TSTP Solution File: SEV446^1 by Leo-III---1.7.15

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.15
% Problem  : SEV446^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d THM

% Computer : n021.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 15:59:02 EDT 2024

% Result   : Theorem 3.39s 1.83s
% Output   : Refutation 3.39s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   11 (   8 unt;   0 typ;   0 def)
%            Number of atoms       :   42 (  14 equ;   0 cnn)
%            Maximal formula atoms :    2 (   3 avg)
%            Number of connectives :   74 (   7   ~;   2   |;   0   &;  65   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   5 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   5 usr;   3 con; 0-4 aty)
%            Number of variables   :   23 (   0   ^  23   !;   0   ?;  23   :)

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

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

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

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

thf(sk1_type,type,
    sk1: skt1 ).

thf(sk2_type,type,
    sk2: skt1 ).

thf(1,conjecture,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/INSERT\'' @ TA @ B @ ( '\'const/sets/EMPTY\'' @ TA ) ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_SING_') ).

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

thf(5,plain,
    ~ ! [TA: $tType,A: TA,B: TA] :
        ( ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/INSERT\'' @ TA @ B @ ( '\'const/sets/EMPTY\'' @ TA ) ) )
        = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

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

thf(10,plain,
    ! [TA: $tType,A: TA,B: TA,C: TA > $o] :
      ( ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/INSERT\'' @ TA @ B @ C ) )
      = ( ( A = B )
        | ( '\'const/sets/IN\'' @ TA @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(3,axiom,
    ! [TA: $tType,A: TA] :
      ~ ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/EMPTY\'' @ TA ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/NOT_IN_EMPTY_') ).

thf(8,plain,
    ! [TA: $tType,A: TA] :
      ~ ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/EMPTY\'' @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(9,plain,
    ! [TA: $tType,A: TA] :
      ~ ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/EMPTY\'' @ TA ) ),
    inference(cnf,[status(esa)],[8]) ).

thf(6,plain,
    ( ( '\'const/sets/IN\'' @ skt1 @ sk1 @ ( '\'const/sets/INSERT\'' @ skt1 @ sk2 @ ( '\'const/sets/EMPTY\'' @ skt1 ) ) )
   != ( sk1 = sk2 ) ),
    inference(cnf,[status(esa)],[5]) ).

thf(7,plain,
    ( ( '\'const/sets/IN\'' @ skt1 @ sk1 @ ( '\'const/sets/INSERT\'' @ skt1 @ sk2 @ ( '\'const/sets/EMPTY\'' @ skt1 ) ) )
   != ( sk1 = sk2 ) ),
    inference(lifteq,[status(thm)],[6]) ).

thf(30,plain,
    $false,
    inference(e,[status(thm)],[5,10,9,7,8]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SEV446^1 : TPTP v8.2.0. Released v7.0.0.
% 0.04/0.12  % Command  : run_Leo-III %s %d THM
% 0.11/0.33  % Computer : n021.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Fri Jun 21 19:00:10 EDT 2024
% 0.11/0.33  % CPUTime  : 
% 0.99/0.91  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.34/1.03  % [INFO] 	 Parsing done (119ms). 
% 1.34/1.03  % [INFO] 	 Running in sequential loop mode. 
% 1.75/1.24  % [INFO] 	 eprover registered as external prover. 
% 1.75/1.25  % [INFO] 	 Scanning for conjecture ... 
% 1.75/1.30  % [INFO] 	 Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ... 
% 1.93/1.32  % [INFO] 	 Axiom selection finished. Selected 2 axioms (removed 0 axioms). 
% 1.93/1.33  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.93/1.33  % [INFO] 	 Type checking passed. 
% 1.93/1.33  % [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 ... 
% 3.39/1.83  % External prover 'e' found a proof!
% 3.39/1.83  % [INFO] 	 Killing All external provers ... 
% 3.39/1.83  % Time passed: 1304ms (effective reasoning time: 791ms)
% 3.39/1.83  % 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)>
% 3.39/1.83  % Axioms used in derivation (2): thm/sets/IN_INSERT_, thm/sets/NOT_IN_EMPTY_
% 3.39/1.83  % No. of inferences in proof: 11
% 3.39/1.83  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1304 ms resp. 791 ms w/o parsing
% 3.39/1.86  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.39/1.86  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------