TSTP Solution File: SET609^3 by Leo-III---1.7.10

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.10
% Problem  : SET609^3 : TPTP v8.1.2. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n010.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 08:07:36 EDT 2024

% Result   : Theorem 3.92s 1.83s
% Output   : Refutation 3.92s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   26 (  15 unt;   7 typ;   3 def)
%            Number of atoms       :   80 (  12 equ;   0 cnn)
%            Maximal formula atoms :    7 (   4 avg)
%            Number of connectives :  167 (  41   ~;  15   |;  29   &;  82   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   33 (  33   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   7 usr;   3 con; 0-3 aty)
%            Number of variables   :   24 (  15   ^   9   !;   0   ?;  24   :)

% Comments : 
%------------------------------------------------------------------------------
thf(union_type,type,
    union: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(union_def,definition,
    ( union
    = ( ^ [A: $i > $o,B: $i > $o,C: $i] :
          ( ( A @ C )
          | ( B @ C ) ) ) ) ).

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 > $o ).

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

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

thf(2,negated_conjecture,
    ~ ! [A: $i > $o,B: $i > $o,C: $i > $o] :
        ( ( setminus @ A @ ( setminus @ B @ C ) )
        = ( union @ ( setminus @ A @ B ) @ ( intersection @ A @ 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 ) )
              | ( ( A @ 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 ) )
          | ( ( sk1 @ 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 ) )
          | ( ( sk1 @ A )
            & ( sk3 @ A ) ) ) ) ),
    inference(lifteq,[status(thm)],[4]) ).

thf(6,plain,
    ( ( ( sk1 @ sk4 )
      & ~ ( ( sk2 @ sk4 )
          & ~ ( sk3 @ sk4 ) ) )
   != ( ( ( sk1 @ sk4 )
        & ~ ( sk2 @ sk4 ) )
      | ( ( sk1 @ sk4 )
        & ( sk3 @ sk4 ) ) ) ),
    inference(func_ext,[status(esa)],[5]) ).

thf(8,plain,
    ( ( ( sk1 @ sk4 )
      & ~ ( ( sk2 @ sk4 )
          & ~ ( sk3 @ sk4 ) ) )
    | ( ( sk1 @ sk4 )
      & ~ ( sk2 @ sk4 ) )
    | ( ( sk1 @ sk4 )
      & ( sk3 @ sk4 ) ) ),
    inference(bool_ext,[status(thm)],[6]) ).

thf(17,plain,
    ( ( sk1 @ sk4 )
    | ( sk1 @ sk4 )
    | ( sk1 @ sk4 ) ),
    inference(cnf,[status(esa)],[8]) ).

thf(25,plain,
    sk1 @ sk4,
    inference(simp,[status(thm)],[17]) ).

thf(30,plain,
    ( ( $true
      & ~ ( ( sk2 @ sk4 )
          & ~ ( sk3 @ sk4 ) ) )
   != ( ( $true
        & ~ ( sk2 @ sk4 ) )
      | ( $true
        & ( sk3 @ sk4 ) ) ) ),
    inference(rewrite,[status(thm)],[6,25]) ).

thf(31,plain,
    ( ( ~ ( ( sk2 @ sk4 )
          & ~ ( sk3 @ sk4 ) ) )
   != ( ~ ( sk2 @ sk4 )
      | ( sk3 @ sk4 ) ) ),
    inference(simp,[status(thm)],[30]) ).

thf(32,plain,
    ( ~ ~ ( ( sk2 @ sk4 )
          & ~ ( sk3 @ sk4 ) )
    | ~ ( ~ ( sk2 @ sk4 )
        | ( sk3 @ sk4 ) ) ),
    inference(bool_ext,[status(thm)],[31]) ).

thf(35,plain,
    ( ~ ( sk3 @ sk4 )
    | ~ ( sk3 @ sk4 ) ),
    inference(cnf,[status(esa)],[32]) ).

thf(37,plain,
    ~ ( sk3 @ sk4 ),
    inference(simp,[status(thm)],[35]) ).

thf(41,plain,
    ( ( ~ ( ( sk2 @ sk4 )
          & ~ $false ) )
   != ( ~ ( sk2 @ sk4 )
      | $false ) ),
    inference(rewrite,[status(thm)],[31,37]) ).

thf(42,plain,
    $false,
    inference(simp,[status(thm)],[41]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SET609^3 : TPTP v8.1.2. Released v3.6.0.
% 0.12/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n010.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Mon May  6 13:21:09 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 1.01/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.21/1.00  % [INFO] 	 Parsing done (140ms). 
% 1.21/1.01  % [INFO] 	 Running in sequential loop mode. 
% 1.85/1.22  % [INFO] 	 eprover registered as external prover. 
% 1.85/1.22  % [INFO] 	 cvc4 registered as external prover. 
% 1.85/1.23  % [INFO] 	 Scanning for conjecture ... 
% 1.96/1.30  % [INFO] 	 Found a conjecture and 0 axioms. Running axiom selection ... 
% 1.96/1.33  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.96/1.33  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.96/1.33  % [INFO] 	 Type checking passed. 
% 1.96/1.33  % [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 ... 
% 3.69/1.83  % [INFO] 	 Killing All external provers ... 
% 3.92/1.83  % Time passed: 1298ms (effective reasoning time: 817ms)
% 3.92/1.83  % 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)>
% 3.92/1.83  % Axioms used in derivation (0): 
% 3.92/1.83  % No. of inferences in proof: 16
% 3.92/1.83  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1298 ms resp. 817 ms w/o parsing
% 3.92/1.86  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.92/1.86  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------