TSTP Solution File: SET606^3 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SET606^3 : TPTP v8.2.0. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n004.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 03:03:08 EDT 2024

% Result   : Theorem 3.80s 1.98s
% Output   : Refutation 3.80s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   18 (  11 unt;   5 typ;   2 def)
%            Number of atoms       :   46 (   9 equ;   0 cnn)
%            Maximal formula atoms :    5 (   3 avg)
%            Number of connectives :   87 (  19   ~;   2   |;  20   &;  46   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   22 (  22   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   5 usr;   3 con; 0-3 aty)
%            Number of variables   :   18 (  12   ^   6   !;   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(setminus_type,type,
    setminus: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(setminus_def,definition,
    ( setminus
    = ( ^ [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 ).

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

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

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

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

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

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

thf(37,plain,
    ( ( ( sk1 @ sk3 )
      & ~ ( ( sk1 @ sk3 )
          & ( sk2 @ sk3 ) ) )
    | ( ( sk1 @ sk3 )
      & ~ ( sk2 @ sk3 ) ) ),
    inference(bool_ext,[status(thm)],[7]) ).

thf(49,plain,
    ( ( sk1 @ sk3 )
    | ( sk1 @ sk3 ) ),
    inference(cnf,[status(esa)],[37]) ).

thf(52,plain,
    sk1 @ sk3,
    inference(simp,[status(thm)],[49]) ).

thf(58,plain,
    ( ( $true
      & ~ ( $true
          & ( sk2 @ sk3 ) ) )
   != ( $true
      & ~ ( sk2 @ sk3 ) ) ),
    inference(rewrite,[status(thm)],[7,52]) ).

thf(59,plain,
    $false,
    inference(simp,[status(thm)],[58]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SET606^3 : TPTP v8.2.0. Released v3.6.0.
% 0.06/0.15  % Command  : run_Leo-III %s %d
% 0.14/0.36  % Computer : n004.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Mon May 20 12:27:24 EDT 2024
% 0.14/0.36  % CPUTime  : 
% 0.93/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.32/1.00  % [INFO] 	 Parsing done (133ms). 
% 1.32/1.01  % [INFO] 	 Running in sequential loop mode. 
% 1.78/1.26  % [INFO] 	 eprover registered as external prover. 
% 1.78/1.26  % [INFO] 	 cvc4 registered as external prover. 
% 1.78/1.26  % [INFO] 	 Scanning for conjecture ... 
% 1.99/1.34  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.08/1.36  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.08/1.36  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.08/1.36  % [INFO] 	 Type checking passed. 
% 2.08/1.37  % [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 ... 
% 3.64/1.98  % [INFO] 	 Killing All external provers ... 
% 3.80/1.98  % Time passed: 1471ms (effective reasoning time: 963ms)
% 3.80/1.98  % 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)>
% 3.80/1.98  % Axioms used in derivation (0): 
% 3.80/1.98  % No. of inferences in proof: 11
% 3.80/1.98  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1471 ms resp. 963 ms w/o parsing
% 3.80/2.00  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.80/2.00  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------