%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEU609^2 : 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 03:38:33 EDT 2024

% Result   : Theorem 3.20s 2.25s
% Output   : Refutation 3.20s
% 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       :   22 (   2 equ;   0 cnn)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives :   50 (   2   ~;   0   |;   0   &;  36   @)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   18 (   0   ^  18   !;   0   ?;  18   :)

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

thf(subset_type,type,
    subset: $i > $i > $o ).

thf(subsetI2_type,type,
    subsetI2: $o ).

thf(subsetI2_def,definition,
    ( subsetI2
    = ( ! [A: $i,B: $i] :
          ( ! [C: $i] :
              ( ( in @ C @ A )
             => ( in @ C @ B ) )
         => ( subset @ A @ B ) ) ) ) ).

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

thf(setminusEL_type,type,
    setminusEL: $o ).

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

thf(1,conjecture,
    ( subsetI2
   => ( setminusEL
     => ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusLsub) ).

thf(2,negated_conjecture,
    ~ ( subsetI2
     => ( setminusEL
       => ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(11,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : SEU609^2 : TPTP v8.2.0. Released v3.7.0.
% 0.10/0.13  % Command  : run_Leo-III %s %d
% 0.12/0.33  % Computer : n004.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 May 19 16:52:09 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 0.99/1.12  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.27/1.29  % [INFO] 	 Parsing done (158ms). 
% 1.27/1.30  % [INFO] 	 Running in sequential loop mode. 
% 1.72/1.61  % [INFO] 	 eprover registered as external prover. 
% 1.72/1.61  % [INFO] 	 cvc4 registered as external prover. 
% 1.72/1.62  % [INFO] 	 Scanning for conjecture ... 
% 2.03/1.72  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.03/1.75  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.03/1.76  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.03/1.76  % [INFO] 	 Type checking passed. 
% 2.03/1.76  % [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 ... 
% 3.20/2.25  % External prover 'e' found a proof!
% 3.20/2.25  % [INFO] 	 Killing All external provers ... 
% 3.20/2.25  % Time passed: 1728ms (effective reasoning time: 942ms)
% 3.20/2.25  % 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)>
% 3.20/2.25  % Axioms used in derivation (0): 
% 3.20/2.25  % No. of inferences in proof: 4
% 3.20/2.25  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1728 ms resp. 942 ms w/o parsing
% 3.20/2.28  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.20/2.28  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------