TSTP Solution File: NLP265_17 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : NLP265_17 : TPTP v8.2.0. Released v8.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n002.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 01:00:35 EDT 2024

% Result   : ContradictoryAxioms 3.76s 2.18s
% Output   : Refutation 3.76s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   27 (   9 unt;   8 typ;   0 def)
%            Number of atoms       :   33 (   0 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  103 (  16   ~;   8   |;   0   &;  73   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   6 avg)
%            Number of types       :    4 (   2 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   6 usr;   6 con; 0-3 aty)
%            Number of variables   :   28 (   0   ^  28   !;   0   ?;  28   :)

% Comments : 
%------------------------------------------------------------------------------
thf('\'$ki_world\'_type',type,
    '\'$ki_world\'': $tType ).

thf('\'$ki_local_world\'_type',type,
    '\'$ki_local_world\'': '\'$ki_world\'' ).

thf('\'$ki_index\'_type',type,
    '\'$ki_index\'': $tType ).

thf('\'$ki_accessible\'_type',type,
    '\'$ki_accessible\'': '\'$ki_index\'' > '\'$ki_world\'' > '\'$ki_world\'' > $o ).

thf('\'#idx(b_alice)\'_type',type,
    '\'#idx(b_alice)\'': '\'$ki_index\'' ).

thf('\'#idx(b_bob)\'_type',type,
    '\'#idx(b_bob)\'': '\'$ki_index\'' ).

thf(portland_type,type,
    portland: $i ).

thf(bigcity_type,type,
    bigcity: '\'$ki_world\'' > $i > $o ).

thf(9,axiom,
    ! [A: '\'$ki_world\''] :
      ( ( '\'$ki_accessible\'' @ '\'#idx(b_alice)\'' @ '\'$ki_local_world\'' @ A )
     => ( bigcity @ A @ portland ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).

thf(31,plain,
    ! [A: '\'$ki_world\''] :
      ( ( '\'$ki_accessible\'' @ '\'#idx(b_alice)\'' @ '\'$ki_local_world\'' @ A )
     => ( bigcity @ A @ portland ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(32,plain,
    ! [A: '\'$ki_world\''] :
      ( ~ ( '\'$ki_accessible\'' @ '\'#idx(b_alice)\'' @ '\'$ki_local_world\'' @ A )
      | ( bigcity @ A @ portland ) ),
    inference(cnf,[status(esa)],[31]) ).

thf(3,axiom,
    ! [A: '\'$ki_world\'',B: '\'$ki_world\''] : ( '\'$ki_accessible\'' @ '\'#idx(b_alice)\'' @ A @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','mrel_universal_#idx(b_alice)') ).

thf(15,plain,
    ! [A: '\'$ki_world\'',B: '\'$ki_world\''] : ( '\'$ki_accessible\'' @ '\'#idx(b_alice)\'' @ A @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(16,plain,
    ! [B: '\'$ki_world\'',A: '\'$ki_world\''] : ( '\'$ki_accessible\'' @ '\'#idx(b_alice)\'' @ A @ B ),
    inference(cnf,[status(esa)],[15]) ).

thf(10,axiom,
    ! [A: '\'$ki_world\''] :
      ( ( '\'$ki_accessible\'' @ '\'#idx(b_alice)\'' @ '\'$ki_local_world\'' @ A )
     => ! [B: '\'$ki_world\''] :
          ( ( '\'$ki_accessible\'' @ '\'#idx(b_bob)\'' @ A @ B )
         => ~ ( bigcity @ B @ portland ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).

thf(33,plain,
    ! [A: '\'$ki_world\''] :
      ( ( '\'$ki_accessible\'' @ '\'#idx(b_alice)\'' @ '\'$ki_local_world\'' @ A )
     => ! [B: '\'$ki_world\''] :
          ( ( '\'$ki_accessible\'' @ '\'#idx(b_bob)\'' @ A @ B )
         => ~ ( bigcity @ B @ portland ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(34,plain,
    ! [B: '\'$ki_world\'',A: '\'$ki_world\''] :
      ( ~ ( '\'$ki_accessible\'' @ '\'#idx(b_alice)\'' @ '\'$ki_local_world\'' @ A )
      | ~ ( '\'$ki_accessible\'' @ '\'#idx(b_bob)\'' @ A @ B )
      | ~ ( bigcity @ B @ portland ) ),
    inference(cnf,[status(esa)],[33]) ).

thf(35,plain,
    ! [B: '\'$ki_world\'',A: '\'$ki_world\''] :
      ( ~ $true
      | ~ ( '\'$ki_accessible\'' @ '\'#idx(b_bob)\'' @ A @ B )
      | ~ ( bigcity @ B @ portland ) ),
    inference(rewrite,[status(thm)],[34,16]) ).

thf(36,plain,
    ! [B: '\'$ki_world\'',A: '\'$ki_world\''] :
      ( ~ ( '\'$ki_accessible\'' @ '\'#idx(b_bob)\'' @ A @ B )
      | ~ ( bigcity @ B @ portland ) ),
    inference(simp,[status(thm)],[35]) ).

thf(4,axiom,
    ! [A: '\'$ki_world\'',B: '\'$ki_world\''] : ( '\'$ki_accessible\'' @ '\'#idx(b_bob)\'' @ A @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','mrel_universal_#idx(b_bob)') ).

thf(17,plain,
    ! [A: '\'$ki_world\'',B: '\'$ki_world\''] : ( '\'$ki_accessible\'' @ '\'#idx(b_bob)\'' @ A @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(18,plain,
    ! [B: '\'$ki_world\'',A: '\'$ki_world\''] : ( '\'$ki_accessible\'' @ '\'#idx(b_bob)\'' @ A @ B ),
    inference(cnf,[status(esa)],[17]) ).

thf(46,plain,
    ! [A: '\'$ki_world\''] :
      ( ~ $true
      | ~ ( bigcity @ A @ portland ) ),
    inference(rewrite,[status(thm)],[36,18]) ).

thf(47,plain,
    ! [A: '\'$ki_world\''] :
      ~ ( bigcity @ A @ portland ),
    inference(simp,[status(thm)],[46]) ).

thf(48,plain,
    ! [A: '\'$ki_world\''] :
      ~ ( bigcity @ A @ portland ),
    inference(simp,[status(thm)],[47]) ).

thf(52,plain,
    ( ~ $true
    | $false ),
    inference(rewrite,[status(thm)],[32,16,48]) ).

thf(53,plain,
    $false,
    inference(simp,[status(thm)],[52]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.16  % Problem  : NLP265_17 : TPTP v8.2.0. Released v8.2.0.
% 0.20/0.20  % Command  : run_Leo-III %s %d
% 0.21/0.43  % Computer : n002.cluster.edu
% 0.21/0.43  % Model    : x86_64 x86_64
% 0.21/0.43  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.43  % Memory   : 8042.1875MB
% 0.21/0.43  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.21/0.43  % CPULimit : 300
% 0.21/0.43  % WCLimit  : 300
% 0.21/0.43  % DateTime : Sun May 19 22:45:39 EDT 2024
% 0.21/0.43  % CPUTime  : 
% 1.07/1.00  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.31/1.17  % [INFO] 	 Parsing done (166ms). 
% 1.54/1.18  % [INFO] 	 Running in sequential loop mode. 
% 1.91/1.43  % [INFO] 	 nitpick registered as external prover. 
% 1.91/1.44  % [INFO] 	 Scanning for conjecture ... 
% 2.08/1.52  % [INFO] 	 Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ... 
% 2.08/1.55  % [INFO] 	 Axiom selection finished. Selected 8 axioms (removed 0 axioms). 
% 2.33/1.58  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 2.33/1.58  % [INFO] 	 Type checking passed. 
% 2.33/1.59  % [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 ... 
% 3.63/2.17  % [INFO] 	 Killing All external provers ... 
% 3.76/2.18  % Time passed: 1577ms (effective reasoning time: 991ms)
% 3.76/2.18  % Axioms used in derivation (4): axiom_2, mrel_universal_#idx(b_alice), axiom_3, mrel_universal_#idx(b_bob)
% 3.76/2.18  % No. of inferences in proof: 19
% 3.76/2.18  % SZS status ContradictoryAxioms for /export/starexec/sandbox/benchmark/theBenchmark.p : 1577 ms resp. 991 ms w/o parsing
% 3.76/2.21  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.76/2.21  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------