TSTP Solution File: SET143^3 by Leo-III---1.7.10

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.10
% Problem  : SET143^3 : TPTP v8.1.2. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n015.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  7 08:06:49 EDT 2024

% Result   : Theorem 3.33s 1.81s
% Output   : Refutation 3.33s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   17 (  10 unt;   5 typ;   1 def)
%            Number of atoms       :   51 (   8 equ;   0 cnn)
%            Maximal formula atoms :    6 (   4 avg)
%            Number of connectives :   88 (   6   ~;   2   |;  25   &;  55   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   19 (  19   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   5 usr;   3 con; 0-3 aty)
%            Number of variables   :   18 (   9   ^   9   !;   0   ?;  18   :)

% Comments : 
%------------------------------------------------------------------------------
thf(intersection_type,type,
    intersection: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(intersection_def,definition,
    ( intersection
    = ( ^ [A: $i > $o,B: $i > $o,C: $i] :
          ( ( A @ C )
          & ( B @ C ) ) ) ) ).

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

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

thf(sk3_type,type,
    sk3: $i > $o ).

thf(sk4_type,type,
    sk4: $i ).

thf(1,conjecture,
    ! [A: $i > $o,B: $i > $o,C: $i > $o] :
      ( ( intersection @ ( intersection @ A @ B ) @ C )
      = ( intersection @ A @ ( intersection @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).

thf(2,negated_conjecture,
    ~ ! [A: $i > $o,B: $i > $o,C: $i > $o] :
        ( ( intersection @ ( intersection @ A @ B ) @ C )
        = ( intersection @ A @ ( intersection @ B @ C ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(4,plain,
    ( ( ^ [A: $i] :
          ( ( sk1 @ A )
          & ( sk2 @ A )
          & ( sk3 @ A ) ) )
   != ( ^ [A: $i] :
          ( ( sk1 @ A )
          & ( sk2 @ A )
          & ( sk3 @ A ) ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(5,plain,
    ( ( ^ [A: $i] :
          ( ( sk1 @ A )
          & ( sk2 @ A )
          & ( sk3 @ A ) ) )
   != ( ^ [A: $i] :
          ( ( sk1 @ A )
          & ( sk2 @ A )
          & ( sk3 @ A ) ) ) ),
    inference(lifteq,[status(thm)],[4]) ).

thf(7,plain,
    ( ( ( sk1 @ sk4 )
      & ( sk2 @ sk4 )
      & ( sk3 @ sk4 ) )
   != ( ( sk1 @ sk4 )
      & ( sk2 @ sk4 )
      & ( sk3 @ sk4 ) ) ),
    inference(func_ext,[status(esa)],[5]) ).

thf(10,plain,
    ( ( ( sk1 @ sk4 )
      & ( sk2 @ sk4 )
      & ( sk3 @ sk4 ) )
    | ( ( sk1 @ sk4 )
      & ( sk2 @ sk4 )
      & ( sk3 @ sk4 ) ) ),
    inference(bool_ext,[status(thm)],[7]) ).

thf(14,plain,
    ( ( sk2 @ sk4 )
    | ( sk2 @ sk4 ) ),
    inference(cnf,[status(esa)],[10]) ).

thf(19,plain,
    sk2 @ sk4,
    inference(simp,[status(thm)],[14]) ).

thf(22,plain,
    ( ( ( sk1 @ sk4 )
      & $true
      & ( sk3 @ sk4 ) )
   != ( ( sk1 @ sk4 )
      & $true
      & ( sk3 @ sk4 ) ) ),
    inference(rewrite,[status(thm)],[7,19]) ).

thf(23,plain,
    $false,
    inference(simp,[status(thm)],[22]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : SET143^3 : TPTP v8.1.2. Released v3.6.0.
% 0.03/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.35  % Computer : n015.cluster.edu
% 0.16/0.35  % Model    : x86_64 x86_64
% 0.16/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35  % Memory   : 8042.1875MB
% 0.16/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35  % CPULimit : 300
% 0.16/0.35  % WCLimit  : 300
% 0.16/0.35  % DateTime : Mon May  6 13:19:09 EDT 2024
% 0.16/0.36  % CPUTime  : 
% 0.93/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.14/0.98  % [INFO] 	 Parsing done (132ms). 
% 1.32/0.99  % [INFO] 	 Running in sequential loop mode. 
% 1.64/1.22  % [INFO] 	 eprover registered as external prover. 
% 1.64/1.22  % [INFO] 	 cvc4 registered as external prover. 
% 1.64/1.23  % [INFO] 	 Scanning for conjecture ... 
% 1.90/1.30  % [INFO] 	 Found a conjecture and 0 axioms. Running axiom selection ... 
% 1.90/1.32  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.90/1.32  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.90/1.33  % [INFO] 	 Type checking passed. 
% 1.90/1.33  % [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 ... 
% 3.33/1.80  % [INFO] 	 Killing All external provers ... 
% 3.33/1.81  % Time passed: 1276ms (effective reasoning time: 810ms)
% 3.33/1.81  % 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)>
% 3.33/1.81  % Axioms used in derivation (0): 
% 3.33/1.81  % No. of inferences in proof: 11
% 3.33/1.81  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1276 ms resp. 810 ms w/o parsing
% 3.33/1.83  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.33/1.83  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------