%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SYO547^1 : TPTP v8.2.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n010.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 09:00:53 EDT 2024

% Result   : Theorem 2.54s 1.61s
% Output   : Refutation 2.54s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   16 (   6 unt;   3 typ;   0 def)
%            Number of atoms       :   16 (   0 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   62 (  23   ~;   3   |;   0   &;  31   @)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   10 (  10   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4 usr;   4 con; 0-1 aty)
%            Number of variables   :   20 (   5   ^  10   !;   5   ?;  20   :)

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

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

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

thf(1,conjecture,
    ! [A: $i > $o] :
      ( ? [B: $i] :
          ~ ( A @ B )
     => ~ ( A @ ( epscomp @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choicecomp) ).

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

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

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

thf(7,plain,
    ~ ( sk1 @ sk2 ),
    inference(cnf,[status(esa)],[5]) ).

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
            @ ^ [B: $i] :
                ~ ( sk1 @ B ) ) ) ),
    inference(choice,[status(esa)],[12]) ).

thf(15,plain,
    ! [A: $i] :
      ( ~ ( sk1
          @ ( eps
            @ ^ [B: $i] :
                ~ ( sk1 @ B ) ) )
      | ( sk1 @ A ) ),
    inference(cnf,[status(esa)],[13]) ).

thf(6,plain,
    ( sk1
    @ ( eps
      @ ^ [A: $i] :
          ~ ( sk1 @ A ) ) ),
    inference(cnf,[status(esa)],[5]) ).

thf(16,plain,
    ! [A: $i] :
      ( ~ $true
      | ( sk1 @ A ) ),
    inference(rewrite,[status(thm)],[15,6]) ).

thf(17,plain,
    ! [A: $i] : ( sk1 @ A ),
    inference(simp,[status(thm)],[16]) ).

thf(19,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[7,17]) ).

thf(20,plain,
    $false,
    inference(simp,[status(thm)],[19]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : SYO547^1 : TPTP v8.2.0. Released v5.2.0.
% 0.14/0.16  % Command  : run_Leo-III %s %d
% 0.17/0.38  % Computer : n010.cluster.edu
% 0.17/0.38  % Model    : x86_64 x86_64
% 0.17/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38  % Memory   : 8042.1875MB
% 0.17/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38  % CPULimit : 300
% 0.17/0.38  % WCLimit  : 300
% 0.17/0.38  % DateTime : Mon May 20 10:05:24 EDT 2024
% 0.17/0.38  % CPUTime  : 
% 0.94/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.31/0.98  % [INFO] 	 Parsing done (108ms). 
% 1.31/0.99  % [INFO] 	 Running in sequential loop mode. 
% 1.71/1.21  % [INFO] 	 nitpick registered as external prover. 
% 1.71/1.21  % [INFO] 	 Scanning for conjecture ... 
% 1.87/1.27  % [INFO] 	 Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ... 
% 1.87/1.29  % [INFO] 	 Axiom selection finished. Selected 1 axioms (removed 0 axioms). 
% 1.87/1.29  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.87/1.29  % [INFO] 	 Type checking passed. 
% 1.87/1.30  % [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 ... 
% 2.54/1.56  % [INFO] 	 Killing All external provers ... 
% 2.54/1.60  % Time passed: 1027ms (effective reasoning time: 572ms)
% 2.54/1.60  % 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)>
% 2.54/1.61  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1027 ms resp. 572 ms w/o parsing
% 2.54/1.63  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.54/1.63  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------