%------------------------------------------------------------------------------
% File     : Leo-III---1.7.15
% Problem  : SET047^1 : TPTP v8.2.0. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d THM

% Computer : n029.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 : Mon Jun 24 14:39:38 EDT 2024

% Result   : Theorem 2.58s 1.60s
% Output   : Refutation 2.80s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    5
% Syntax   : Number of formulae    :    9 (   6 unt;   0 typ;   3 def)
%            Number of atoms       :   37 (   7 equ;   0 cnn)
%            Maximal formula atoms :    9 (   4 avg)
%            Number of connectives :   54 (   2   ~;   0   |;   0   &;  52   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   6 usr;   2 con; 0-3 aty)
%            Number of variables   :   19 (  13   ^   6   !;   0   ?;  19   :)

% 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(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(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(set_equal_type,type,
    set_equal: $i > $i > mworld > $o ).

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

thf(1,conjecture,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] : ( mequiv @ ( set_equal @ A @ B ) @ ( set_equal @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel43) ).

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

thf(4,plain,
    ~ ! [A: $i,B: $i] :
        ( ( set_equal @ A @ B @ mactual )
        = ( set_equal @ B @ A @ mactual ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(3,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] :
              ( mequiv @ ( set_equal @ A @ B )
              @ ( mforall_di
                @ ^ [C: $i] : ( mequiv @ ( element @ C @ A ) @ ( element @ C @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel43_1) ).

thf(7,plain,
    ! [A: $i,B: $i] :
      ( ( set_equal @ A @ B @ mactual )
      = ( ! [C: $i] :
            ( ( element @ C @ A @ mactual )
            = ( element @ C @ B @ mactual ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(14,plain,
    $false,
    inference(e,[status(thm)],[4,7]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET047^1 : TPTP v8.2.0. Released v8.1.0.
% 0.07/0.12  % Command  : run_Leo-III %s %d THM
% 0.12/0.33  % Computer : n029.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Sun Jun 23 15:55:25 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 1.01/0.90  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.26/1.04  % [INFO] 	 Parsing done (133ms). 
% 1.26/1.05  % [INFO] 	 Running in sequential loop mode. 
% 1.83/1.26  % [INFO] 	 eprover registered as external prover. 
% 1.83/1.27  % [INFO] 	 Scanning for conjecture ... 
% 1.83/1.34  % [INFO] 	 Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ... 
% 2.06/1.36  % [INFO] 	 Axiom selection finished. Selected 1 axioms (removed 0 axioms). 
% 2.06/1.36  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.06/1.36  % [INFO] 	 Type checking passed. 
% 2.06/1.37  % [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 ... 
% 2.58/1.60  % External prover 'e' found a proof!
% 2.58/1.60  % [INFO] 	 Killing All external provers ... 
% 2.58/1.60  % Time passed: 1083ms (effective reasoning time: 548ms)
% 2.58/1.60  % 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)>
% 2.58/1.60  % Axioms used in derivation (1): pel43_1
% 2.58/1.60  % No. of inferences in proof: 6
% 2.58/1.60  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1083 ms resp. 548 ms w/o parsing
% 2.80/1.67  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.80/1.67  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------