%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.15
% Problem  : SYO548^1 : TPTP v8.2.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d SAT

% Computer : n026.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 20:56:07 EDT 2024

% Result   : Theorem 2.76s 1.68s
% Output   : Refutation 3.01s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    2
% Syntax   : Number of formulae    :   14 (   4 unt;   0 typ;   0 def)
%            Number of atoms       :   14 (   0 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   64 (  26   ~;   3   |;   0   &;  29   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   14 (  14   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   2 usr;   3 con; 0-1 aty)
%            Number of variables   :   25 (   0   ^  11   !;   9   ?;  25   :)
%                                         (   0  !>;   0  ?*;   0  @-;   5  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(sk3_type,type,
    sk3: $i > $o ).

thf(sk4_type,type,
    sk4: $i ).

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

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

thf(3,plain,
    ~ ? [A: ( $i > $o ) > $i] :
      ! [B: $i > $o] :
        ( ? [C: $i] :
            ~ ( B @ C )
       => ~ ( B @ ( A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(5,plain,
    ~ ! [A: $i > $o] :
        ( ? [B: $i] :
            ~ ( A @ B )
       => ~ ( A
            @ @+[B: $i] :
                ~ ( A @ B ) ) ),
    inference(instance,[status(thm)],[3]) ).

thf(9,plain,
    ~ ! [A: $i > $o] :
        ( ~ ! [B: $i] : ( A @ B )
       => ~ ( A
            @ @+[B: $i] :
                ~ ( A @ B ) ) ),
    inference(miniscope,[status(thm)],[5]) ).

thf(11,plain,
    ~ ( sk3 @ sk4 ),
    inference(cnf,[status(esa)],[9]) ).

thf(16,axiom,
    ? [A: ( $i > $o ) > $i] :
    ! [B: $i > $o] :
      ( ? [C: $i] : ( B @ C )
     => ( B @ ( A @ B ) ) ),
    introduced(axiom_of_choice) ).

thf(21,plain,
    ! [A: $i] :
      ( ~ ~ ( sk3 @ A )
      | ~ ( sk3
          @ @+[B: $i] :
              ~ ( sk3 @ B ) ) ),
    inference(choice,[status(esa)],[16]) ).

thf(23,plain,
    ! [A: $i] :
      ( ~ ( sk3
          @ @+[B: $i] :
              ~ ( sk3 @ B ) )
      | ( sk3 @ A ) ),
    inference(cnf,[status(esa)],[21]) ).

thf(10,plain,
    ( sk3
    @ @+[A: $i] :
        ~ ( sk3 @ A ) ),
    inference(cnf,[status(esa)],[9]) ).

thf(28,plain,
    ! [A: $i] :
      ( ~ $true
      | ( sk3 @ A ) ),
    inference(rewrite,[status(thm)],[23,10]) ).

thf(29,plain,
    ! [A: $i] : ( sk3 @ A ),
    inference(simp,[status(thm)],[28]) ).

thf(33,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[11,29]) ).

thf(34,plain,
    $false,
    inference(simp,[status(thm)],[33]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SYO548^1 : TPTP v8.2.0. Released v5.2.0.
% 0.11/0.12  % Command  : run_Leo-III %s %d SAT
% 0.12/0.33  % Computer : n026.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 09:25:25 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 0.99/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.14/0.96  % [INFO] 	 Parsing done (95ms). 
% 1.14/0.97  % [INFO] 	 Running in sequential loop mode. 
% 1.46/1.17  % [INFO] 	 nitpick registered as external prover. 
% 1.46/1.17  % [INFO] 	 Scanning for conjecture ... 
% 1.66/1.22  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.81/1.23  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.81/1.24  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.81/1.24  % [INFO] 	 Type checking passed. 
% 1.81/1.24  % [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 ... 
% 2.76/1.68  % [INFO] 	 Killing All external provers ... 
% 2.76/1.68  % Time passed: 1155ms (effective reasoning time: 708ms)
% 2.76/1.68  % 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)>
% 2.76/1.68  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1155 ms resp. 708 ms w/o parsing
% 3.01/1.70  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.01/1.70  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------