TSTP Solution File: ANA090^1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : ANA090^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n029.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 May 20 18:39:16 EDT 2024

% Result   : Theorem 63.89s 10.14s
% Output   : Refutation 63.99s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   25
% Syntax   : Number of formulae    :   39 (  11 unt;  13 typ;   0 def)
%            Number of atoms       :  132 (  42 equ;   0 cnn)
%            Maximal formula atoms :    8 (   5 avg)
%            Number of connectives :  309 (  11   ~;   2   |;  15   &; 251   @)
%                                         (   0 <=>;  30  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   44 (  44   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  12 usr;   1 con; 0-4 aty)
%            Number of variables   :   85 (   0   ^  70   !;  10   ?;  85   :)
%                                         (   5  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf('\'type/realax/real\'_type',type,
    '\'type/realax/real\'': $tType ).

thf('\'const/sets/sup\'_type',type,
    '\'const/sets/sup\'': ( '\'type/realax/real\'' > $o ) > '\'type/realax/real\'' ).

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

thf('\'const/sets/inf\'_type',type,
    '\'const/sets/inf\'': ( '\'type/realax/real\'' > $o ) > '\'type/realax/real\'' ).

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

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

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

thf('\'const/realax/real_neg\'_type',type,
    '\'const/realax/real_neg\'': '\'type/realax/real\'' > '\'type/realax/real\'' ).

thf('\'const/realax/real_min\'_type',type,
    '\'const/realax/real_min\'': '\'type/realax/real\'' > '\'type/realax/real\'' > '\'type/realax/real\'' ).

thf('\'const/realax/real_max\'_type',type,
    '\'const/realax/real_max\'': '\'type/realax/real\'' > '\'type/realax/real\'' > '\'type/realax/real\'' ).

thf('\'const/realax/real_le\'_type',type,
    '\'const/realax/real_le\'': '\'type/realax/real\'' > '\'type/realax/real\'' > $o ).

thf('\'const/realax/real_abs\'_type',type,
    '\'const/realax/real_abs\'': '\'type/realax/real\'' > '\'type/realax/real\'' ).

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

thf(5,axiom,
    ! [A: '\'type/realax/real\'',B: '\'type/realax/real\'' > $o] :
      ( ( '\'const/sets/FINITE\'' @ '\'type/realax/real\'' @ B )
     => ( ( '\'const/sets/sup\'' @ ( '\'const/sets/INSERT\'' @ '\'type/realax/real\'' @ A @ B ) )
        = ( '\'const/class/COND\'' @ '\'type/realax/real\''
          @ ( B
            = ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
          @ A
          @ ( '\'const/realax/real_max\'' @ A @ ( '\'const/sets/sup\'' @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/SUP_INSERT_FINITE_') ).

thf(25,plain,
    ! [A: '\'type/realax/real\'',B: '\'type/realax/real\'' > $o] :
      ( ( '\'const/sets/FINITE\'' @ '\'type/realax/real\'' @ B )
     => ( ( '\'const/sets/sup\'' @ ( '\'const/sets/INSERT\'' @ '\'type/realax/real\'' @ A @ B ) )
        = ( '\'const/class/COND\'' @ '\'type/realax/real\''
          @ ( B
            = ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
          @ A
          @ ( '\'const/realax/real_max\'' @ A @ ( '\'const/sets/sup\'' @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(1,conjecture,
    ! [A: '\'type/realax/real\'' > $o] :
      ( ( ( A
         != ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
        & ? [B: '\'type/realax/real\''] :
          ! [C: '\'type/realax/real\''] :
            ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ C @ A )
           => ( '\'const/realax/real_le\'' @ ( '\'const/realax/real_abs\'' @ C ) @ B ) ) )
     => ( ( ( '\'const/sets/sup\'' @ A )
          = ( '\'const/sets/inf\'' @ A ) )
        = ( ? [B: '\'type/realax/real\''] :
              ( A
              = ( '\'const/sets/INSERT\'' @ '\'type/realax/real\'' @ B @ ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/REAL_SUP_EQ_INF_') ).

thf(2,negated_conjecture,
    ~ ! [A: '\'type/realax/real\'' > $o] :
        ( ( ( A
           != ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
          & ? [B: '\'type/realax/real\''] :
            ! [C: '\'type/realax/real\''] :
              ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ C @ A )
             => ( '\'const/realax/real_le\'' @ ( '\'const/realax/real_abs\'' @ C ) @ B ) ) )
       => ( ( ( '\'const/sets/sup\'' @ A )
            = ( '\'const/sets/inf\'' @ A ) )
          = ( ? [B: '\'type/realax/real\''] :
                ( A
                = ( '\'const/sets/INSERT\'' @ '\'type/realax/real\'' @ B @ ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(14,plain,
    ~ ! [A: '\'type/realax/real\'' > $o] :
        ( ( ( A
           != ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
          & ? [B: '\'type/realax/real\''] :
            ! [C: '\'type/realax/real\''] :
              ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ C @ A )
             => ( '\'const/realax/real_le\'' @ ( '\'const/realax/real_abs\'' @ C ) @ B ) ) )
       => ( ( ( '\'const/sets/sup\'' @ A )
            = ( '\'const/sets/inf\'' @ A ) )
          = ( ? [B: '\'type/realax/real\''] :
                ( A
                = ( '\'const/sets/INSERT\'' @ '\'type/realax/real\'' @ B @ ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(3,axiom,
    ! [A: '\'type/realax/real\'',B: '\'type/realax/real\'' > $o] :
      ( ( '\'const/sets/FINITE\'' @ '\'type/realax/real\'' @ B )
     => ( ( '\'const/sets/inf\'' @ ( '\'const/sets/INSERT\'' @ '\'type/realax/real\'' @ A @ B ) )
        = ( '\'const/class/COND\'' @ '\'type/realax/real\''
          @ ( B
            = ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
          @ A
          @ ( '\'const/realax/real_min\'' @ A @ ( '\'const/sets/inf\'' @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/INF_INSERT_FINITE_') ).

thf(20,plain,
    ! [A: '\'type/realax/real\'',B: '\'type/realax/real\'' > $o] :
      ( ( '\'const/sets/FINITE\'' @ '\'type/realax/real\'' @ B )
     => ( ( '\'const/sets/inf\'' @ ( '\'const/sets/INSERT\'' @ '\'type/realax/real\'' @ A @ B ) )
        = ( '\'const/class/COND\'' @ '\'type/realax/real\''
          @ ( B
            = ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
          @ A
          @ ( '\'const/realax/real_min\'' @ A @ ( '\'const/sets/inf\'' @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(12,axiom,
    ! [A: '\'type/realax/real\'' > $o] :
      ( ( ( A
         != ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
        & ? [B: '\'type/realax/real\''] :
          ! [C: '\'type/realax/real\''] :
            ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ C @ A )
           => ( '\'const/realax/real_le\'' @ C @ B ) ) )
     => ( ! [B: '\'type/realax/real\''] :
            ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ B @ A )
           => ( '\'const/realax/real_le\'' @ B @ ( '\'const/sets/sup\'' @ A ) ) )
        & ! [B: '\'type/realax/real\''] :
            ( ! [C: '\'type/realax/real\''] :
                ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ C @ A )
               => ( '\'const/realax/real_le\'' @ C @ B ) )
           => ( '\'const/realax/real_le\'' @ ( '\'const/sets/sup\'' @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/SUP_') ).

thf(53,plain,
    ! [A: '\'type/realax/real\'' > $o] :
      ( ( ( A
         != ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
        & ? [B: '\'type/realax/real\''] :
          ! [C: '\'type/realax/real\''] :
            ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ C @ A )
           => ( '\'const/realax/real_le\'' @ C @ B ) ) )
     => ( ! [B: '\'type/realax/real\''] :
            ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ B @ A )
           => ( '\'const/realax/real_le\'' @ B @ ( '\'const/sets/sup\'' @ A ) ) )
        & ! [B: '\'type/realax/real\''] :
            ( ! [C: '\'type/realax/real\''] :
                ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ C @ A )
               => ( '\'const/realax/real_le\'' @ C @ B ) )
           => ( '\'const/realax/real_le\'' @ ( '\'const/sets/sup\'' @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(13,axiom,
    ! [A: '\'type/realax/real\'',B: '\'type/realax/real\''] :
      ( ( ( '\'const/realax/real_le\'' @ A @ B )
        & ( '\'const/realax/real_le\'' @ B @ A ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/realax/REAL_LE_ANTISYM_') ).

thf(64,plain,
    ! [A: '\'type/realax/real\'',B: '\'type/realax/real\''] :
      ( ( ( '\'const/realax/real_le\'' @ A @ B )
        & ( '\'const/realax/real_le\'' @ B @ A ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(10,axiom,
    ! [A: '\'type/realax/real\'' > $o] :
      ( ( ( A
         != ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
        & ? [B: '\'type/realax/real\''] :
          ! [C: '\'type/realax/real\''] :
            ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ C @ A )
           => ( '\'const/realax/real_le\'' @ B @ C ) ) )
     => ( ! [B: '\'type/realax/real\''] :
            ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ B @ A )
           => ( '\'const/realax/real_le\'' @ ( '\'const/sets/inf\'' @ A ) @ B ) )
        & ! [B: '\'type/realax/real\''] :
            ( ! [C: '\'type/realax/real\''] :
                ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ C @ A )
               => ( '\'const/realax/real_le\'' @ B @ C ) )
           => ( '\'const/realax/real_le\'' @ B @ ( '\'const/sets/inf\'' @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/INF_') ).

thf(39,plain,
    ! [A: '\'type/realax/real\'' > $o] :
      ( ( ( A
         != ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
        & ? [B: '\'type/realax/real\''] :
          ! [C: '\'type/realax/real\''] :
            ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ C @ A )
           => ( '\'const/realax/real_le\'' @ B @ C ) ) )
     => ( ! [B: '\'type/realax/real\''] :
            ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ B @ A )
           => ( '\'const/realax/real_le\'' @ ( '\'const/sets/inf\'' @ A ) @ B ) )
        & ! [B: '\'type/realax/real\''] :
            ( ! [C: '\'type/realax/real\''] :
                ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ C @ A )
               => ( '\'const/realax/real_le\'' @ B @ C ) )
           => ( '\'const/realax/real_le\'' @ B @ ( '\'const/sets/inf\'' @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(11,axiom,
    ! [A: '\'type/realax/real\'',B: '\'type/realax/real\''] :
      ( ( '\'const/realax/real_le\'' @ ( '\'const/realax/real_abs\'' @ A ) @ B )
      = ( ( '\'const/realax/real_le\'' @ ( '\'const/realax/real_neg\'' @ B ) @ A )
        & ( '\'const/realax/real_le\'' @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/real/REAL_ABS_BOUNDS_') ).

thf(50,plain,
    ! [A: '\'type/realax/real\'',B: '\'type/realax/real\''] :
      ( ( '\'const/realax/real_le\'' @ ( '\'const/realax/real_abs\'' @ A ) @ B )
      = ( ( '\'const/realax/real_le\'' @ ( '\'const/realax/real_neg\'' @ B ) @ A )
        & ( '\'const/realax/real_le\'' @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(4,axiom,
    ! [TA: $tType] : ( '\'const/sets/FINITE\'' @ TA @ ( '\'const/sets/EMPTY\'' @ TA ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/FINITE_EMPTY_') ).

thf(23,plain,
    ! [TA: $tType] : ( '\'const/sets/FINITE\'' @ TA @ ( '\'const/sets/EMPTY\'' @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(6,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(28,plain,
    ! [TA: $tType,A: TA] :
      ~ ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/EMPTY\'' @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(8,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(33,plain,
    ! [TA: $tType,A: TA > $o,B: TA] :
      ( ( '\'const/sets/IN\'' @ TA @ B @ A )
      = ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(9,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(36,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)],[9]) ).

thf(7,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(30,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)],[7]) ).

thf(9159,plain,
    $false,
    inference(e,[status(thm)],[25,14,20,53,64,39,50,23,28,33,36,30]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : ANA090^1 : TPTP v8.2.0. Released v7.0.0.
% 0.13/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n029.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 20 07:43:54 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 0.95/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.24/1.00  % [INFO] 	 Parsing done (123ms). 
% 1.44/1.01  % [INFO] 	 Running in sequential loop mode. 
% 1.79/1.23  % [INFO] 	 eprover registered as external prover. 
% 1.79/1.23  % [INFO] 	 cvc4 registered as external prover. 
% 1.79/1.23  % [INFO] 	 Scanning for conjecture ... 
% 1.90/1.30  % [INFO] 	 Found a conjecture (or negated_conjecture) and 11 axioms. Running axiom selection ... 
% 1.90/1.32  % [INFO] 	 Axiom selection finished. Selected 11 axioms (removed 0 axioms). 
% 2.17/1.35  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.17/1.35  % [INFO] 	 Type checking passed. 
% 2.17/1.36  % [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 ... 
% 63.89/10.14  % External prover 'e' found a proof!
% 63.89/10.14  % [INFO] 	 Killing All external provers ... 
% 63.89/10.14  % Time passed: 9611ms (effective reasoning time: 9130ms)
% 63.89/10.14  % 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)>
% 63.89/10.14  % Axioms used in derivation (11): thm/sets/IN_INSERT_, thm/real/REAL_ABS_BOUNDS_, thm/sets/EXTENSION_, thm/sets/SUP_, thm/sets/IN_, thm/sets/SUP_INSERT_FINITE_, thm/sets/NOT_IN_EMPTY_, thm/sets/INF_INSERT_FINITE_, thm/sets/INF_, thm/realax/REAL_LE_ANTISYM_, thm/sets/FINITE_EMPTY_
% 63.89/10.14  % No. of inferences in proof: 26
% 63.89/10.14  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 9611 ms resp. 9130 ms w/o parsing
% 63.99/10.18  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 63.99/10.18  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------