TSTP Solution File: SEU519^2 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEU519^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n023.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 03:37:57 EDT 2024

% Result   : Theorem 3.67s 2.30s
% Output   : Refutation 3.67s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   24 (   9 unt;   7 typ;   2 def)
%            Number of atoms       :   42 (   4 equ;   0 cnn)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  112 (  10   ~;   5   |;   0   &;  80   @)
%                                         (   0 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :   33 (   0   ^  32   !;   1   ?;  33   :)

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

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

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

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

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

thf(powersetI_type,type,
    powersetI: $o ).

thf(powersetI_def,definition,
    ( powersetI
    = ( ! [A: $i,B: $i] :
          ( ! [C: $i] :
              ( ( in @ C @ B )
             => ( in @ C @ A ) )
         => ( in @ B @ ( powerset @ A ) ) ) ) ) ).

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

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

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

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

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

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

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

thf(6,plain,
    ! [B: $i,A: $i] :
      ( ( in @ ( sk1 @ B @ A ) @ B )
      | ( in @ B @ ( powerset @ A ) ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(9,plain,
    ! [B: $i,A: $i] :
      ( ( in @ ( sk1 @ B @ A ) @ B )
      | ( in @ B @ ( powerset @ A ) ) ),
    inference(simp,[status(thm)],[6]) ).

thf(8,plain,
    ! [B: $o,A: $i] :
      ( ~ ( in @ A @ emptyset )
      | B ),
    inference(cnf,[status(esa)],[4]) ).

thf(11,plain,
    ! [B: $o,A: $i] :
      ( ~ ( in @ A @ emptyset )
      | ( B
       != ( in @ emptyset @ ( powerset @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[8,5]) ).

thf(12,plain,
    ! [A: $i] :
      ~ ( in @ A @ emptyset ),
    inference(pattern_uni,[status(thm)],[11:[bind(A,$thf( A )),bind(B,$thf( in @ emptyset @ ( powerset @ sk2 ) ))]]) ).

thf(34,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( in @ B @ ( powerset @ A ) )
      | ( ( in @ ( sk1 @ B @ A ) @ B )
       != ( in @ C @ emptyset ) ) ),
    inference(paramod_ordered,[status(thm)],[9,12]) ).

thf(35,plain,
    ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ),
    inference(pattern_uni,[status(thm)],[34:[bind(A,$thf( E )),bind(B,$thf( emptyset )),bind(C,$thf( sk1 @ emptyset @ E ))]]) ).

thf(40,plain,
    ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ),
    inference(simp,[status(thm)],[35]) ).

thf(43,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[5,40]) ).

thf(44,plain,
    $false,
    inference(simp,[status(thm)],[43]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09  % Problem  : SEU519^2 : TPTP v8.2.0. Released v3.7.0.
% 0.02/0.12  % Command  : run_Leo-III %s %d
% 0.11/0.32  % Computer : n023.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Sun May 19 15:39:09 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 1.04/0.96  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.29/1.12  % [INFO] 	 Parsing done (161ms). 
% 1.29/1.14  % [INFO] 	 Running in sequential loop mode. 
% 1.91/1.50  % [INFO] 	 eprover registered as external prover. 
% 1.91/1.50  % [INFO] 	 cvc4 registered as external prover. 
% 1.91/1.51  % [INFO] 	 Scanning for conjecture ... 
% 2.02/1.61  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.14/1.64  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.14/1.64  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.14/1.64  % [INFO] 	 Type checking passed. 
% 2.14/1.65  % [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 ... 
% 3.67/2.30  % [INFO] 	 Killing All external provers ... 
% 3.67/2.30  % Time passed: 1826ms (effective reasoning time: 1155ms)
% 3.67/2.30  % 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)>
% 3.67/2.30  % Axioms used in derivation (0): 
% 3.67/2.30  % No. of inferences in proof: 15
% 3.67/2.30  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1826 ms resp. 1155 ms w/o parsing
% 3.67/2.34  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.67/2.34  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------