%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEU728^2 : 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 03:39:23 EDT 2024

% Result   : Theorem 2.85s 1.56s
% Output   : Refutation 2.85s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   11 (   3 unt;   5 typ;   2 def)
%            Number of atoms       :   31 (   2 equ;   0 cnn)
%            Maximal formula atoms :    9 (   5 avg)
%            Number of connectives :   94 (   6   ~;   0   |;   0   &;  67   @)
%                                         (   0 <=>;  21  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   21 (   0   ^  21   !;   0   ?;  21   :)

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

thf(powerset_type,type,
    powerset: $i > $i ).

thf(setminus_type,type,
    setminus: $i > $i > $i ).

thf(setminusI_type,type,
    setminusI: $o ).

thf(setminusI_def,definition,
    ( setminusI
    = ( ! [A: $i,B: $i,C: $i] :
          ( ( in @ C @ A )
         => ( ~ ( in @ C @ B )
           => ( in @ C @ ( setminus @ A @ B ) ) ) ) ) ) ).

thf(setminusER_type,type,
    setminusER: $o ).

thf(setminusER_def,definition,
    ( setminusER
    = ( ! [A: $i,B: $i,C: $i] :
          ( ( in @ C @ ( setminus @ A @ B ) )
         => ~ ( in @ C @ B ) ) ) ) ).

thf(1,conjecture,
    ( setminusI
   => ( setminusER
     => ! [A: $i,B: $i] :
          ( ( in @ B @ ( powerset @ A ) )
         => ! [C: $i] :
              ( ( in @ C @ A )
             => ( ( in @ C @ ( setminus @ A @ ( setminus @ A @ B ) ) )
               => ( in @ C @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',doubleComplementE1) ).

thf(2,negated_conjecture,
    ~ ( setminusI
     => ( setminusER
       => ! [A: $i,B: $i] :
            ( ( in @ B @ ( powerset @ A ) )
           => ! [C: $i] :
                ( ( in @ C @ A )
               => ( ( in @ C @ ( setminus @ A @ ( setminus @ A @ B ) ) )
                 => ( in @ C @ B ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(14,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU728^2 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n004.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 : Sun May 19 17:16:39 EDT 2024
% 0.15/0.37  % CPUTime  : 
% 0.98/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.22/0.96  % [INFO] 	 Parsing done (97ms). 
% 1.22/0.97  % [INFO] 	 Running in sequential loop mode. 
% 1.57/1.16  % [INFO] 	 eprover registered as external prover. 
% 1.57/1.17  % [INFO] 	 cvc4 registered as external prover. 
% 1.57/1.17  % [INFO] 	 Scanning for conjecture ... 
% 1.70/1.23  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.87/1.25  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.87/1.25  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.87/1.25  % [INFO] 	 Type checking passed. 
% 1.87/1.25  % [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 ... 
% 2.85/1.56  % External prover 'e' found a proof!
% 2.85/1.56  % [INFO] 	 Killing All external provers ... 
% 2.85/1.56  % Time passed: 1036ms (effective reasoning time: 594ms)
% 2.85/1.56  % 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)>
% 2.85/1.56  % Axioms used in derivation (0): 
% 2.85/1.56  % No. of inferences in proof: 4
% 2.85/1.56  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1036 ms resp. 594 ms w/o parsing
% 2.85/1.58  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.85/1.58  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------