%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SYO557^1 : TPTP v8.2.0. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n015.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 09:00:55 EDT 2024

% Result   : Theorem 2.96s 1.72s
% Output   : Refutation 2.96s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   20 (  10 unt;   3 typ;   0 def)
%            Number of atoms       :   36 (   6 equ;   0 cnn)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :   59 (  15   ~;   6   |;   0   &;  37   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   10 (  10   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   4 usr;   4 con; 0-2 aty)
%            Number of variables   :   15 (   4   ^   6   !;   5   ?;  15   :)

% Comments : 
%------------------------------------------------------------------------------
thf(eps_type,type,
    eps: ( $i > $o ) > $i ).

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

thf(sk3_type,type,
    sk3: $i ).

thf(1,conjecture,
    ( ( ^ [A: $i > $o] : ( A @ ( eps @ A ) ) )
    = ( '?' @ $i ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).

thf(2,negated_conjecture,
    ( ( ^ [A: $i > $o] : ( A @ ( eps @ A ) ) )
   != ( '?' @ $i ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(4,plain,
    ( ( ^ [A: $i > $o] : ( A @ ( eps @ A ) ) )
   != ( '?' @ $i ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(5,plain,
    ( ( ^ [A: $i > $o] : ( A @ ( eps @ A ) ) )
   != ( '?' @ $i ) ),
    inference(lifteq,[status(thm)],[4]) ).

thf(9,plain,
    ( ( sk1 @ ( eps @ sk1 ) )
   != ( ? [A: $i] : ( sk1 @ A ) ) ),
    inference(func_ext,[status(esa)],[5]) ).

thf(10,plain,
    ( ~ ( sk1 @ ( eps @ sk1 ) )
    | ~ ? [A: $i] : ( sk1 @ A ) ),
    inference(bool_ext,[status(thm)],[9]) ).

thf(14,plain,
    ! [A: $i] :
      ( ~ ( sk1 @ A )
      | ~ ( sk1 @ ( eps @ sk1 ) ) ),
    inference(cnf,[status(esa)],[10]) ).

thf(33,plain,
    ! [A: $i] :
      ( ~ ( sk1 @ A )
      | ( ( sk1 @ ( eps @ sk1 ) )
       != ( sk1 @ A ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[14]) ).

thf(35,plain,
    ~ ( sk1 @ ( eps @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[33:[bind(A,$thf( eps @ sk1 ))]]) ).

thf(37,plain,
    ? [A: $i] : ( sk1 @ A ),
    inference(rewrite,[status(thm)],[9,35]) ).

thf(42,plain,
    sk1 @ sk3,
    inference(cnf,[status(esa)],[37]) ).

thf(12,axiom,
    ? [A: ( $i > $o ) > $i] :
    ! [B: $i > $o] :
      ( ? [C: $i] : ( B @ C )
     => ( B @ ( A @ B ) ) ),
    introduced(axiom_of_choice) ).

thf(13,plain,
    ! [A: $i] :
      ( ~ ( sk1 @ A )
      | ( sk1 @ ( eps @ sk1 ) ) ),
    inference(choice,[status(esa)],[12]) ).

thf(48,plain,
    ! [A: $i] :
      ( ~ ( sk1 @ A )
      | $false ),
    inference(rewrite,[status(thm)],[13,35]) ).

thf(49,plain,
    ! [A: $i] :
      ~ ( sk1 @ A ),
    inference(simp,[status(thm)],[48]) ).

thf(50,plain,
    $false,
    inference(rewrite,[status(thm)],[42,49]) ).

thf(51,plain,
    $false,
    inference(simp,[status(thm)],[50]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SYO557^1 : TPTP v8.2.0. Bugfixed v7.5.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n015.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 : Mon May 20 10:44:54 EDT 2024
% 0.15/0.36  % CPUTime  : 
% 0.97/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.14/0.96  % [INFO] 	 Parsing done (105ms). 
% 1.14/0.97  % [INFO] 	 Running in sequential loop mode. 
% 1.57/1.19  % [INFO] 	 nitpick registered as external prover. 
% 1.57/1.19  % [INFO] 	 Scanning for conjecture ... 
% 1.73/1.24  % [INFO] 	 Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ... 
% 1.73/1.26  % [INFO] 	 Axiom selection finished. Selected 1 axioms (removed 0 axioms). 
% 1.84/1.27  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.84/1.27  % [INFO] 	 Type checking passed. 
% 1.84/1.27  % [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 ... 
% 2.96/1.72  % [INFO] 	 Killing All external provers ... 
% 2.96/1.72  % Time passed: 1196ms (effective reasoning time: 744ms)
% 2.96/1.72  % 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)>
% 2.96/1.72  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1196 ms resp. 744 ms w/o parsing
% 2.96/1.75  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.96/1.75  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------