TSTP Solution File: PLA053^5 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : PLA053^5 : TPTP v8.2.0. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n005.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 02:19:57 EDT 2024

% Result   : Theorem 3.57s 2.31s
% Output   : Refutation 4.02s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   32 (   9 unt;  12 typ;   6 def)
%            Number of atoms       :   80 (   6 equ;   0 cnn)
%            Maximal formula atoms :   10 (   4 avg)
%            Number of connectives :  130 (   2   ~;   0   |;   6   &; 109   @)
%                                         (   0 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   41 (  41   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  11 usr;   2 con; 0-3 aty)
%            Number of variables   :   45 (  21   ^  19   !;   5   ?;  45   :)

% Comments : 
%------------------------------------------------------------------------------
thf(mworld_type,type,
    mworld: $tType ).

thf(mrel_type,type,
    mrel: mworld > mworld > $o ).

thf(mactual_type,type,
    mactual: mworld ).

thf(mlocal_type,type,
    mlocal: ( mworld > $o ) > $o ).

thf(mlocal_def,definition,
    ( mlocal
    = ( ^ [A: mworld > $o] : ( A @ mactual ) ) ) ).

thf(mand_type,type,
    mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).

thf(mand_def,definition,
    ( mand
    = ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
          ( ( A @ C )
          & ( B @ C ) ) ) ) ).

thf(mimplies_type,type,
    mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).

thf(mimplies_def,definition,
    ( mimplies
    = ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
          ( ( A @ C )
         => ( B @ C ) ) ) ) ).

thf(mbox_type,type,
    mbox: ( mworld > $o ) > mworld > $o ).

thf(mbox_def,definition,
    ( mbox
    = ( ^ [A: mworld > $o,B: mworld] :
        ! [C: mworld] :
          ( ( mrel @ B @ C )
         => ( A @ C ) ) ) ) ).

thf(mforall_di_type,type,
    mforall_di: ( $i > mworld > $o ) > mworld > $o ).

thf(mforall_di_def,definition,
    ( mforall_di
    = ( ^ [A: $i > mworld > $o,B: mworld] :
        ! [C: $i] : ( A @ C @ B ) ) ) ).

thf(mexists_di_type,type,
    mexists_di: ( $i > mworld > $o ) > mworld > $o ).

thf(mexists_di_def,definition,
    ( mexists_di
    = ( ^ [A: $i > mworld > $o,B: mworld] :
        ? [C: $i] : ( A @ C @ B ) ) ) ).

thf(h_type,type,
    h: $i > mworld > $o ).

thf(bomb_type,type,
    bomb: $i > mworld > $o ).

thf(defused_type,type,
    defused: $i > mworld > $o ).

thf(3,axiom,
    ! [A: mworld] : ( mrel @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_reflexive) ).

thf(14,plain,
    ! [A: mworld] : ( mrel @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(6,axiom,
    ( mlocal
    @ ( mexists_di
      @ ^ [A: $i] :
          ( mbox
          @ ( mforall_di
            @ ^ [B: $i] : ( mimplies @ ( mand @ ( bomb @ B ) @ ( h @ A ) ) @ ( mbox @ ( bomb @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).

thf(20,plain,
    ? [A: $i] :
    ! [B: mworld] :
      ( ( mrel @ mactual @ B )
     => ! [C: $i] :
          ( ( ( bomb @ C @ B )
            & ( h @ A @ B ) )
         => ! [D: mworld] :
              ( ( mrel @ B @ D )
             => ( bomb @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(7,axiom,
    ( mlocal
    @ ( mbox
      @ ( mforall_di
        @ ^ [A: $i] :
            ( mexists_di
            @ ^ [B: $i] : ( mbox @ ( mimplies @ ( mand @ ( bomb @ A ) @ ( h @ B ) ) @ ( defused @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).

thf(22,plain,
    ! [A: mworld] :
      ( ( mrel @ mactual @ A )
     => ! [B: $i] :
        ? [C: $i] :
        ! [D: mworld] :
          ( ( mrel @ A @ D )
         => ( ( ( bomb @ B @ D )
              & ( h @ C @ D ) )
           => ( defused @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(5,axiom,
    mlocal @ ( mbox @ ( mexists_di @ bomb ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).

thf(18,plain,
    ! [A: mworld] :
      ( ( mrel @ mactual @ A )
     => ? [B: $i] : ( bomb @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(4,axiom,
    ! [A: mworld,B: mworld,C: mworld] :
      ( ( ( mrel @ A @ C )
        & ( mrel @ A @ B ) )
     => ( mrel @ C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_euclidean) ).

thf(16,plain,
    ! [A: mworld,B: mworld,C: mworld] :
      ( ( ( mrel @ A @ C )
        & ( mrel @ A @ B ) )
     => ( mrel @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(1,conjecture,
    ( mlocal
    @ ( mbox
      @ ( mforall_di
        @ ^ [A: $i] :
            ( mexists_di
            @ ^ [B: $i] : ( mimplies @ ( mand @ ( bomb @ A ) @ ( h @ B ) ) @ ( defused @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).

thf(2,negated_conjecture,
    ~ ( mlocal
      @ ( mbox
        @ ( mforall_di
          @ ^ [A: $i] :
              ( mexists_di
              @ ^ [B: $i] : ( mimplies @ ( mand @ ( bomb @ A ) @ ( h @ B ) ) @ ( defused @ A ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(8,plain,
    ~ ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ! [B: $i] :
          ? [C: $i] :
            ( ( ( bomb @ B @ A )
              & ( h @ C @ A ) )
           => ( defused @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(24,plain,
    $false,
    inference(e,[status(thm)],[14,20,22,18,16,8]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.11  % Problem  : PLA053^5 : TPTP v8.2.0. Released v8.1.0.
% 0.05/0.13  % Command  : run_Leo-III %s %d
% 0.14/0.34  % Computer : n005.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Sat May 18 13:41:39 EDT 2024
% 0.14/0.34  % CPUTime  : 
% 1.03/1.02  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.50/1.21  % [INFO] 	 Parsing done (188ms). 
% 1.50/1.22  % [INFO] 	 Running in sequential loop mode. 
% 2.10/1.61  % [INFO] 	 eprover registered as external prover. 
% 2.10/1.61  % [INFO] 	 cvc4 registered as external prover. 
% 2.10/1.62  % [INFO] 	 Scanning for conjecture ... 
% 2.35/1.75  % [INFO] 	 Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ... 
% 2.43/1.78  % [INFO] 	 Axiom selection finished. Selected 5 axioms (removed 0 axioms). 
% 2.43/1.80  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.43/1.80  % [INFO] 	 Type checking passed. 
% 2.43/1.80  % [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 ... 
% 3.57/2.31  % External prover 'e' found a proof!
% 3.57/2.31  % [INFO] 	 Killing All external provers ... 
% 3.57/2.31  % Time passed: 1802ms (effective reasoning time: 1083ms)
% 3.57/2.31  % 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)>
% 3.57/2.31  % Axioms used in derivation (5): mrel_euclidean, mrel_reflexive, ax1, ax2, ax3
% 3.57/2.31  % No. of inferences in proof: 14
% 3.57/2.31  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1802 ms resp. 1083 ms w/o parsing
% 4.02/2.42  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.02/2.42  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------