TSTP Solution File: PLA053_2 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : PLA053_2 : 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 02:19:56 EDT 2024

% Result   : Theorem 3.30s 1.84s
% Output   : Refutation 3.30s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   23 (   7 unt;   7 typ;   0 def)
%            Number of atoms       :   59 (   0 equ;   0 cnn)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives :  161 (   2   ~;   0   |;  16   &; 116   @)
%                                         (   0 <=>;  27  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   8 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   10 (  10   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :   39 (   0   ^  28   !;  11   ?;  39   :)

% 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(h_type,type,
    h: '\'$ki_world\'' > $i > $o ).

thf(bomb_type,type,
    bomb: '\'$ki_world\'' > $i > $o ).

thf(defused_type,type,
    defused: '\'$ki_world\'' > $i > $o ).

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

thf(7,axiom,
    ? [A: $i] :
      ( ( '\'$ki_exists_in_world_$i\'' @ '\'$ki_local_world\'' @ A )
      & ! [B: '\'$ki_world\''] :
          ( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ B )
         => ! [C: $i] :
              ( ( '\'$ki_exists_in_world_$i\'' @ B @ C )
             => ( ( ( bomb @ B @ C )
                  & ( h @ B @ A ) )
               => ! [D: '\'$ki_world\''] :
                    ( ( '\'$ki_accessible\'' @ B @ D )
                   => ( bomb @ D @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).

thf(24,plain,
    ? [A: $i] :
      ( ( '\'$ki_exists_in_world_$i\'' @ '\'$ki_local_world\'' @ A )
      & ! [B: '\'$ki_world\''] :
          ( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ B )
         => ! [C: $i] :
              ( ( '\'$ki_exists_in_world_$i\'' @ B @ C )
             => ( ( ( bomb @ B @ C )
                  & ( h @ B @ A ) )
               => ! [D: '\'$ki_world\''] :
                    ( ( '\'$ki_accessible\'' @ B @ D )
                   => ( bomb @ D @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(6,axiom,
    ! [A: '\'$ki_world\''] :
      ( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
     => ? [B: $i] :
          ( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
          & ( bomb @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).

thf(21,plain,
    ! [A: '\'$ki_world\''] :
      ( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
     => ? [B: $i] :
          ( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
          & ( bomb @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

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 )
              & ( ( ( bomb @ A @ B )
                  & ( h @ A @ C ) )
               => ( defused @ A @ B ) ) ) ) ),
    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 )
                & ( ( ( bomb @ A @ B )
                    & ( h @ A @ C ) )
                 => ( defused @ A @ B ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(9,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 )
                & ( ( ( bomb @ A @ B )
                    & ( h @ A @ C ) )
                 => ( defused @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,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(17,plain,
    ! [A: '\'$ki_world\'',B: $i] : ( '\'$ki_exists_in_world_$i\'' @ A @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(8,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_$i\'' @ A @ C )
              & ! [D: '\'$ki_world\''] :
                  ( ( '\'$ki_accessible\'' @ A @ D )
                 => ( ( ( bomb @ D @ B )
                      & ( h @ D @ C ) )
                   => ( defused @ D @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).

thf(27,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_$i\'' @ A @ C )
              & ! [D: '\'$ki_world\''] :
                  ( ( '\'$ki_accessible\'' @ A @ D )
                 => ( ( ( bomb @ D @ B )
                      & ( h @ D @ C ) )
                   => ( defused @ D @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

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_nonempty') ).

thf(19,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(15,plain,
    ! [A: '\'$ki_world\''] : ( '\'$ki_accessible\'' @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(30,plain,
    $false,
    inference(e,[status(thm)],[24,21,9,17,27,19,15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : PLA053_2 : TPTP v8.2.0. Released v8.2.0.
% 0.12/0.16  % Command  : run_Leo-III %s %d
% 0.17/0.37  % Computer : n002.cluster.edu
% 0.17/0.37  % Model    : x86_64 x86_64
% 0.17/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37  % Memory   : 8042.1875MB
% 0.17/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37  % CPULimit : 300
% 0.17/0.37  % WCLimit  : 300
% 0.17/0.37  % DateTime : Sat May 18 13:44:24 EDT 2024
% 0.17/0.37  % CPUTime  : 
% 0.98/0.91  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.29/1.02  % [INFO] 	 Parsing done (115ms). 
% 1.29/1.03  % [INFO] 	 Running in sequential loop mode. 
% 1.83/1.31  % [INFO] 	 eprover registered as external prover. 
% 1.83/1.31  % [INFO] 	 cvc4 registered as external prover. 
% 1.83/1.32  % [INFO] 	 Scanning for conjecture ... 
% 1.97/1.39  % [INFO] 	 Found a conjecture (or negated_conjecture) and 6 axioms. Running axiom selection ... 
% 1.97/1.42  % [INFO] 	 Axiom selection finished. Selected 6 axioms (removed 0 axioms). 
% 1.97/1.44  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 1.97/1.44  % [INFO] 	 Type checking passed. 
% 1.97/1.44  % [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 ... 
% 3.30/1.83  % External prover 'e' found a proof!
% 3.30/1.83  % [INFO] 	 Killing All external provers ... 
% 3.30/1.83  % Time passed: 1294ms (effective reasoning time: 799ms)
% 3.30/1.83  % 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)>
% 3.30/1.84  % Axioms used in derivation (6): $ki_exists_in_world_$i_nonempty, mrel_reflexive, ax1, ax2, $ki_exists_in_world_$i_const, ax3
% 3.30/1.84  % No. of inferences in proof: 16
% 3.30/1.84  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1294 ms resp. 799 ms w/o parsing
% 3.30/1.87  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.30/1.87  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------