TSTP Solution File: DAT320^1 by Leo-III---1.7.10

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.10
% Problem  : DAT320^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n020.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 07:39:57 EDT 2024

% Result   : Theorem 3.30s 1.77s
% Output   : Refutation 3.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   20 (  14 unt;   6 typ;   0 def)
%            Number of atoms       :   48 (  24 equ;   0 cnn)
%            Maximal formula atoms :    1 (   3 avg)
%            Number of connectives :  189 (   8   ~;   4   |;   4   &; 173   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   4 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   6 usr;   4 con; 0-3 aty)
%            Number of variables   :   58 (   0   ^  37   !;  18   ?;  58   :)
%                                         (   3  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf('\'const/lists/MEM\'_type',type,
    '\'const/lists/MEM\'': 
      !>[TA: $tType] : ( TA > ( '\'type/ind_types/list\'' @ TA ) > $o ) ).

thf('\'const/lists/APPEND\'_type',type,
    '\'const/lists/APPEND\'': 
      !>[TA: $tType] : ( ( '\'type/ind_types/list\'' @ TA ) > ( '\'type/ind_types/list\'' @ TA ) > ( '\'type/ind_types/list\'' @ TA ) ) ).

thf('\'const/ind_types/CONS\'_type',type,
    '\'const/ind_types/CONS\'': 
      !>[TA: $tType] : ( TA > ( '\'type/ind_types/list\'' @ TA ) > ( '\'type/ind_types/list\'' @ TA ) ) ).

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

thf(sk1_type,type,
    sk1: skt1 ).

thf(sk2_type,type,
    sk2: '\'type/ind_types/list\'' @ skt1 ).

thf(1,conjecture,
    ! [TA: $tType,A: TA,B: '\'type/ind_types/list\'' @ TA] :
      ( ( '\'const/lists/MEM\'' @ TA @ A @ B )
      = ( ? [C: '\'type/ind_types/list\'' @ TA,D: '\'type/ind_types/list\'' @ TA] :
            ( B
            = ( '\'const/lists/APPEND\'' @ TA @ C @ ( '\'const/ind_types/CONS\'' @ TA @ A @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/lists/MEM_APPEND_DECOMPOSE_') ).

thf(2,negated_conjecture,
    ~ ! [TA: $tType,A: TA,B: '\'type/ind_types/list\'' @ TA] :
        ( ( '\'const/lists/MEM\'' @ TA @ A @ B )
        = ( ? [C: '\'type/ind_types/list\'' @ TA,D: '\'type/ind_types/list\'' @ TA] :
              ( B
              = ( '\'const/lists/APPEND\'' @ TA @ C @ ( '\'const/ind_types/CONS\'' @ TA @ A @ D ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(6,plain,
    ~ ! [TA: $tType,A: TA,B: '\'type/ind_types/list\'' @ TA] :
        ( ( '\'const/lists/MEM\'' @ TA @ A @ B )
        = ( ? [C: '\'type/ind_types/list\'' @ TA,D: '\'type/ind_types/list\'' @ TA] :
              ( B
              = ( '\'const/lists/APPEND\'' @ TA @ C @ ( '\'const/ind_types/CONS\'' @ TA @ A @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(3,axiom,
    ! [TA: $tType,A: TA,B: '\'type/ind_types/list\'' @ TA] :
      ( ( '\'const/lists/MEM\'' @ TA @ A @ B )
      = ( ? [C: '\'type/ind_types/list\'' @ TA,D: '\'type/ind_types/list\'' @ TA] :
            ( ~ ( '\'const/lists/MEM\'' @ TA @ A @ C )
            & ( B
              = ( '\'const/lists/APPEND\'' @ TA @ C @ ( '\'const/ind_types/CONS\'' @ TA @ A @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/lists/MEM_APPEND_DECOMPOSE_LEFT_') ).

thf(9,plain,
    ! [TA: $tType,A: TA,B: '\'type/ind_types/list\'' @ TA] :
      ( ( '\'const/lists/MEM\'' @ TA @ A @ B )
      = ( ? [C: '\'type/ind_types/list\'' @ TA,D: '\'type/ind_types/list\'' @ TA] :
            ( ~ ( '\'const/lists/MEM\'' @ TA @ A @ C )
            & ( B
              = ( '\'const/lists/APPEND\'' @ TA @ C @ ( '\'const/ind_types/CONS\'' @ TA @ A @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(4,axiom,
    ! [TA: $tType,A: TA,B: TA,C: '\'type/ind_types/list\'' @ TA] :
      ( ( '\'const/lists/MEM\'' @ TA @ B @ ( '\'const/ind_types/CONS\'' @ TA @ A @ C ) )
      = ( ( B = A )
        | ( '\'const/lists/MEM\'' @ TA @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/lists/MEM_1') ).

thf(12,plain,
    ! [TA: $tType,A: TA,B: TA,C: '\'type/ind_types/list\'' @ TA] :
      ( ( '\'const/lists/MEM\'' @ TA @ B @ ( '\'const/ind_types/CONS\'' @ TA @ A @ C ) )
      = ( ( B = A )
        | ( '\'const/lists/MEM\'' @ TA @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(10,plain,
    ! [TA: $tType,B: '\'type/ind_types/list\'' @ TA,A: TA] :
      ( ( '\'const/lists/MEM\'' @ TA @ A @ B )
      = ( ? [C: '\'type/ind_types/list\'' @ TA,D: '\'type/ind_types/list\'' @ TA] :
            ( ~ ( '\'const/lists/MEM\'' @ TA @ A @ C )
            & ( B
              = ( '\'const/lists/APPEND\'' @ TA @ C @ ( '\'const/ind_types/CONS\'' @ TA @ A @ D ) ) ) ) ) ),
    inference(cnf,[status(esa)],[9]) ).

thf(11,plain,
    ! [TA: $tType,B: '\'type/ind_types/list\'' @ TA,A: TA] :
      ( ( '\'const/lists/MEM\'' @ TA @ A @ B )
      = ( ? [C: '\'type/ind_types/list\'' @ TA,D: '\'type/ind_types/list\'' @ TA] :
            ( ~ ( '\'const/lists/MEM\'' @ TA @ A @ C )
            & ( B
              = ( '\'const/lists/APPEND\'' @ TA @ C @ ( '\'const/ind_types/CONS\'' @ TA @ A @ D ) ) ) ) ) ),
    inference(lifteq,[status(thm)],[10]) ).

thf(7,plain,
    ( ( '\'const/lists/MEM\'' @ skt1 @ sk1 @ sk2 )
   != ( ? [A: '\'type/ind_types/list\'' @ skt1,B: '\'type/ind_types/list\'' @ skt1] :
          ( sk2
          = ( '\'const/lists/APPEND\'' @ skt1 @ A @ ( '\'const/ind_types/CONS\'' @ skt1 @ sk1 @ B ) ) ) ) ),
    inference(cnf,[status(esa)],[6]) ).

thf(8,plain,
    ( ( '\'const/lists/MEM\'' @ skt1 @ sk1 @ sk2 )
   != ( ? [A: '\'type/ind_types/list\'' @ skt1,B: '\'type/ind_types/list\'' @ skt1] :
          ( sk2
          = ( '\'const/lists/APPEND\'' @ skt1 @ A @ ( '\'const/ind_types/CONS\'' @ skt1 @ sk1 @ B ) ) ) ) ),
    inference(lifteq,[status(thm)],[7]) ).

thf(5,axiom,
    ! [TA: $tType,A: TA,B: '\'type/ind_types/list\'' @ TA,C: '\'type/ind_types/list\'' @ TA] :
      ( ( '\'const/lists/MEM\'' @ TA @ A @ ( '\'const/lists/APPEND\'' @ TA @ B @ C ) )
      = ( ( '\'const/lists/MEM\'' @ TA @ A @ B )
        | ( '\'const/lists/MEM\'' @ TA @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/lists/MEM_APPEND_') ).

thf(15,plain,
    ! [TA: $tType,A: TA,B: '\'type/ind_types/list\'' @ TA,C: '\'type/ind_types/list\'' @ TA] :
      ( ( '\'const/lists/MEM\'' @ TA @ A @ ( '\'const/lists/APPEND\'' @ TA @ B @ C ) )
      = ( ( '\'const/lists/MEM\'' @ TA @ A @ B )
        | ( '\'const/lists/MEM\'' @ TA @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(46,plain,
    $false,
    inference(e,[status(thm)],[6,9,12,11,8,15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : DAT320^1 : TPTP v8.1.2. Released v7.0.0.
% 0.12/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n020.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Mon May  6 11:34:24 EDT 2024
% 0.16/0.36  % CPUTime  : 
% 0.83/0.84  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.23/0.96  % [INFO] 	 Parsing done (116ms). 
% 1.23/0.97  % [INFO] 	 Running in sequential loop mode. 
% 1.49/1.16  % [INFO] 	 eprover registered as external prover. 
% 1.49/1.16  % [INFO] 	 cvc4 registered as external prover. 
% 1.49/1.17  % [INFO] 	 Scanning for conjecture ... 
% 1.80/1.22  % [INFO] 	 Found a conjecture and 3 axioms. Running axiom selection ... 
% 1.86/1.24  % [INFO] 	 Axiom selection finished. Selected 3 axioms (removed 0 axioms). 
% 1.86/1.26  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.86/1.26  % [INFO] 	 Type checking passed. 
% 1.86/1.26  % [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 ... 
% 3.30/1.76  % External prover 'e' found a proof!
% 3.30/1.77  % [INFO] 	 Killing All external provers ... 
% 3.30/1.77  % Time passed: 1251ms (effective reasoning time: 796ms)
% 3.30/1.77  % 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)>
% 3.30/1.77  % Axioms used in derivation (3): thm/lists/MEM_APPEND_DECOMPOSE_LEFT_, thm/lists/MEM_1, thm/lists/MEM_APPEND_
% 3.30/1.77  % No. of inferences in proof: 14
% 3.30/1.77  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1251 ms resp. 796 ms w/o parsing
% 3.61/1.80  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.61/1.80  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------