TSTP Solution File: SET044^23 by Leo-III-SAT---1.7.10

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.10
% Problem  : SET044^23 : TPTP v8.1.2. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n019.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  7 10:48:52 EDT 2024

% Result   : Theorem 6.19s 2.24s
% Output   : Refutation 6.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   38 (  10 unt;  12 typ;   6 def)
%            Number of atoms       :  116 (  21 equ;   0 cnn)
%            Maximal formula atoms :   15 (   4 avg)
%            Number of connectives :  268 (  31   ~;  19   |;   3   &; 209   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   5 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   39 (  39   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  11 usr;   4 con; 0-3 aty)
%            Number of variables   :   44 (  23   ^  18   !;   3   ?;  44   :)

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

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(mnot_type,type,
    mnot: ( mworld > $o ) > mworld > $o ).

thf(mnot_def,definition,
    ( mnot
    = ( ^ [A: mworld > $o,B: mworld] :
          ~ ( A @ B ) ) ) ).

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(mequiv_type,type,
    mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).

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

thf(eiw_di_type,type,
    eiw_di: $i > mworld > $o ).

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] :
          ( ( eiw_di @ C @ B )
         => ( 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] :
          ( ( eiw_di @ C @ B )
          & ( A @ C @ B ) ) ) ) ).

thf(element_type,type,
    element: $i > $i > mworld > $o ).

thf(sk1_type,type,
    sk1: $i ).

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

thf(1,conjecture,
    ( mlocal
    @ ( mimplies
      @ ( mexists_di
        @ ^ [A: $i] :
            ( mforall_di
            @ ^ [B: $i] : ( mequiv @ ( element @ B @ A ) @ ( element @ B @ B ) ) ) )
      @ ( mnot
        @ ( mforall_di
          @ ^ [A: $i] :
              ( mexists_di
              @ ^ [B: $i] :
                  ( mforall_di
                  @ ^ [C: $i] : ( mequiv @ ( element @ C @ B ) @ ( mnot @ ( element @ C @ A ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel40) ).

thf(2,negated_conjecture,
    ~ ( mlocal
      @ ( mimplies
        @ ( mexists_di
          @ ^ [A: $i] :
              ( mforall_di
              @ ^ [B: $i] : ( mequiv @ ( element @ B @ A ) @ ( element @ B @ B ) ) ) )
        @ ( mnot
          @ ( mforall_di
            @ ^ [A: $i] :
                ( mexists_di
                @ ^ [B: $i] :
                    ( mforall_di
                    @ ^ [C: $i] : ( mequiv @ ( element @ C @ B ) @ ( mnot @ ( element @ C @ A ) ) ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(7,plain,
    ~ ( ? [A: $i] :
          ( ( eiw_di @ A @ mactual )
          & ! [B: $i] :
              ( ( eiw_di @ B @ mactual )
             => ( ( element @ B @ A @ mactual )
                = ( element @ B @ B @ mactual ) ) ) )
     => ~ ! [A: $i] :
            ( ( eiw_di @ A @ mactual )
           => ? [B: $i] :
                ( ( eiw_di @ B @ mactual )
                & ! [C: $i] :
                    ( ( eiw_di @ C @ mactual )
                   => ( ( element @ C @ B @ mactual )
                      = ( ~ ( element @ C @ A @ mactual ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(11,plain,
    eiw_di @ sk1 @ mactual,
    inference(cnf,[status(esa)],[7]) ).

thf(8,plain,
    ! [A: $i] :
      ( ~ ( eiw_di @ A @ mactual )
      | ( eiw_di @ ( sk2 @ A ) @ mactual ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(12,plain,
    ! [A: $i] :
      ( ~ ( eiw_di @ A @ mactual )
      | ( eiw_di @ ( sk2 @ A ) @ mactual ) ),
    inference(simp,[status(thm)],[8]) ).

thf(26,plain,
    ! [A: $i] :
      ( ( eiw_di @ ( sk2 @ A ) @ mactual )
      | ( ( eiw_di @ sk1 @ mactual )
       != ( eiw_di @ A @ mactual ) ) ),
    inference(paramod_ordered,[status(thm)],[11,12]) ).

thf(27,plain,
    eiw_di @ ( sk2 @ sk1 ) @ mactual,
    inference(pattern_uni,[status(thm)],[26:[bind(A,$thf( sk1 ))]]) ).

thf(10,plain,
    ! [A: $i] :
      ( ~ ( eiw_di @ A @ mactual )
      | ( ( element @ A @ sk1 @ mactual )
        = ( element @ A @ A @ mactual ) ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(15,plain,
    ! [A: $i] :
      ( ( ( element @ A @ sk1 @ mactual )
        = ( element @ A @ A @ mactual ) )
      | ~ ( eiw_di @ A @ mactual ) ),
    inference(lifteq,[status(thm)],[10]) ).

thf(293,plain,
    ! [A: $i] :
      ( ( ( element @ A @ sk1 @ mactual )
        = ( element @ A @ A @ mactual ) )
      | ( ( eiw_di @ ( sk2 @ sk1 ) @ mactual )
       != ( eiw_di @ A @ mactual ) ) ),
    inference(paramod_ordered,[status(thm)],[27,15]) ).

thf(294,plain,
    ( ( element @ ( sk2 @ sk1 ) @ ( sk2 @ sk1 ) @ mactual )
    = ( element @ ( sk2 @ sk1 ) @ sk1 @ mactual ) ),
    inference(pattern_uni,[status(thm)],[293:[bind(A,$thf( sk2 @ sk1 ))]]) ).

thf(9,plain,
    ! [B: $i,A: $i] :
      ( ~ ( eiw_di @ A @ mactual )
      | ~ ( eiw_di @ B @ mactual )
      | ( ( element @ B @ ( sk2 @ A ) @ mactual )
        = ( ~ ( element @ B @ A @ mactual ) ) ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(13,plain,
    ! [B: $i,A: $i] :
      ( ( ( element @ B @ ( sk2 @ A ) @ mactual )
        = ( ~ ( element @ B @ A @ mactual ) ) )
      | ~ ( eiw_di @ A @ mactual )
      | ~ ( eiw_di @ B @ mactual ) ),
    inference(lifteq,[status(thm)],[9]) ).

thf(14,plain,
    ! [B: $i,A: $i] :
      ( ( ( element @ B @ ( sk2 @ A ) @ mactual )
        = ( ~ ( element @ B @ A @ mactual ) ) )
      | ~ ( eiw_di @ A @ mactual )
      | ~ ( eiw_di @ B @ mactual ) ),
    inference(simp,[status(thm)],[13]) ).

thf(429,plain,
    ! [B: $i,A: $i] :
      ( ( ( element @ ( sk2 @ sk1 ) @ sk1 @ mactual )
        = ( ~ ( element @ B @ A @ mactual ) ) )
      | ~ ( eiw_di @ A @ mactual )
      | ~ ( eiw_di @ B @ mactual )
      | ( ( element @ ( sk2 @ sk1 ) @ ( sk2 @ sk1 ) @ mactual )
       != ( element @ B @ ( sk2 @ A ) @ mactual ) ) ),
    inference(paramod_ordered,[status(thm)],[294,14]) ).

thf(430,plain,
    ( ( ( ~ ( element @ ( sk2 @ sk1 ) @ sk1 @ mactual ) )
      = ( element @ ( sk2 @ sk1 ) @ sk1 @ mactual ) )
    | ~ ( eiw_di @ sk1 @ mactual )
    | ~ ( eiw_di @ ( sk2 @ sk1 ) @ mactual ) ),
    inference(pattern_uni,[status(thm)],[429:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 @ sk1 ))]]) ).

thf(462,plain,
    ( ~ ( eiw_di @ sk1 @ mactual )
    | ~ ( eiw_di @ ( sk2 @ sk1 ) @ mactual ) ),
    inference(simp,[status(thm)],[430]) ).

thf(466,plain,
    ( ~ $true
    | ~ $true ),
    inference(rewrite,[status(thm)],[462,11,27]) ).

thf(467,plain,
    $false,
    inference(simp,[status(thm)],[466]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08  % Problem  : SET044^23 : TPTP v8.1.2. Released v8.1.0.
% 0.08/0.11  % Command  : run_Leo-III %s %d
% 0.11/0.31  % Computer : n019.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit : 300
% 0.11/0.31  % WCLimit  : 300
% 0.11/0.31  % DateTime : Mon May  6 20:39:39 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 0.86/0.77  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.01/0.89  % [INFO] 	 Parsing done (114ms). 
% 1.01/0.90  % [INFO] 	 Running in sequential loop mode. 
% 1.54/1.09  % [INFO] 	 nitpick registered as external prover. 
% 1.54/1.09  % [INFO] 	 Scanning for conjecture ... 
% 1.75/1.16  % [INFO] 	 Found a conjecture and 4 axioms. Running axiom selection ... 
% 1.75/1.19  % [INFO] 	 Axiom selection finished. Selected 4 axioms (removed 0 axioms). 
% 1.75/1.19  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.75/1.19  % [INFO] 	 Type checking passed. 
% 1.75/1.20  % [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 ... 
% 6.19/2.23  % [INFO] 	 Killing All external provers ... 
% 6.19/2.23  % Time passed: 1747ms (effective reasoning time: 1331ms)
% 6.19/2.23  % 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)>
% 6.19/2.23  % Axioms used in derivation (0): 
% 6.19/2.23  % No. of inferences in proof: 20
% 6.19/2.24  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1747 ms resp. 1331 ms w/o parsing
% 6.19/2.27  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.19/2.27  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------