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

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---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 : n012.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 02:20:10 EDT 2024

% Result   : Theorem 5.63s 2.49s
% Output   : Refutation 5.63s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   43 (  14 unt;  10 typ;   0 def)
%            Number of atoms       :   98 (   3 equ;   0 cnn)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  289 (  44   ~;  32   |;  10   &; 186   @)
%                                         (   0 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   7 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   12 (  12   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (   9 usr;   5 con; 0-2 aty)
%            Number of variables   :   48 (   0   ^  43   !;   5   ?;  48   :)

% 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(sk1_type,type,
    sk1: '\'$ki_world\'' ).

thf(sk2_type,type,
    sk2: $i ).

thf(sk6_type,type,
    sk6: $i > '\'$ki_world\'' > $i ).

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/sandbox/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(11,plain,
    '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ sk1,
    inference(cnf,[status(esa)],[9]) ).

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/sandbox/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(28,plain,
    ! [C: '\'$ki_world\'',B: $i,A: '\'$ki_world\''] :
      ( ~ ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
      | ~ ( '\'$ki_exists_in_world_$i\'' @ A @ B )
      | ~ ( '\'$ki_accessible\'' @ A @ C )
      | ~ ( bomb @ C @ B )
      | ~ ( h @ C @ ( sk6 @ B @ A ) )
      | ( defused @ C @ B ) ),
    inference(cnf,[status(esa)],[27]) ).

thf(4,axiom,
    ! [A: '\'$ki_world\'',B: $i] : ( '\'$ki_exists_in_world_$i\'' @ A @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$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(18,plain,
    ! [B: $i,A: '\'$ki_world\''] : ( '\'$ki_exists_in_world_$i\'' @ A @ B ),
    inference(cnf,[status(esa)],[17]) ).

thf(162,plain,
    ! [C: '\'$ki_world\'',B: $i,A: '\'$ki_world\''] :
      ( ~ ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
      | ~ $true
      | ~ ( '\'$ki_accessible\'' @ A @ C )
      | ~ ( bomb @ C @ B )
      | ~ ( h @ C @ ( sk6 @ B @ A ) )
      | ( defused @ C @ B ) ),
    inference(rewrite,[status(thm)],[28,18]) ).

thf(163,plain,
    ! [C: '\'$ki_world\'',B: $i,A: '\'$ki_world\''] :
      ( ~ ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
      | ~ ( '\'$ki_accessible\'' @ A @ C )
      | ~ ( bomb @ C @ B )
      | ~ ( h @ C @ ( sk6 @ B @ A ) )
      | ( defused @ C @ B ) ),
    inference(simp,[status(thm)],[162]) ).

thf(10,plain,
    '\'$ki_exists_in_world_$i\'' @ sk1 @ sk2,
    inference(cnf,[status(esa)],[9]) ).

thf(12,plain,
    ! [A: $i] :
      ( ~ ( '\'$ki_exists_in_world_$i\'' @ sk1 @ A )
      | ~ ( defused @ sk1 @ sk2 ) ),
    inference(cnf,[status(esa)],[9]) ).

thf(30,plain,
    ! [A: $i] :
      ( ~ ( defused @ sk1 @ sk2 )
      | ( ( '\'$ki_exists_in_world_$i\'' @ sk1 @ sk2 )
       != ( '\'$ki_exists_in_world_$i\'' @ sk1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[10,12]) ).

thf(31,plain,
    ~ ( defused @ sk1 @ sk2 ),
    inference(pattern_uni,[status(thm)],[30:[bind(A,$thf( sk2 ))]]) ).

thf(186,plain,
    ! [C: '\'$ki_world\'',B: $i,A: '\'$ki_world\''] :
      ( ~ ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
      | ~ ( '\'$ki_accessible\'' @ A @ C )
      | ~ ( bomb @ C @ B )
      | ~ ( h @ C @ ( sk6 @ B @ A ) )
      | ( ( defused @ C @ B )
       != ( defused @ sk1 @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[163,31]) ).

thf(187,plain,
    ! [A: '\'$ki_world\''] :
      ( ~ ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
      | ~ ( '\'$ki_accessible\'' @ A @ sk1 )
      | ~ ( bomb @ sk1 @ sk2 )
      | ~ ( h @ sk1 @ ( sk6 @ sk2 @ A ) ) ),
    inference(pattern_uni,[status(thm)],[186:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( sk1 ))]]) ).

thf(13,plain,
    ! [A: $i] :
      ( ~ ( '\'$ki_exists_in_world_$i\'' @ sk1 @ A )
      | ( bomb @ sk1 @ sk2 ) ),
    inference(cnf,[status(esa)],[9]) ).

thf(38,plain,
    ( ~ $true
    | ( bomb @ sk1 @ sk2 ) ),
    inference(rewrite,[status(thm)],[13,18]) ).

thf(39,plain,
    bomb @ sk1 @ sk2,
    inference(simp,[status(thm)],[38]) ).

thf(14,plain,
    ! [A: $i] :
      ( ~ ( '\'$ki_exists_in_world_$i\'' @ sk1 @ A )
      | ( h @ sk1 @ A ) ),
    inference(cnf,[status(esa)],[9]) ).

thf(40,plain,
    ! [A: $i] :
      ( ~ $true
      | ( h @ sk1 @ A ) ),
    inference(rewrite,[status(thm)],[14,18]) ).

thf(41,plain,
    ! [A: $i] : ( h @ sk1 @ A ),
    inference(simp,[status(thm)],[40]) ).

thf(255,plain,
    ! [A: '\'$ki_world\''] :
      ( ~ ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
      | ~ ( '\'$ki_accessible\'' @ A @ sk1 )
      | ~ $true
      | ~ $true ),
    inference(rewrite,[status(thm)],[187,39,41]) ).

thf(256,plain,
    ! [A: '\'$ki_world\''] :
      ( ~ ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
      | ~ ( '\'$ki_accessible\'' @ A @ sk1 ) ),
    inference(simp,[status(thm)],[255]) ).

thf(257,plain,
    ! [A: '\'$ki_world\''] :
      ( ~ ( '\'$ki_accessible\'' @ A @ sk1 )
      | ( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ sk1 )
       != ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[11,256]) ).

thf(258,plain,
    ~ ( '\'$ki_accessible\'' @ sk1 @ sk1 ),
    inference(pattern_uni,[status(thm)],[257:[bind(A,$thf( sk1 ))]]) ).

thf(3,axiom,
    ! [A: '\'$ki_world\''] : ( '\'$ki_accessible\'' @ A @ A ),
    file('/export/starexec/sandbox/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(16,plain,
    ! [A: '\'$ki_world\''] : ( '\'$ki_accessible\'' @ A @ A ),
    inference(cnf,[status(esa)],[15]) ).

thf(269,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[258,16]) ).

thf(270,plain,
    $false,
    inference(simp,[status(thm)],[269]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14  % Problem  : PLA053_2 : TPTP v8.2.0. Released v8.2.0.
% 0.09/0.18  % Command  : run_Leo-III %s %d
% 0.19/0.40  % Computer : n012.cluster.edu
% 0.19/0.40  % Model    : x86_64 x86_64
% 0.19/0.40  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.40  % Memory   : 8042.1875MB
% 0.19/0.40  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.19/0.40  % CPULimit : 300
% 0.19/0.40  % WCLimit  : 300
% 0.19/0.40  % DateTime : Sat May 18 13:44:24 EDT 2024
% 0.19/0.40  % CPUTime  : 
% 1.03/1.00  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.36/1.14  % [INFO] 	 Parsing done (145ms). 
% 1.36/1.15  % [INFO] 	 Running in sequential loop mode. 
% 1.90/1.40  % [INFO] 	 nitpick registered as external prover. 
% 1.90/1.41  % [INFO] 	 Scanning for conjecture ... 
% 2.15/1.48  % [INFO] 	 Found a conjecture (or negated_conjecture) and 6 axioms. Running axiom selection ... 
% 2.15/1.51  % [INFO] 	 Axiom selection finished. Selected 6 axioms (removed 0 axioms). 
% 2.28/1.53  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 2.28/1.54  % [INFO] 	 Type checking passed. 
% 2.28/1.54  % [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 ... 
% 5.63/2.48  % [INFO] 	 Killing All external provers ... 
% 5.63/2.48  % Time passed: 1913ms (effective reasoning time: 1321ms)
% 5.63/2.48  % 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)>
% 5.63/2.48  % Axioms used in derivation (3): ax3, $ki_exists_in_world_$i_const, mrel_reflexive
% 5.63/2.48  % No. of inferences in proof: 33
% 5.63/2.49  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1913 ms resp. 1321 ms w/o parsing
% 5.63/2.52  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.63/2.52  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------