%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEU722^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n032.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 03:39:20 EDT 2024

% Result   : Theorem 2.04s 1.36s
% Output   : Refutation 2.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    6
% Syntax   : Number of formulae    :    9 (   2 unt;   4 typ;   1 def)
%            Number of atoms       :   24 (   1 equ;   0 cnn)
%            Maximal formula atoms :    7 (   4 avg)
%            Number of connectives :   79 (   8   ~;   0   |;   0   &;  54   @)
%                                         (   0 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   9 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   18 (   0   ^  18   !;   0   ?;  18   :)

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

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

thf(binintersect_type,type,
    binintersect: $i > $i > $i ).

thf(binintersectER_type,type,
    binintersectER: $o ).

thf(binintersectER_def,definition,
    ( binintersectER
    = ( ! [A: $i,B: $i,C: $i] :
          ( ( in @ C @ ( binintersect @ A @ B ) )
         => ( in @ C @ B ) ) ) ) ).

thf(1,conjecture,
    ( binintersectER
   => ! [A: $i,B: $i] :
        ( ( in @ B @ ( powerset @ A ) )
       => ! [C: $i] :
            ( ( in @ C @ ( powerset @ A ) )
           => ! [D: $i] :
                ( ( in @ D @ A )
               => ( ~ ( in @ D @ C )
                 => ~ ( in @ D @ ( binintersect @ B @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectTERcontra) ).

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

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

thf(13,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09  % Problem  : SEU722^2 : TPTP v8.2.0. Released v3.7.0.
% 0.02/0.11  % Command  : run_Leo-III %s %d
% 0.10/0.30  % Computer : n032.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit : 300
% 0.10/0.30  % WCLimit  : 300
% 0.10/0.30  % DateTime : Sun May 19 16:42:09 EDT 2024
% 0.10/0.30  % CPUTime  : 
% 0.68/0.69  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 0.91/0.80  % [INFO] 	 Parsing done (99ms). 
% 0.91/0.80  % [INFO] 	 Running in sequential loop mode. 
% 1.22/1.01  % [INFO] 	 eprover registered as external prover. 
% 1.22/1.01  % [INFO] 	 cvc4 registered as external prover. 
% 1.22/1.01  % [INFO] 	 Scanning for conjecture ... 
% 1.40/1.07  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.51/1.09  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.51/1.09  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.51/1.09  % [INFO] 	 Type checking passed. 
% 1.51/1.10  % [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 ... 
% 2.04/1.36  % External prover 'e' found a proof!
% 2.04/1.36  % [INFO] 	 Killing All external provers ... 
% 2.04/1.36  % Time passed: 958ms (effective reasoning time: 553ms)
% 2.04/1.36  % 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)>
% 2.04/1.36  % Axioms used in derivation (0): 
% 2.04/1.36  % No. of inferences in proof: 4
% 2.04/1.36  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 958 ms resp. 553 ms w/o parsing
% 2.26/1.41  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.26/1.41  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------