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

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%------------------------------------------------------------------------------
% File     : Leo-III---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 : n007.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 00:59:27 EDT 2024

% Result   : Theorem 4.02s 2.43s
% Output   : Refutation 4.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   30 (   9 unt;  10 typ;   0 def)
%            Number of atoms       :   60 (   0 equ;   0 cnn)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  206 (   8   ~;   0   |;   4   &; 158   @)
%                                         (   0 <=>;  36  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   8 avg)
%            Number of types       :    4 (   2 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   8 usr;   7 con; 0-3 aty)
%            Number of variables   :   48 (   0   ^  48   !;   0   ?;  48   :)

% 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('\'#idx(i_bob)\'_type',type,
    '\'#idx(i_bob)\'': '\'$ki_index\'' ).

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

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

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

thf(4,axiom,
    ! [A: '\'$ki_world\'',B: '\'$ki_world\''] : ( '\'$ki_accessible\'' @ '\'#idx(b_bob)\'' @ A @ B ),
    file('/export/starexec/sandbox2/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(8,axiom,
    ! [A: '\'$ki_world\''] :
      ( ( '\'$ki_accessible\'' @ '\'#idx(b_bob)\'' @ '\'$ki_local_world\'' @ A )
     => ( ( ( bigcity @ A @ portland )
          & ! [B: '\'$ki_world\''] :
              ( ( '\'$ki_accessible\'' @ '\'#idx(b_bob)\'' @ A @ B )
             => ! [C: '\'$ki_world\''] :
                  ( ( '\'$ki_accessible\'' @ '\'#idx(b_alice)\'' @ B @ C )
                 => ~ ( bigcity @ C @ portland ) ) ) )
       => ! [B: '\'$ki_world\''] :
            ( ( '\'$ki_accessible\'' @ '\'#idx(i_bob)\'' @ A @ B )
           => ! [C: '\'$ki_world\''] :
                ( ( '\'$ki_accessible\'' @ '\'#idx(b_alice)\'' @ B @ C )
               => ( bigcity @ C @ portland ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_bob) ).

thf(27,plain,
    ! [A: '\'$ki_world\''] :
      ( ( '\'$ki_accessible\'' @ '\'#idx(b_bob)\'' @ '\'$ki_local_world\'' @ A )
     => ( ( ( bigcity @ A @ portland )
          & ! [B: '\'$ki_world\''] :
              ( ( '\'$ki_accessible\'' @ '\'#idx(b_bob)\'' @ A @ B )
             => ! [C: '\'$ki_world\''] :
                  ( ( '\'$ki_accessible\'' @ '\'#idx(b_alice)\'' @ B @ C )
                 => ~ ( bigcity @ C @ portland ) ) ) )
       => ! [B: '\'$ki_world\''] :
            ( ( '\'$ki_accessible\'' @ '\'#idx(i_bob)\'' @ A @ B )
           => ! [C: '\'$ki_world\''] :
                ( ( '\'$ki_accessible\'' @ '\'#idx(b_alice)\'' @ B @ C )
               => ( bigcity @ C @ portland ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(9,axiom,
    ! [A: '\'$ki_world\''] :
      ( ( '\'$ki_accessible\'' @ '\'#idx(b_alice)\'' @ '\'$ki_local_world\'' @ A )
     => ( bigcity @ A @ portland ) ),
    file('/export/starexec/sandbox2/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(1,conjecture,
    ! [A: '\'$ki_world\''] :
      ( ( '\'$ki_accessible\'' @ '\'#idx(i_alice)\'' @ '\'$ki_local_world\'' @ A )
     => ! [B: '\'$ki_world\''] :
          ( ( '\'$ki_accessible\'' @ '\'#idx(b_bob)\'' @ A @ B )
         => ( bigcity @ B @ portland ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).

thf(2,negated_conjecture,
    ~ ! [A: '\'$ki_world\''] :
        ( ( '\'$ki_accessible\'' @ '\'#idx(i_alice)\'' @ '\'$ki_local_world\'' @ A )
       => ! [B: '\'$ki_world\''] :
            ( ( '\'$ki_accessible\'' @ '\'#idx(b_bob)\'' @ A @ B )
           => ( bigcity @ B @ portland ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(11,plain,
    ~ ! [A: '\'$ki_world\''] :
        ( ( '\'$ki_accessible\'' @ '\'#idx(i_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)],[2]) ).

thf(7,axiom,
    ! [A: '\'$ki_world\''] :
      ( ( '\'$ki_accessible\'' @ '\'#idx(b_alice)\'' @ '\'$ki_local_world\'' @ A )
     => ( ( ( bigcity @ A @ portland )
          & ! [B: '\'$ki_world\''] :
              ( ( '\'$ki_accessible\'' @ '\'#idx(b_alice)\'' @ A @ B )
             => ! [C: '\'$ki_world\''] :
                  ( ( '\'$ki_accessible\'' @ '\'#idx(b_bob)\'' @ B @ C )
                 => ~ ( bigcity @ C @ portland ) ) ) )
       => ! [B: '\'$ki_world\''] :
            ( ( '\'$ki_accessible\'' @ '\'#idx(i_alice)\'' @ A @ B )
           => ! [C: '\'$ki_world\''] :
                ( ( '\'$ki_accessible\'' @ '\'#idx(b_bob)\'' @ B @ C )
               => ( bigcity @ C @ portland ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_alice) ).

thf(23,plain,
    ! [A: '\'$ki_world\''] :
      ( ( '\'$ki_accessible\'' @ '\'#idx(b_alice)\'' @ '\'$ki_local_world\'' @ A )
     => ( ( ( bigcity @ A @ portland )
          & ! [B: '\'$ki_world\''] :
              ( ( '\'$ki_accessible\'' @ '\'#idx(b_alice)\'' @ A @ B )
             => ! [C: '\'$ki_world\''] :
                  ( ( '\'$ki_accessible\'' @ '\'#idx(b_bob)\'' @ B @ C )
                 => ~ ( bigcity @ C @ portland ) ) ) )
       => ! [B: '\'$ki_world\''] :
            ( ( '\'$ki_accessible\'' @ '\'#idx(i_alice)\'' @ A @ B )
           => ! [C: '\'$ki_world\''] :
                ( ( '\'$ki_accessible\'' @ '\'#idx(b_bob)\'' @ B @ C )
               => ( bigcity @ C @ portland ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(5,axiom,
    ! [A: '\'$ki_world\'',B: '\'$ki_world\''] : ( '\'$ki_accessible\'' @ '\'#idx(i_bob)\'' @ A @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_universal_#idx(i_bob)') ).

thf(19,plain,
    ! [A: '\'$ki_world\'',B: '\'$ki_world\''] : ( '\'$ki_accessible\'' @ '\'#idx(i_bob)\'' @ A @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(3,axiom,
    ! [A: '\'$ki_world\'',B: '\'$ki_world\''] : ( '\'$ki_accessible\'' @ '\'#idx(b_alice)\'' @ A @ B ),
    file('/export/starexec/sandbox2/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(6,axiom,
    ! [A: '\'$ki_world\'',B: '\'$ki_world\''] : ( '\'$ki_accessible\'' @ '\'#idx(i_alice)\'' @ A @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_universal_#idx(i_alice)') ).

thf(21,plain,
    ! [A: '\'$ki_world\'',B: '\'$ki_world\''] : ( '\'$ki_accessible\'' @ '\'#idx(i_alice)\'' @ A @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

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/sandbox2/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(35,plain,
    $false,
    inference(e,[status(thm)],[17,27,31,11,23,19,15,21,33]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.16  % Problem  : NLP265_17 : TPTP v8.2.0. Released v8.2.0.
% 0.16/0.20  % Command  : run_Leo-III %s %d
% 0.20/0.43  % Computer : n007.cluster.edu
% 0.20/0.43  % Model    : x86_64 x86_64
% 0.20/0.43  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.43  % Memory   : 8042.1875MB
% 0.20/0.43  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.20/0.43  % CPULimit : 300
% 0.20/0.43  % WCLimit  : 300
% 0.20/0.43  % DateTime : Sun May 19 22:45:39 EDT 2024
% 0.20/0.43  % CPUTime  : 
% 1.27/1.10  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.60/1.29  % [INFO] 	 Parsing done (187ms). 
% 1.60/1.31  % [INFO] 	 Running in sequential loop mode. 
% 2.46/1.79  % [INFO] 	 eprover registered as external prover. 
% 2.46/1.79  % [INFO] 	 cvc4 registered as external prover. 
% 2.46/1.80  % [INFO] 	 Scanning for conjecture ... 
% 2.63/1.88  % [INFO] 	 Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ... 
% 2.79/1.92  % [INFO] 	 Axiom selection finished. Selected 8 axioms (removed 0 axioms). 
% 2.79/1.95  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 2.92/1.96  % [INFO] 	 Type checking passed. 
% 2.92/1.96  % [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 ... 
% 4.02/2.42  % External prover 'e' found a proof!
% 4.02/2.42  % [INFO] 	 Killing All external provers ... 
% 4.02/2.43  % Time passed: 1802ms (effective reasoning time: 1107ms)
% 4.02/2.43  % Solved by 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)>
% 4.02/2.43  % Axioms used in derivation (8): axiom_2, axiom_3, axiom_1_bob, mrel_universal_#idx(b_alice), axiom_1_alice, mrel_universal_#idx(i_alice), mrel_universal_#idx(b_bob), mrel_universal_#idx(i_bob)
% 4.02/2.43  % No. of inferences in proof: 20
% 4.02/2.43  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1802 ms resp. 1107 ms w/o parsing
% 4.15/2.47  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.15/2.47  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------