TSTP Solution File: SEU753^2 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEU753^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n014.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 03:39:36 EDT 2024

% Result   : Theorem 88.27s 16.69s
% Output   : Refutation 88.27s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   21 (   7 unt;  11 typ;   6 def)
%            Number of atoms       :   88 (  11 equ;   0 cnn)
%            Maximal formula atoms :   30 (   8 avg)
%            Number of connectives :  300 (   2   ~;   0   |;   0   &; 232   @)
%                                         (   0 <=>;  66  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  11 usr;   7 con; 0-2 aty)
%            Number of variables   :   51 (   0   ^  51   !;   0   ?;  51   :)

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

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

thf(binunion_type,type,
    binunion: $i > $i > $i ).

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

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

thf(binintersectT_lem_type,type,
    binintersectT_lem: $o ).

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

thf(binunionT_lem_type,type,
    binunionT_lem: $o ).

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

thf(complementT_lem_type,type,
    complementT_lem: $o ).

thf(complementT_lem_def,definition,
    ( complementT_lem
    = ( ! [A: $i,B: $i] :
          ( ( in @ B @ ( powerset @ A ) )
         => ( in @ ( setminus @ A @ B ) @ ( powerset @ A ) ) ) ) ) ).

thf(setextT_type,type,
    setextT: $o ).

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

thf(demorgan1a_type,type,
    demorgan1a: $o ).

thf(demorgan1a_def,definition,
    ( demorgan1a
    = ( ! [A: $i,B: $i] :
          ( ( in @ B @ ( powerset @ A ) )
         => ! [C: $i] :
              ( ( in @ C @ ( powerset @ A ) )
             => ! [D: $i] :
                  ( ( in @ D @ A )
                 => ( ( in @ D @ ( setminus @ A @ ( binintersect @ B @ C ) ) )
                   => ( in @ D @ ( binunion @ ( setminus @ A @ B ) @ ( setminus @ A @ C ) ) ) ) ) ) ) ) ) ).

thf(demorgan1b_type,type,
    demorgan1b: $o ).

thf(demorgan1b_def,definition,
    ( demorgan1b
    = ( ! [A: $i,B: $i] :
          ( ( in @ B @ ( powerset @ A ) )
         => ! [C: $i] :
              ( ( in @ C @ ( powerset @ A ) )
             => ! [D: $i] :
                  ( ( in @ D @ A )
                 => ( ( in @ D @ ( binunion @ ( setminus @ A @ B ) @ ( setminus @ A @ C ) ) )
                   => ( in @ D @ ( setminus @ A @ ( binintersect @ B @ C ) ) ) ) ) ) ) ) ) ).

thf(1,conjecture,
    ( binintersectT_lem
   => ( binunionT_lem
     => ( complementT_lem
       => ( setextT
         => ( demorgan1a
           => ( demorgan1b
             => ! [A: $i,B: $i] :
                  ( ( in @ B @ ( powerset @ A ) )
                 => ! [C: $i] :
                      ( ( in @ C @ ( powerset @ A ) )
                     => ( ( setminus @ A @ ( binintersect @ B @ C ) )
                        = ( binunion @ ( setminus @ A @ B ) @ ( setminus @ A @ C ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan1) ).

thf(2,negated_conjecture,
    ~ ( binintersectT_lem
     => ( binunionT_lem
       => ( complementT_lem
         => ( setextT
           => ( demorgan1a
             => ( demorgan1b
               => ! [A: $i,B: $i] :
                    ( ( in @ B @ ( powerset @ A ) )
                   => ! [C: $i] :
                        ( ( in @ C @ ( powerset @ A ) )
                       => ( ( setminus @ A @ ( binintersect @ B @ C ) )
                          = ( binunion @ ( setminus @ A @ B ) @ ( setminus @ A @ C ) ) ) ) ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(42996,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SEU753^2 : TPTP v8.2.0. Released v3.7.0.
% 0.06/0.15  % Command  : run_Leo-III %s %d
% 0.14/0.35  % Computer : n014.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Sun May 19 16:31:54 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.94/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.21/0.97  % [INFO] 	 Parsing done (119ms). 
% 1.21/0.98  % [INFO] 	 Running in sequential loop mode. 
% 1.69/1.19  % [INFO] 	 eprover registered as external prover. 
% 1.69/1.19  % [INFO] 	 cvc4 registered as external prover. 
% 1.69/1.19  % [INFO] 	 Scanning for conjecture ... 
% 2.04/1.28  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.04/1.30  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.04/1.30  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.04/1.30  % [INFO] 	 Type checking passed. 
% 2.04/1.31  % [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 ... 
% 88.27/16.69  % External prover 'e' found a proof!
% 88.27/16.69  % [INFO] 	 Killing All external provers ... 
% 88.27/16.69  % Time passed: 16174ms (effective reasoning time: 15707ms)
% 88.27/16.69  % 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)>
% 88.27/16.69  % Axioms used in derivation (0): 
% 88.27/16.69  % No. of inferences in proof: 4
% 88.27/16.69  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 16174 ms resp. 15707 ms w/o parsing
% 88.27/16.71  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 88.27/16.71  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------