8,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( killed @ A @ B )
      | ( hates @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',killer_hates_victim) ).

thf(26,plain,
    ! [B: $i,A: $i] :
      ( ~ ( killed @ A @ B )
      | ( hates @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(7,axiom,
    ! [A: $i] :
      ( ~ ( lives_at_dreadsbury @ A )
      | ( A = aunt_agatha )
      | ( A = butler )
      | ( A = charles ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',noone_else_lives_at_mansion) ).

thf(23,plain,
    ! [A: $i] :
      ( ~ ( lives_at_dreadsbury @ A )
      | ( A = aunt_agatha )
      | ( A = butler )
      | ( A = charles ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(10,axiom,
    ! [A: $i] :
      ( ~ ( hates @ aunt_agatha @ A )
      | ~ ( hates @ charles @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',charles_and_agatha_hate_different_people) ).

thf(30,plain,
    ! [A: $i] :
      ( ~ ( hates @ aunt_agatha @ A )
      | ~ ( hates @ charles @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(3,axiom,
    killed @ someone @ aunt_agatha,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',someone_killed_agatha) ).

thf(19,plain,
    killed @ someone @ aunt_agatha,
    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
% 0.00/0.10  % Problem  : PUZ001-2 : TPTP v8.2.0. Released v1.0.0.
% 0.10/0.13  % Command  : run_Leo-III %s %d
% 0.14/0.34  % Computer : n026.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Sat May 18 11:02:09 EDT 2024
% 0.14/0.34  % CPUTime  : 
% 1.13/1.12  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.53/1.30  % [INFO] 	 Parsing done (182ms). 
% 1.53/1.32  % [INFO] 	 Running in sequential loop mode. 
% 2.19/1.73  % [INFO] 	 eprover registered as external prover. 
% 2.21/1.73  % [INFO] 	 cvc4 registered as external prover. 
% 2.21/1.74  % [INFO] 	 Scanning for conjecture ... 
% 2.38/1.82  % [INFO] 	 Found a conjecture (or negated_conjecture) and 14 axioms. Running axiom selection ... 
% 2.38/1.84  % [INFO] 	 Axiom selection finished. Selected 14 axioms (removed 0 axioms). 
% 2.38/1.86  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 2.38/1.86  % [INFO] 	 Type checking passed. 
% 2.38/1.86  % [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 ... 
% 3.32/2.31  % External prover 'e' found a proof!
% 3.49/2.31  % [INFO] 	 Killing All external provers ... 
% 3.49/2.31  % Time passed: 1810ms (effective reasoning time: 985ms)
% 3.49/2.31  % 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
% 3.49/2.31  % No. of inferences in proof: 31
% 3.49/2.32  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1810 ms resp. 985 ms w/o parsing
% 3.50/2.35  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.50/2.35  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------