%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEU535^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n004.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 03:42:33 EDT 2024

% Result   : Theorem 2.84s 1.70s
% Output   : Refutation 2.84s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   18 (   7 unt;   5 typ;   1 def)
%            Number of atoms       :   19 (   2 equ;   0 cnn)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   47 (   7   ~;   2   |;   0   &;  27   @)
%                                         (   0 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   5 usr;   5 con; 0-2 aty)
%            Number of variables   :   20 (   0   ^  19   !;   1   ?;  20   :)

% Comments : 
%------------------------------------------------------------------------------
thf(in_type,type,
    in: $i > $i > $o ).

thf(emptyset_type,type,
    emptyset: $i ).

thf(emptysetE_type,type,
    emptysetE: $o ).

thf(emptysetE_def,definition,
    ( emptysetE
    = ( ! [A: $i] :
          ( ( in @ A @ emptyset )
         => ! [B: $o] : B ) ) ) ).

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

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

thf(1,conjecture,
    ( emptysetE
   => ! [A: $i > $o,B: $i] :
        ( ( in @ B @ emptyset )
       => ( A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',vacuousDall) ).

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

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

thf(4,plain,
    ~ ( ( ? [A: $i] : ( in @ A @ emptyset )
       => ! [A: $o] : A )
     => ! [A: $i > $o,B: $i] :
          ( ( in @ B @ emptyset )
         => ( A @ B ) ) ),
    inference(miniscope,[status(thm)],[3]) ).

thf(5,plain,
    ~ ( sk1 @ sk2 ),
    inference(cnf,[status(esa)],[4]) ).

thf(6,plain,
    in @ sk2 @ emptyset,
    inference(cnf,[status(esa)],[4]) ).

thf(7,plain,
    ! [B: $o,A: $i] :
      ( ~ ( in @ A @ emptyset )
      | B ),
    inference(cnf,[status(esa)],[4]) ).

thf(9,plain,
    ! [B: $o,A: $i] :
      ( B
      | ( ( in @ sk2 @ emptyset )
       != ( in @ A @ emptyset ) ) ),
    inference(paramod_ordered,[status(thm)],[6,7]) ).

thf(10,plain,
    ! [A: $o] : A,
    inference(pattern_uni,[status(thm)],[9:[bind(A,$thf( sk2 ))]]) ).

thf(28,plain,
    ! [A: $o] : A,
    inference(simp,[status(thm)],[10]) ).

thf(31,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[5,28]) ).

thf(32,plain,
    $false,
    inference(simp,[status(thm)],[31]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14  % Problem  : SEU535^2 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.17  % Command  : run_Leo-III %s %d
% 0.17/0.38  % Computer : n004.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 : Sun May 19 17:19:24 EDT 2024
% 0.17/0.39  % CPUTime  : 
% 1.01/0.90  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.12/1.00  % [INFO] 	 Parsing done (102ms). 
% 1.12/1.01  % [INFO] 	 Running in sequential loop mode. 
% 1.66/1.24  % [INFO] 	 nitpick registered as external prover. 
% 1.66/1.24  % [INFO] 	 Scanning for conjecture ... 
% 1.76/1.30  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.76/1.32  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.76/1.32  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.76/1.32  % [INFO] 	 Type checking passed. 
% 1.76/1.32  % [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 ... 
% 2.66/1.69  % [INFO] 	 Killing All external provers ... 
% 2.66/1.69  % Time passed: 1140ms (effective reasoning time: 675ms)
% 2.66/1.69  % 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)>
% 2.84/1.69  % Axioms used in derivation (0): 
% 2.84/1.69  % No. of inferences in proof: 12
% 2.84/1.70  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1140 ms resp. 675 ms w/o parsing
% 2.84/1.72  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.84/1.72  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------