TSTP Solution File: SEV450^1 by Leo-III---1.7.15

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.15
% Problem  : SEV450^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d THM

% Computer : n032.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 : Mon Jun 24 15:59:03 EDT 2024

% Result   : Theorem 2.67s 1.61s
% Output   : Refutation 2.90s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   13 (  13 unt;   0 typ;   0 def)
%            Number of atoms       :   46 (  16 equ;   0 cnn)
%            Maximal formula atoms :    1 (   3 avg)
%            Number of connectives :   71 (   5   ~;   2   |;   0   &;  64   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   13 (  13   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4 usr;   2 con; 0-4 aty)
%            Number of variables   :   28 (   0   ^  28   !;   0   ?;  28   :)

% Comments : 
%------------------------------------------------------------------------------
thf('\'const/sets/UNION\'_type',type,
    '\'const/sets/UNION\'': 
      !>[TA: $tType] : ( ( TA > $o ) > ( TA > $o ) > TA > $o ) ).

thf('\'const/sets/IN\'_type',type,
    '\'const/sets/IN\'': 
      !>[TA: $tType] : ( TA > ( TA > $o ) > $o ) ).

thf(skt1_type,type,
    skt1: $tType ).

thf(sk1_type,type,
    sk1: skt1 > $o ).

thf(sk2_type,type,
    sk2: skt1 ).

thf(1,conjecture,
    ! [TA: $tType,A: TA > $o] :
      ( ( '\'const/sets/UNION\'' @ TA @ A @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/UNION_IDEMPOT_') ).

thf(2,negated_conjecture,
    ~ ! [TA: $tType,A: TA > $o] :
        ( ( '\'const/sets/UNION\'' @ TA @ A @ A )
        = A ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(6,plain,
    ~ ! [TA: $tType,A: TA > $o] :
        ( ( '\'const/sets/UNION\'' @ TA @ A @ A )
        = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(3,axiom,
    ! [TA: $tType,A: TA > $o,B: TA] :
      ( ( '\'const/sets/IN\'' @ TA @ B @ A )
      = ( A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_') ).

thf(9,plain,
    ! [TA: $tType,A: TA > $o,B: TA] :
      ( ( '\'const/sets/IN\'' @ TA @ B @ A )
      = ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(4,axiom,
    ! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
      ( ( '\'const/sets/IN\'' @ TA @ C @ ( '\'const/sets/UNION\'' @ TA @ A @ B ) )
      = ( ( '\'const/sets/IN\'' @ TA @ C @ A )
        | ( '\'const/sets/IN\'' @ TA @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_UNION_') ).

thf(12,plain,
    ! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
      ( ( '\'const/sets/IN\'' @ TA @ C @ ( '\'const/sets/UNION\'' @ TA @ A @ B ) )
      = ( ( '\'const/sets/IN\'' @ TA @ C @ A )
        | ( '\'const/sets/IN\'' @ TA @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(7,plain,
    ( ( '\'const/sets/UNION\'' @ skt1 @ sk1 @ sk1 )
   != sk1 ),
    inference(cnf,[status(esa)],[6]) ).

thf(8,plain,
    ( ( '\'const/sets/UNION\'' @ skt1 @ sk1 @ sk1 )
   != sk1 ),
    inference(lifteq,[status(thm)],[7]) ).

thf(18,plain,
    ( ( '\'const/sets/UNION\'' @ skt1 @ sk1 @ sk1 @ sk2 )
   != ( sk1 @ sk2 ) ),
    inference(func_ext,[status(esa)],[8]) ).

thf(5,axiom,
    ! [TA: $tType,A: TA > $o,B: TA > $o] :
      ( ( A = B )
      = ( ! [C: TA] :
            ( ( '\'const/sets/IN\'' @ TA @ C @ A )
            = ( '\'const/sets/IN\'' @ TA @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/EXTENSION_') ).

thf(15,plain,
    ! [TA: $tType,A: TA > $o,B: TA > $o] :
      ( ( A = B )
      = ( ! [C: TA] :
            ( ( '\'const/sets/IN\'' @ TA @ C @ A )
            = ( '\'const/sets/IN\'' @ TA @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(29,plain,
    $false,
    inference(e,[status(thm)],[6,9,12,18,8,15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09  % Problem  : SEV450^1 : TPTP v8.2.0. Released v7.0.0.
% 0.02/0.09  % Command  : run_Leo-III %s %d THM
% 0.09/0.28  % Computer : n032.cluster.edu
% 0.09/0.28  % Model    : x86_64 x86_64
% 0.09/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28  % Memory   : 8042.1875MB
% 0.09/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28  % CPULimit : 300
% 0.09/0.28  % WCLimit  : 300
% 0.09/0.28  % DateTime : Fri Jun 21 19:32:55 EDT 2024
% 0.09/0.28  % CPUTime  : 
% 0.77/0.75  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.10/0.86  % [INFO] 	 Parsing done (114ms). 
% 1.10/0.87  % [INFO] 	 Running in sequential loop mode. 
% 1.35/1.07  % [INFO] 	 eprover registered as external prover. 
% 1.47/1.08  % [INFO] 	 Scanning for conjecture ... 
% 1.47/1.13  % [INFO] 	 Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ... 
% 1.47/1.15  % [INFO] 	 Axiom selection finished. Selected 3 axioms (removed 0 axioms). 
% 1.47/1.16  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.47/1.16  % [INFO] 	 Type checking passed. 
% 1.47/1.16  % [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 ... 
% 2.67/1.60  % External prover 'e' found a proof!
% 2.67/1.61  % [INFO] 	 Killing All external provers ... 
% 2.67/1.61  % Time passed: 1186ms (effective reasoning time: 729ms)
% 2.67/1.61  % 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)>
% 2.67/1.61  % Axioms used in derivation (3): thm/sets/IN_, thm/sets/IN_UNION_, thm/sets/EXTENSION_
% 2.67/1.61  % No. of inferences in proof: 13
% 2.67/1.61  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1186 ms resp. 729 ms w/o parsing
% 2.90/1.63  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.90/1.63  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------