TSTP Solution File: SEU742^2 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEU742^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n026.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 03:39:30 EDT 2024

% Result   : Theorem 2.83s 1.69s
% Output   : Refutation 3.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   14 (   4 unt;   7 typ;   3 def)
%            Number of atoms       :   61 (   3 equ;   0 cnn)
%            Maximal formula atoms :   21 (   8 avg)
%            Number of connectives :  211 (   2   ~;   0   |;   0   &; 161   @)
%                                         (   0 <=>;  48  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   9 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   41 (   0   ^  41   !;   0   ?;  41   :)

% 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(binintersectI_type,type,
    binintersectI: $o ).

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

thf(inIntersectImpInUnion_type,type,
    inIntersectImpInUnion: $o ).

thf(inIntersectImpInUnion_def,definition,
    ( inIntersectImpInUnion
    = ( ! [A: $i,B: $i] :
          ( ( in @ B @ ( powerset @ A ) )
         => ! [C: $i] :
              ( ( in @ C @ ( powerset @ A ) )
             => ! [D: $i] :
                  ( ( in @ D @ ( powerset @ A ) )
                 => ! [E: $i] :
                      ( ( in @ E @ A )
                     => ( ( in @ E @ ( binintersect @ B @ C ) )
                       => ( in @ E @ ( binunion @ B @ D ) ) ) ) ) ) ) ) ) ).

thf(inIntersectImpInUnion2_type,type,
    inIntersectImpInUnion2: $o ).

thf(inIntersectImpInUnion2_def,definition,
    ( inIntersectImpInUnion2
    = ( ! [A: $i,B: $i] :
          ( ( in @ B @ ( powerset @ A ) )
         => ! [C: $i] :
              ( ( in @ C @ ( powerset @ A ) )
             => ! [D: $i] :
                  ( ( in @ D @ ( powerset @ A ) )
                 => ! [E: $i] :
                      ( ( in @ E @ A )
                     => ( ( in @ E @ ( binintersect @ B @ C ) )
                       => ( in @ E @ ( binunion @ C @ D ) ) ) ) ) ) ) ) ) ).

thf(1,conjecture,
    ( binintersectI
   => ( inIntersectImpInUnion
     => ( inIntersectImpInUnion2
       => ! [A: $i,B: $i] :
            ( ( in @ B @ ( powerset @ A ) )
           => ! [C: $i] :
                ( ( in @ C @ ( powerset @ A ) )
               => ! [D: $i] :
                    ( ( in @ D @ ( powerset @ A ) )
                   => ! [E: $i] :
                        ( ( in @ E @ A )
                       => ( ( in @ E @ ( binintersect @ B @ C ) )
                         => ( in @ E @ ( binintersect @ ( binunion @ B @ D ) @ ( binunion @ C @ D ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inIntersectImpInIntersectUnions) ).

thf(2,negated_conjecture,
    ~ ( binintersectI
     => ( inIntersectImpInUnion
       => ( inIntersectImpInUnion2
         => ! [A: $i,B: $i] :
              ( ( in @ B @ ( powerset @ A ) )
             => ! [C: $i] :
                  ( ( in @ C @ ( powerset @ A ) )
                 => ! [D: $i] :
                      ( ( in @ D @ ( powerset @ A ) )
                     => ! [E: $i] :
                          ( ( in @ E @ A )
                         => ( ( in @ E @ ( binintersect @ B @ C ) )
                           => ( in @ E @ ( binintersect @ ( binunion @ B @ D ) @ ( binunion @ C @ D ) ) ) ) ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(15,plain,
    $false,
    inference(cvc4,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SEU742^2 : TPTP v8.2.0. Released v3.7.0.
% 0.11/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n026.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Sun May 19 18:04:39 EDT 2024
% 0.16/0.36  % CPUTime  : 
% 0.86/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.17/0.97  % [INFO] 	 Parsing done (108ms). 
% 1.17/0.98  % [INFO] 	 Running in sequential loop mode. 
% 1.72/1.19  % [INFO] 	 eprover registered as external prover. 
% 1.74/1.19  % [INFO] 	 cvc4 registered as external prover. 
% 1.74/1.19  % [INFO] 	 Scanning for conjecture ... 
% 1.85/1.27  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.85/1.29  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.85/1.29  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.85/1.30  % [INFO] 	 Type checking passed. 
% 1.85/1.30  % [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 ... 
% 2.83/1.63  % External prover 'cvc4' found a proof!
% 2.83/1.64  % [INFO] 	 Killing All external provers ... 
% 2.83/1.64  % Time passed: 1117ms (effective reasoning time: 659ms)
% 2.83/1.64  % 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)>
% 2.83/1.69  % Axioms used in derivation (0): 
% 2.83/1.69  % No. of inferences in proof: 4
% 2.83/1.69  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1117 ms resp. 659 ms w/o parsing
% 3.15/1.72  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.15/1.72  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------