TSTP Solution File: SEU735^2 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEU735^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n002.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 03:39:26 EDT 2024

% Result   : Theorem 2.88s 1.58s
% Output   : Refutation 2.88s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   13 (   3 unt;   7 typ;   2 def)
%            Number of atoms       :   28 (   2 equ;   0 cnn)
%            Maximal formula atoms :    8 (   4 avg)
%            Number of connectives :  103 (   2   ~;   0   |;   0   &;  83   @)
%                                         (   0 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   19 (   0   ^  19   !;   0   ?;  19   :)

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

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

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

thf(powersetI1_type,type,
    powersetI1: $o ).

thf(powersetI1_def,definition,
    ( powersetI1
    = ( ! [A: $i,B: $i] :
          ( ( subset @ B @ A )
         => ( in @ B @ ( powerset @ A ) ) ) ) ) ).

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

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

thf(complementSubsetComplementIntersect_type,type,
    complementSubsetComplementIntersect: $o ).

thf(complementSubsetComplementIntersect_def,definition,
    ( complementSubsetComplementIntersect
    = ( ! [A: $i,B: $i] :
          ( ( in @ B @ ( powerset @ A ) )
         => ! [C: $i] :
              ( ( in @ C @ ( powerset @ A ) )
             => ( subset @ ( setminus @ A @ B ) @ ( setminus @ A @ ( binintersect @ B @ C ) ) ) ) ) ) ) ).

thf(1,conjecture,
    ( powersetI1
   => ( complementSubsetComplementIntersect
     => ! [A: $i,B: $i] :
          ( ( in @ B @ ( powerset @ A ) )
         => ! [C: $i] :
              ( ( in @ C @ ( powerset @ A ) )
             => ( in @ ( setminus @ A @ B ) @ ( powerset @ ( setminus @ A @ ( binintersect @ B @ C ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementInPowersetComplementIntersect) ).

thf(2,negated_conjecture,
    ~ ( powersetI1
     => ( complementSubsetComplementIntersect
       => ! [A: $i,B: $i] :
            ( ( in @ B @ ( powerset @ A ) )
           => ! [C: $i] :
                ( ( in @ C @ ( powerset @ A ) )
               => ( in @ ( setminus @ A @ B ) @ ( powerset @ ( setminus @ A @ ( binintersect @ B @ C ) ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(14,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : SEU735^2 : TPTP v8.2.0. Released v3.7.0.
% 0.11/0.14  % Command  : run_Leo-III %s %d
% 0.14/0.35  % Computer : n002.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 16:30:09 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.83/0.84  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.23/0.95  % [INFO] 	 Parsing done (99ms). 
% 1.23/0.95  % [INFO] 	 Running in sequential loop mode. 
% 1.48/1.16  % [INFO] 	 eprover registered as external prover. 
% 1.48/1.16  % [INFO] 	 cvc4 registered as external prover. 
% 1.48/1.16  % [INFO] 	 Scanning for conjecture ... 
% 1.78/1.23  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.92/1.25  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.92/1.25  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.92/1.25  % [INFO] 	 Type checking passed. 
% 1.92/1.25  % [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 ... 
% 2.88/1.58  % External prover 'e' found a proof!
% 2.88/1.58  % [INFO] 	 Killing All external provers ... 
% 2.88/1.58  % Time passed: 1071ms (effective reasoning time: 625ms)
% 2.88/1.58  % 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)>
% 2.88/1.58  % Axioms used in derivation (0): 
% 2.88/1.58  % No. of inferences in proof: 4
% 2.88/1.58  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1071 ms resp. 625 ms w/o parsing
% 2.88/1.61  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.88/1.61  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------