TSTP Solution File: ANA079^1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : ANA079^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n024.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 18:39:13 EDT 2024

% Result   : Theorem 2.99s 2.04s
% Output   : Refutation 3.33s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   15 (   3 unt;   5 typ;   0 def)
%            Number of atoms       :   48 (   6 equ;   0 cnn)
%            Maximal formula atoms :    8 (   4 avg)
%            Number of connectives :  135 (   6   ~;   0   |;  12   &;  99   @)
%                                         (   0 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   9 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   15 (  15   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4 usr;   1 con; 0-3 aty)
%            Number of variables   :   41 (   0   ^  35   !;   4   ?;  41   :)
%                                         (   2  !>;   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/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('\'const/realax/real_le\'_type',type,
    '\'const/realax/real_le\'': '\'type/realax/real\'' > '\'type/realax/real\'' > $o ).

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

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

thf(6,plain,
    ~ ! [A: '\'type/realax/real\'' > $o,B: '\'type/realax/real\'',C: '\'type/realax/real\'',D: '\'type/realax/real\''] :
        ( ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ D @ A )
          & ( '\'const/realax/real_le\'' @ B @ D )
          & ! [E: '\'type/realax/real\''] :
              ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ E @ A )
             => ( '\'const/realax/real_le\'' @ E @ C ) ) )
       => ( '\'const/realax/real_le\'' @ B @ ( '\'const/sets/sup\'' @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(3,axiom,
    ! [A: '\'type/realax/real\'',B: '\'type/realax/real\'',C: '\'type/realax/real\''] :
      ( ( ( '\'const/realax/real_le\'' @ A @ B )
        & ( '\'const/realax/real_le\'' @ B @ C ) )
     => ( '\'const/realax/real_le\'' @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/realax/REAL_LE_TRANS_') ).

thf(12,plain,
    ! [A: '\'type/realax/real\'',B: '\'type/realax/real\'',C: '\'type/realax/real\''] :
      ( ( ( '\'const/realax/real_le\'' @ A @ B )
        & ( '\'const/realax/real_le\'' @ B @ C ) )
     => ( '\'const/realax/real_le\'' @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

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

thf(14,plain,
    ! [TA: $tType,A: TA > $o] :
      ( ( ? [B: TA] : ( '\'const/sets/IN\'' @ TA @ B @ A ) )
      = ( A
       != ( '\'const/sets/EMPTY\'' @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(5,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(17,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)],[5]) ).

thf(28,plain,
    $false,
    inference(e,[status(thm)],[6,12,14,17]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10  % Problem  : ANA079^1 : TPTP v8.2.0. Released v7.0.0.
% 0.02/0.13  % Command  : run_Leo-III %s %d
% 0.13/0.34  % Computer : n024.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Mon May 20 07:42:39 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 0.89/0.90  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.10/1.02  % [INFO] 	 Parsing done (122ms). 
% 1.10/1.04  % [INFO] 	 Running in sequential loop mode. 
% 1.65/1.35  % [INFO] 	 eprover registered as external prover. 
% 1.65/1.35  % [INFO] 	 cvc4 registered as external prover. 
% 1.65/1.35  % [INFO] 	 Scanning for conjecture ... 
% 1.80/1.42  % [INFO] 	 Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ... 
% 1.96/1.45  % [INFO] 	 Axiom selection finished. Selected 3 axioms (removed 0 axioms). 
% 1.96/1.47  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.03/1.47  % [INFO] 	 Type checking passed. 
% 2.03/1.48  % [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 ... 
% 2.99/2.04  % External prover 'e' found a proof!
% 2.99/2.04  % [INFO] 	 Killing All external provers ... 
% 2.99/2.04  % Time passed: 1561ms (effective reasoning time: 1000ms)
% 2.99/2.04  % 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)>
% 2.99/2.04  % Axioms used in derivation (3): thm/realax/REAL_LE_TRANS_, thm/sets/MEMBER_NOT_EMPTY_, thm/sets/SUP_
% 2.99/2.04  % No. of inferences in proof: 10
% 2.99/2.04  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1561 ms resp. 1000 ms w/o parsing
% 3.33/2.10  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.33/2.10  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------