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

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---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 : n025.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 02:27:05 EDT 2024

% Result   : Unsatisfiable 9.84s 3.74s
% Output   : Refutation 9.84s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   77 (  29 unt;   9 typ;   0 def)
%            Number of atoms       :  139 (  52 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  288 (  63   ~;  51   |;   0   &; 174   @)
%                                         (   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   :   49 (   0   ^  49   !;   0   ?;  49   :)

% 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(11,axiom,
    ! [A: $i] :
      ( ( A = butler )
      | ( hates @ aunt_agatha @ A ) ),
    file('/export/starexec/sandbox/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(33,plain,
    ! [A: $i] :
      ( ( A = butler )
      | ( hates @ aunt_agatha @ A ) ),
    inference(cnf,[status(esa)],[32]) ).

thf(34,plain,
    ! [A: $i] :
      ( ( A = butler )
      | ( hates @ aunt_agatha @ A ) ),
    inference(lifteq,[status(thm)],[33]) ).

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

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

thf(7,axiom,
    ! [A: $i] :
      ( ~ ( lives_at_dreadsbury @ A )
      | ( A = aunt_agatha )
      | ( A = butler )
      | ( A = charles ) ),
    file('/export/starexec/sandbox/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(24,plain,
    ! [A: $i] :
      ( ~ ( lives_at_dreadsbury @ A )
      | ( A = aunt_agatha )
      | ( A = butler )
      | ( A = charles ) ),
    inference(cnf,[status(esa)],[23]) ).

thf(25,plain,
    ! [A: $i] :
      ( ( A = aunt_agatha )
      | ( A = butler )
      | ( A = charles )
      | ~ ( lives_at_dreadsbury @ A ) ),
    inference(lifteq,[status(thm)],[24]) ).

thf(59,plain,
    ! [A: $i] :
      ( ( A = aunt_agatha )
      | ( A = butler )
      | ( A = charles )
      | ( ( lives_at_dreadsbury @ someone )
       != ( lives_at_dreadsbury @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[18,25]) ).

thf(60,plain,
    ( ( someone = aunt_agatha )
    | ( butler = someone )
    | ( charles = someone ) ),
    inference(pattern_uni,[status(thm)],[59:[bind(A,$thf( someone ))]]) ).

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

thf(19,plain,
    killed @ someone @ aunt_agatha,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(8,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( killed @ A @ B )
      | ( hates @ A @ B ) ),
    file('/export/starexec/sandbox/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(27,plain,
    ! [B: $i,A: $i] :
      ( ~ ( killed @ A @ B )
      | ( hates @ A @ B ) ),
    inference(cnf,[status(esa)],[26]) ).

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(42,plain,
    aunt_agatha != butler,
    inference(polarity_switch,[status(thm)],[41]) ).

thf(43,plain,
    butler != aunt_agatha,
    inference(lifteq,[status(thm)],[42]) ).

thf(86,plain,
    ! [A: $i] :
      ( ( hates @ aunt_agatha @ A )
      | ( A != aunt_agatha )
      | ( butler != butler ) ),
    inference(paramod_ordered,[status(thm)],[34,43]) ).

thf(87,plain,
    ! [A: $i] :
      ( ( hates @ aunt_agatha @ A )
      | ( A != aunt_agatha ) ),
    inference(pattern_uni,[status(thm)],[86:[]]) ).

thf(99,plain,
    hates @ aunt_agatha @ aunt_agatha,
    inference(simp,[status(thm)],[87]) ).

thf(10,axiom,
    ! [A: $i] :
      ( ~ ( hates @ aunt_agatha @ A )
      | ~ ( hates @ charles @ A ) ),
    file('/export/starexec/sandbox/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(31,plain,
    ! [A: $i] :
      ( ~ ( hates @ aunt_agatha @ A )
      | ~ ( hates @ charles @ A ) ),
    inference(cnf,[status(esa)],[30]) ).

thf(135,plain,
    ! [A: $i] :
      ( ~ ( hates @ charles @ A )
      | ( ( hates @ aunt_agatha @ aunt_agatha )
       != ( hates @ aunt_agatha @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[99,31]) ).

thf(136,plain,
    ~ ( hates @ charles @ aunt_agatha ),
    inference(pattern_uni,[status(thm)],[135:[bind(A,$thf( aunt_agatha ))]]) ).

thf(184,plain,
    ! [B: $i,A: $i] :
      ( ~ ( killed @ A @ B )
      | ( ( hates @ A @ B )
       != ( hates @ charles @ aunt_agatha ) ) ),
    inference(paramod_ordered,[status(thm)],[27,136]) ).

thf(185,plain,
    ~ ( killed @ charles @ aunt_agatha ),
    inference(pattern_uni,[status(thm)],[184:[bind(A,$thf( charles )),bind(B,$thf( aunt_agatha ))]]) ).

thf(208,plain,
    ( ( killed @ charles @ aunt_agatha )
   != ( killed @ someone @ aunt_agatha ) ),
    inference(paramod_ordered,[status(thm)],[19,185]) ).

thf(209,plain,
    ( ( charles != someone )
    | ( aunt_agatha != aunt_agatha ) ),
    inference(simp,[status(thm)],[208]) ).

thf(210,plain,
    charles != someone,
    inference(simp,[status(thm)],[209]) ).

thf(1,negated_conjecture,
    ~ ( killed @ aunt_agatha @ aunt_agatha ),
    file('/export/starexec/sandbox/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(17,plain,
    ~ ( killed @ aunt_agatha @ aunt_agatha ),
    inference(polarity_switch,[status(thm)],[16]) ).

thf(44,plain,
    ( ( killed @ someone @ aunt_agatha )
   != ( killed @ aunt_agatha @ aunt_agatha ) ),
    inference(paramod_ordered,[status(thm)],[19,17]) ).

thf(45,plain,
    ( ( someone != aunt_agatha )
    | ( aunt_agatha != aunt_agatha ) ),
    inference(simp,[status(thm)],[44]) ).

thf(46,plain,
    someone != aunt_agatha,
    inference(simp,[status(thm)],[45]) ).

thf(268,plain,
    butler = someone,
    inference(simplifyReflect,[status(thm)],[60,210,46]) ).

thf(274,plain,
    ! [A: $i] :
      ( ( A = someone )
      | ( hates @ aunt_agatha @ A ) ),
    inference(rewrite,[status(thm)],[34,268]) ).

thf(13,axiom,
    ! [A: $i] :
      ( ~ ( hates @ aunt_agatha @ A )
      | ( hates @ butler @ A ) ),
    file('/export/starexec/sandbox/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(38,plain,
    ! [A: $i] :
      ( ~ ( hates @ aunt_agatha @ A )
      | ( hates @ butler @ A ) ),
    inference(cnf,[status(esa)],[37]) ).

thf(331,plain,
    ! [A: $i] :
      ( ~ ( hates @ aunt_agatha @ A )
      | ( hates @ someone @ A ) ),
    inference(rewrite,[status(thm)],[38,268]) ).

thf(14,axiom,
    ! [A: $i] :
      ~ ( hates @ A @ ( every_one_but @ A ) ),
    file('/export/starexec/sandbox/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(40,plain,
    ! [A: $i] :
      ~ ( hates @ A @ ( every_one_but @ A ) ),
    inference(polarity_switch,[status(thm)],[39]) ).

thf(337,plain,
    ! [B: $i,A: $i] :
      ( ~ ( hates @ aunt_agatha @ A )
      | ( ( hates @ someone @ A )
       != ( hates @ B @ ( every_one_but @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[331,40]) ).

thf(338,plain,
    ~ ( hates @ aunt_agatha @ ( every_one_but @ someone ) ),
    inference(pattern_uni,[status(thm)],[337:[bind(A,$thf( every_one_but @ someone )),bind(B,$thf( someone ))]]) ).

thf(484,plain,
    ! [A: $i] :
      ( ( A = someone )
      | ( ( hates @ aunt_agatha @ A )
       != ( hates @ aunt_agatha @ ( every_one_but @ someone ) ) ) ),
    inference(paramod_ordered,[status(thm)],[274,338]) ).

thf(485,plain,
    ( ( every_one_but @ someone )
    = someone ),
    inference(pattern_uni,[status(thm)],[484:[bind(A,$thf( every_one_but @ someone ))]]) ).

thf(12,axiom,
    ! [A: $i] :
      ( ( richer @ A @ aunt_agatha )
      | ( hates @ butler @ A ) ),
    file('/export/starexec/sandbox/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(36,plain,
    ! [A: $i] :
      ( ( richer @ A @ aunt_agatha )
      | ( hates @ butler @ A ) ),
    inference(cnf,[status(esa)],[35]) ).

thf(291,plain,
    ! [A: $i] :
      ( ( richer @ A @ aunt_agatha )
      | ( hates @ someone @ A ) ),
    inference(rewrite,[status(thm)],[36,268]) ).

thf(9,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( killed @ A @ B )
      | ~ ( richer @ A @ B ) ),
    file('/export/starexec/sandbox/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(29,plain,
    ! [B: $i,A: $i] :
      ( ~ ( killed @ A @ B )
      | ~ ( richer @ A @ B ) ),
    inference(cnf,[status(esa)],[28]) ).

thf(246,plain,
    ! [B: $i,A: $i] :
      ( ~ ( richer @ A @ B )
      | ( ( killed @ someone @ aunt_agatha )
       != ( killed @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[19,29]) ).

thf(247,plain,
    ~ ( richer @ someone @ aunt_agatha ),
    inference(pattern_uni,[status(thm)],[246:[bind(A,$thf( someone )),bind(B,$thf( aunt_agatha ))]]) ).

thf(292,plain,
    ! [A: $i] :
      ( ( hates @ someone @ A )
      | ( ( richer @ A @ aunt_agatha )
       != ( richer @ someone @ aunt_agatha ) ) ),
    inference(paramod_ordered,[status(thm)],[291,247]) ).

thf(293,plain,
    hates @ someone @ someone,
    inference(pattern_uni,[status(thm)],[292:[bind(A,$thf( someone ))]]) ).

thf(303,plain,
    ! [A: $i] :
      ( ( hates @ someone @ someone )
     != ( hates @ A @ ( every_one_but @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[293,40]) ).

thf(308,plain,
    ! [A: $i] :
      ( ( someone != A )
      | ( ( every_one_but @ A )
       != someone ) ),
    inference(simp,[status(thm)],[303]) ).

thf(313,plain,
    ( ( every_one_but @ someone )
   != someone ),
    inference(simp,[status(thm)],[308]) ).

thf(520,plain,
    $false,
    inference(simplifyReflect,[status(thm)],[485,313]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : PUZ001-2 : TPTP v8.2.0. Released v1.0.0.
% 0.03/0.14  % Command  : run_Leo-III %s %d
% 0.14/0.35  % Computer : n025.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 : Sat May 18 11:02:09 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 1.27/1.15  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.61/1.34  % [INFO] 	 Parsing done (188ms). 
% 1.61/1.35  % [INFO] 	 Running in sequential loop mode. 
% 2.32/1.81  % [INFO] 	 nitpick registered as external prover. 
% 2.37/1.82  % [INFO] 	 Scanning for conjecture ... 
% 2.57/1.92  % [INFO] 	 Found a conjecture (or negated_conjecture) and 14 axioms. Running axiom selection ... 
% 2.57/1.96  % [INFO] 	 Axiom selection finished. Selected 14 axioms (removed 0 axioms). 
% 2.57/1.98  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 2.74/1.99  % [INFO] 	 Type checking passed. 
% 2.74/1.99  % [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 ... 
% 9.84/3.73  % [INFO] 	 Killing All external provers ... 
% 9.84/3.73  % Time passed: 3195ms (effective reasoning time: 2370ms)
% 9.84/3.74  % Axioms used in derivation (11): butler_hates_poor_people, charles_and_agatha_hate_different_people, noone_else_lives_at_mansion, butler_and_agatha_hate_the_same_people, killer_hates_victim, agatha_is_not_the_butler, killer_poorer_than_victim, agatha_likes_only_butler, someone_killed_agatha, someone_in_mansion, noone_hates_everyone
% 9.84/3.74  % No. of inferences in proof: 68
% 9.84/3.74  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 3195 ms resp. 2370 ms w/o parsing
% 9.84/3.81  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.84/3.81  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------