TSTP Solution File: SYO896_7 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SYO896_7 : TPTP v8.2.0. Released v8.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n013.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 09:02:00 EDT 2024

% Result   : Theorem 2.62s 1.62s
% Output   : Refutation 2.62s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   22 (   4 unt;   6 typ;   0 def)
%            Number of atoms       :   55 (   2 equ;   0 cnn)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  128 (  27   ~;  14   |;   6   &;  66   @)
%                                         (   0 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   14 (   0   ^  11   !;   3   ?;  14   :)

% 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(p_type,type,
    p: '\'$ki_world\'' > $o ).

thf(q_type,type,
    q: '\'$ki_world\'' > $o ).

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

thf(1,conjecture,
    ( ( ! [A: '\'$ki_world\''] :
          ( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
         => ( ( p @ A )
           => ( q @ A ) ) )
      & ! [A: '\'$ki_world\''] :
          ( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
         => ( ( p @ A )
           => ~ ( q @ A ) ) ) )
   => ~ ? [A: '\'$ki_world\''] :
          ( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
          & ( p @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).

thf(2,negated_conjecture,
    ~ ( ( ! [A: '\'$ki_world\''] :
            ( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
           => ( ( p @ A )
             => ( q @ A ) ) )
        & ! [A: '\'$ki_world\''] :
            ( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
           => ( ( p @ A )
             => ~ ( q @ A ) ) ) )
     => ~ ? [A: '\'$ki_world\''] :
            ( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
            & ( p @ A ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ( ( ! [A: '\'$ki_world\''] :
            ( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
           => ( ( p @ A )
             => ( q @ A ) ) )
        & ! [A: '\'$ki_world\''] :
            ( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
           => ( ( p @ A )
             => ~ ( q @ A ) ) ) )
     => ~ ? [A: '\'$ki_world\''] :
            ( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
            & ( p @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(5,plain,
    '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ sk1,
    inference(cnf,[status(esa)],[3]) ).

thf(6,plain,
    ! [A: '\'$ki_world\''] :
      ( ~ ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
      | ~ ( p @ A )
      | ~ ( q @ A ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(8,plain,
    ! [A: '\'$ki_world\''] :
      ( ~ ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
      | ~ ( p @ A )
      | ~ ( q @ A ) ),
    inference(simp,[status(thm)],[6]) ).

thf(15,plain,
    ! [A: '\'$ki_world\''] :
      ( ~ ( p @ A )
      | ~ ( q @ A )
      | ( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ sk1 )
       != ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[5,8]) ).

thf(16,plain,
    ( ~ ( p @ sk1 )
    | ~ ( q @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[15:[bind(A,$thf( sk1 ))]]) ).

thf(4,plain,
    p @ sk1,
    inference(cnf,[status(esa)],[3]) ).

thf(7,plain,
    ! [A: '\'$ki_world\''] :
      ( ~ ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
      | ~ ( p @ A )
      | ( q @ A ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(11,plain,
    ! [A: '\'$ki_world\''] :
      ( ~ ( p @ A )
      | ( q @ A )
      | ( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ sk1 )
       != ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[5,7]) ).

thf(12,plain,
    ( ~ ( p @ sk1 )
    | ( q @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[11:[bind(A,$thf( sk1 ))]]) ).

thf(13,plain,
    ( ~ $true
    | ( q @ sk1 ) ),
    inference(rewrite,[status(thm)],[12,4]) ).

thf(14,plain,
    q @ sk1,
    inference(simp,[status(thm)],[13]) ).

thf(21,plain,
    ( ~ $true
    | ~ $true ),
    inference(rewrite,[status(thm)],[16,4,14]) ).

thf(22,plain,
    $false,
    inference(simp,[status(thm)],[21]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SYO896_7 : TPTP v8.2.0. Released v8.2.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n013.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Mon May 20 10:30:39 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 0.98/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.18/0.96  % [INFO] 	 Parsing done (102ms). 
% 1.18/0.97  % [INFO] 	 Running in sequential loop mode. 
% 1.61/1.19  % [INFO] 	 nitpick registered as external prover. 
% 1.66/1.19  % [INFO] 	 Scanning for conjecture ... 
% 1.78/1.25  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.78/1.27  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.78/1.27  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 1.78/1.28  % [INFO] 	 Type checking passed. 
% 1.78/1.28  % [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 ... 
% 2.45/1.57  % [INFO] 	 Killing All external provers ... 
% 2.62/1.62  % Time passed: 1087ms (effective reasoning time: 637ms)
% 2.62/1.62  % 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)>
% 2.62/1.62  % Axioms used in derivation (0): 
% 2.62/1.62  % No. of inferences in proof: 16
% 2.62/1.62  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1087 ms resp. 637 ms w/o parsing
% 2.62/1.66  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.62/1.66  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------