TSTP Solution File: NLP266_4 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : NLP266_4 : TPTP v8.2.0. Released v8.2.0.
% 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 00:59:28 EDT 2024

% Result   : Theorem 3.82s 2.38s
% Output   : Refutation 4.37s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   30 (   7 unt;  12 typ;   0 def)
%            Number of atoms       :   92 (   0 equ;   0 cnn)
%            Maximal formula atoms :   13 (   5 avg)
%            Number of connectives :  288 (   2   ~;   0   |;  35   &; 212   @)
%                                         (   0 <=>;  39  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (  11 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   22 (  22   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (  11 usr;   4 con; 0-4 aty)
%            Number of variables   :   64 (   0   ^  44   !;  20   ?;  64   :)

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

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

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

thf(u_type,type,
    u: $i ).

thf(one_type,type,
    one: $i ).

thf(number_type,type,
    number: '\'$ki_world\'' > $i > $i > $o ).

thf(string_type,type,
    string: '\'$ki_world\'' > $i > $o ).

thf(in_type,type,
    in: '\'$ki_world\'' > $i > $i > $i > $o ).

thf(do_type,type,
    do: '\'$ki_world\'' > $i > $i > $i > $o ).

thf(entry_box_type,type,
    entry_box: '\'$ki_world\'' > $i > $o ).

thf(userid_type,type,
    userid: '\'$ki_world\'' > $i > $i > $o ).

thf('\'$ki_exists_in_world_$i\'_type',type,
    '\'$ki_exists_in_world_$i\'': '\'$ki_world\'' > $i > $o ).

thf(1,conjecture,
    ! [A: '\'$ki_world\''] :
      ( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
     => ? [B: $i] :
          ( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
          & ? [C: $i] :
              ( ( '\'$ki_exists_in_world_$i\'' @ A @ C )
              & ? [D: $i] :
                  ( ( '\'$ki_exists_in_world_$i\'' @ A @ D )
                  & ? [E: $i] :
                      ( ( '\'$ki_exists_in_world_$i\'' @ A @ E )
                      & ! [F: '\'$ki_world\''] :
                          ( ( '\'$ki_accessible\'' @ A @ F )
                         => ( ( userid @ F @ u @ B )
                            & ( entry_box @ F @ C )
                            & ( number @ F @ C @ one ) ) )
                      & ! [F: '\'$ki_world\''] :
                          ( ( '\'$ki_accessible\'' @ A @ F )
                         => ! [G: $i] :
                              ( ( '\'$ki_exists_in_world_$i\'' @ F @ G )
                             => ( ( do @ F @ E @ D @ G )
                               => ( in @ F @ B @ C @ G ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).

thf(2,negated_conjecture,
    ~ ! [A: '\'$ki_world\''] :
        ( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
       => ? [B: $i] :
            ( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
            & ? [C: $i] :
                ( ( '\'$ki_exists_in_world_$i\'' @ A @ C )
                & ? [D: $i] :
                    ( ( '\'$ki_exists_in_world_$i\'' @ A @ D )
                    & ? [E: $i] :
                        ( ( '\'$ki_exists_in_world_$i\'' @ A @ E )
                        & ! [F: '\'$ki_world\''] :
                            ( ( '\'$ki_accessible\'' @ A @ F )
                           => ( ( userid @ F @ u @ B )
                              & ( entry_box @ F @ C )
                              & ( number @ F @ C @ one ) ) )
                        & ! [F: '\'$ki_world\''] :
                            ( ( '\'$ki_accessible\'' @ A @ F )
                           => ! [G: $i] :
                                ( ( '\'$ki_exists_in_world_$i\'' @ F @ G )
                               => ( ( do @ F @ E @ D @ G )
                                 => ( in @ F @ B @ C @ G ) ) ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(10,plain,
    ~ ! [A: '\'$ki_world\''] :
        ( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
       => ? [B: $i] :
            ( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
            & ? [C: $i] :
                ( ( '\'$ki_exists_in_world_$i\'' @ A @ C )
                & ? [D: $i] :
                    ( ( '\'$ki_exists_in_world_$i\'' @ A @ D )
                    & ? [E: $i] :
                        ( ( '\'$ki_exists_in_world_$i\'' @ A @ E )
                        & ! [F: '\'$ki_world\''] :
                            ( ( '\'$ki_accessible\'' @ A @ F )
                           => ( ( userid @ F @ u @ B )
                              & ( entry_box @ F @ C )
                              & ( number @ F @ C @ one ) ) )
                        & ! [F: '\'$ki_world\''] :
                            ( ( '\'$ki_accessible\'' @ A @ F )
                           => ! [G: $i] :
                                ( ( '\'$ki_exists_in_world_$i\'' @ F @ G )
                               => ( ( do @ F @ E @ D @ G )
                                 => ( in @ F @ B @ C @ G ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(6,axiom,
    ! [A: '\'$ki_world\''] :
    ? [B: $i] : ( '\'$ki_exists_in_world_$i\'' @ A @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$ki_exists_in_world_$i_nonempty') ).

thf(24,plain,
    ! [A: '\'$ki_world\''] :
    ? [B: $i] : ( '\'$ki_exists_in_world_$i\'' @ A @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(4,axiom,
    ! [A: '\'$ki_world\'',B: '\'$ki_world\'',C: '\'$ki_world\''] :
      ( ( ( '\'$ki_accessible\'' @ A @ B )
        & ( '\'$ki_accessible\'' @ B @ C ) )
     => ( '\'$ki_accessible\'' @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_transitive) ).

thf(20,plain,
    ! [A: '\'$ki_world\'',B: '\'$ki_world\'',C: '\'$ki_world\''] :
      ( ( ( '\'$ki_accessible\'' @ A @ B )
        & ( '\'$ki_accessible\'' @ B @ C ) )
     => ( '\'$ki_accessible\'' @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(9,axiom,
    ! [A: '\'$ki_world\''] :
      ( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
     => ! [B: $i] :
          ( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
         => ! [C: $i] :
              ( ( '\'$ki_exists_in_world_$i\'' @ A @ C )
             => ! [D: $i] :
                  ( ( '\'$ki_exists_in_world_$i\'' @ A @ D )
                 => ( ( ( string @ A @ C )
                      & ( entry_box @ A @ D ) )
                   => ? [E: $i] :
                        ( ( '\'$ki_exists_in_world_$i\'' @ A @ E )
                        & ! [F: '\'$ki_world\''] :
                            ( ( '\'$ki_accessible\'' @ A @ F )
                           => ! [G: $i] :
                                ( ( '\'$ki_exists_in_world_$i\'' @ F @ G )
                               => ( ( do @ F @ B @ E @ G )
                                 => ( in @ F @ C @ D @ G ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).

thf(34,plain,
    ! [A: '\'$ki_world\''] :
      ( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
     => ! [B: $i] :
          ( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
         => ! [C: $i] :
              ( ( '\'$ki_exists_in_world_$i\'' @ A @ C )
             => ! [D: $i] :
                  ( ( '\'$ki_exists_in_world_$i\'' @ A @ D )
                 => ( ( ( string @ A @ C )
                      & ( entry_box @ A @ D ) )
                   => ? [E: $i] :
                        ( ( '\'$ki_exists_in_world_$i\'' @ A @ E )
                        & ! [F: '\'$ki_world\''] :
                            ( ( '\'$ki_accessible\'' @ A @ F )
                           => ! [G: $i] :
                                ( ( '\'$ki_exists_in_world_$i\'' @ F @ G )
                               => ( ( do @ F @ B @ E @ G )
                                 => ( in @ F @ C @ D @ G ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(5,axiom,
    ! [A: '\'$ki_world\'',B: $i] : ( '\'$ki_exists_in_world_$i\'' @ A @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$ki_exists_in_world_$i_const') ).

thf(22,plain,
    ! [A: '\'$ki_world\'',B: $i] : ( '\'$ki_exists_in_world_$i\'' @ A @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(3,axiom,
    ! [A: '\'$ki_world\''] : ( '\'$ki_accessible\'' @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).

thf(18,plain,
    ! [A: '\'$ki_world\''] : ( '\'$ki_accessible\'' @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(7,axiom,
    ! [A: '\'$ki_world\''] :
      ( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
     => ? [B: $i] :
          ( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
          & ! [C: '\'$ki_world\''] :
              ( ( '\'$ki_accessible\'' @ A @ C )
             => ( ( userid @ C @ u @ B )
                & ( string @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).

thf(26,plain,
    ! [A: '\'$ki_world\''] :
      ( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
     => ? [B: $i] :
          ( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
          & ! [C: '\'$ki_world\''] :
              ( ( '\'$ki_accessible\'' @ A @ C )
             => ( ( userid @ C @ u @ B )
                & ( string @ C @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(8,axiom,
    ? [A: $i] :
      ( ( '\'$ki_exists_in_world_$i\'' @ '\'$ki_local_world\'' @ A )
      & ! [B: '\'$ki_world\''] :
          ( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ B )
         => ( ( entry_box @ B @ A )
            & ( number @ B @ A @ one ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).

thf(30,plain,
    ? [A: $i] :
      ( ( '\'$ki_exists_in_world_$i\'' @ '\'$ki_local_world\'' @ A )
      & ! [B: '\'$ki_world\''] :
          ( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ B )
         => ( ( entry_box @ B @ A )
            & ( number @ B @ A @ one ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(37,plain,
    $false,
    inference(e,[status(thm)],[10,24,20,34,22,18,26,30]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.09  % Problem  : NLP266_4 : TPTP v8.2.0. Released v8.2.0.
% 0.10/0.12  % Command  : run_Leo-III %s %d
% 0.11/0.32  % Computer : n026.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Sun May 19 22:35:09 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 1.00/0.96  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.30/1.14  % [INFO] 	 Parsing done (182ms). 
% 1.30/1.16  % [INFO] 	 Running in sequential loop mode. 
% 2.05/1.53  % [INFO] 	 eprover registered as external prover. 
% 2.05/1.54  % [INFO] 	 cvc4 registered as external prover. 
% 2.05/1.54  % [INFO] 	 Scanning for conjecture ... 
% 2.23/1.67  % [INFO] 	 Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ... 
% 2.41/1.71  % [INFO] 	 Axiom selection finished. Selected 7 axioms (removed 0 axioms). 
% 2.41/1.74  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 2.41/1.75  % [INFO] 	 Type checking passed. 
% 2.41/1.75  % [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 ... 
% 3.82/2.38  % External prover 'e' found a proof!
% 3.82/2.38  % [INFO] 	 Killing All external provers ... 
% 3.82/2.38  % Time passed: 1910ms (effective reasoning time: 1220ms)
% 3.82/2.38  % 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)>
% 3.82/2.38  % Axioms used in derivation (7): $ki_exists_in_world_$i_nonempty, mrel_reflexive, ax1, ax2, mrel_transitive, $ki_exists_in_world_$i_const, ax3
% 3.82/2.38  % No. of inferences in proof: 18
% 3.82/2.38  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1910 ms resp. 1220 ms w/o parsing
% 4.37/2.52  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.37/2.52  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------