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

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---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 : n023.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 49.50s 15.41s
% Output   : Refutation 49.50s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   43 (  16 unt;  15 typ;   6 def)
%            Number of atoms       :   90 (   8 equ;   0 cnn)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  194 (  27   ~;  16   |;   4   &; 138   @)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   43 (  43   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  14 usr;   5 con; 0-3 aty)
%            Number of variables   :   47 (  19   ^  25   !;   3   ?;  47   :)

% 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(sk1_type,type,
    sk1: mworld ).

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

thf(sk5_type,type,
    sk5: $i > mworld > $i ).

thf(3,axiom,
    ! [A: mworld] : ( mrel @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).

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

thf(15,plain,
    ! [A: mworld] : ( mrel @ A @ A ),
    inference(cnf,[status(esa)],[14]) ).

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/sandbox2/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(23,plain,
    ! [C: mworld,B: $i,A: mworld] :
      ( ~ ( mrel @ mactual @ A )
      | ~ ( mrel @ A @ C )
      | ~ ( bomb @ B @ C )
      | ~ ( h @ ( sk5 @ B @ A ) @ C )
      | ( defused @ B @ C ) ),
    inference(cnf,[status(esa)],[22]) ).

thf(1,conjecture,
    ( mlocal
    @ ( mbox
      @ ( mforall_di
        @ ^ [A: $i] :
            ( mexists_di
            @ ^ [B: $i] : ( mimplies @ ( mand @ ( bomb @ A ) @ ( h @ B ) ) @ ( defused @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/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(9,plain,
    ~ ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ! [B: $i] :
            ( ( ( bomb @ B @ A )
              & ! [C: $i] : ( h @ C @ A ) )
           => ( defused @ B @ A ) ) ),
    inference(miniscope,[status(thm)],[8]) ).

thf(10,plain,
    ~ ( defused @ sk2 @ sk1 ),
    inference(cnf,[status(esa)],[9]) ).

thf(10794,plain,
    ! [C: mworld,B: $i,A: mworld] :
      ( ~ ( mrel @ mactual @ A )
      | ~ ( mrel @ A @ C )
      | ~ ( bomb @ B @ C )
      | ~ ( h @ ( sk5 @ B @ A ) @ C )
      | ( ( defused @ B @ C )
       != ( defused @ sk2 @ sk1 ) ) ),
    inference(paramod_ordered,[status(thm)],[23,10]) ).

thf(10795,plain,
    ! [A: mworld] :
      ( ~ ( mrel @ mactual @ A )
      | ~ ( mrel @ A @ sk1 )
      | ~ ( bomb @ sk2 @ sk1 )
      | ~ ( h @ ( sk5 @ sk2 @ A ) @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[10794:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( sk1 ))]]) ).

thf(11,plain,
    ! [A: $i] : ( h @ A @ sk1 ),
    inference(cnf,[status(esa)],[9]) ).

thf(12,plain,
    bomb @ sk2 @ sk1,
    inference(cnf,[status(esa)],[9]) ).

thf(10898,plain,
    ! [A: mworld] :
      ( ~ ( mrel @ mactual @ A )
      | ~ ( mrel @ A @ sk1 )
      | ~ $true
      | ~ $true ),
    inference(rewrite,[status(thm)],[10795,11,12]) ).

thf(10899,plain,
    ! [A: mworld] :
      ( ~ ( mrel @ mactual @ A )
      | ~ ( mrel @ A @ sk1 ) ),
    inference(simp,[status(thm)],[10898]) ).

thf(10904,plain,
    ! [B: mworld,A: mworld] :
      ( ~ ( mrel @ B @ sk1 )
      | ( ( mrel @ A @ A )
       != ( mrel @ mactual @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[15,10899]) ).

thf(10905,plain,
    ~ ( mrel @ mactual @ sk1 ),
    inference(pattern_uni,[status(thm)],[10904:[bind(A,$thf( mactual )),bind(B,$thf( mactual ))]]) ).

thf(13,plain,
    mrel @ mactual @ sk1,
    inference(cnf,[status(esa)],[9]) ).

thf(10934,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[10905,13]) ).

thf(10935,plain,
    $false,
    inference(simp,[status(thm)],[10934]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : PLA053^5 : TPTP v8.2.0. Released v8.1.0.
% 0.12/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n023.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Sat May 18 13:41:39 EDT 2024
% 0.15/0.36  % CPUTime  : 
% 0.97/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.19/0.99  % [INFO] 	 Parsing done (121ms). 
% 1.19/1.00  % [INFO] 	 Running in sequential loop mode. 
% 1.67/1.21  % [INFO] 	 nitpick registered as external prover. 
% 1.76/1.21  % [INFO] 	 Scanning for conjecture ... 
% 1.84/1.29  % [INFO] 	 Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ... 
% 1.84/1.31  % [INFO] 	 Axiom selection finished. Selected 5 axioms (removed 0 axioms). 
% 1.84/1.32  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.84/1.32  % [INFO] 	 Type checking passed. 
% 1.84/1.32  % [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 ... 
% 49.50/15.40  % [INFO] 	 Killing All external provers ... 
% 49.50/15.40  % Time passed: 14877ms (effective reasoning time: 14401ms)
% 49.50/15.40  % 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)>
% 49.50/15.41  % Axioms used in derivation (2): mrel_reflexive, ax3
% 49.50/15.41  % No. of inferences in proof: 22
% 49.50/15.41  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 14877 ms resp. 14401 ms w/o parsing
% 49.50/15.43  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 49.50/15.43  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------