TSTP Solution File: ANA068^1 by Leo-III---1.7.10

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.10
% Problem  : ANA068^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n009.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 07:27:49 EDT 2024

% Result   : Theorem 3.49s 1.68s
% Output   : Refutation 3.49s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   20 (   3 unt;   8 typ;   0 def)
%            Number of atoms       :   31 (   2 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   69 (   6   ~;   0   |;   2   &;  59   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   25 (  25   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7 usr;   1 con; 0-4 aty)
%            Number of variables   :   26 (   2   ^  16   !;   2   ?;  26   :)
%                                         (   6  !>;   0  ?*;   0  @-;   0  @+)

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

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

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

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

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

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

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

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

thf(5,axiom,
    ! [TA: $tType,A: TA > $o,B: TA > $o] :
      ( ( ( '\'const/sets/FINITE\'' @ TA @ B )
        & ( '\'const/sets/SUBSET\'' @ TA @ A @ B ) )
     => ( '\'const/sets/FINITE\'' @ TA @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/FINITE_SUBSET_') ).

thf(13,plain,
    ! [TA: $tType,A: TA > $o,B: TA > $o] :
      ( ( ( '\'const/sets/FINITE\'' @ TA @ B )
        & ( '\'const/sets/SUBSET\'' @ TA @ A @ B ) )
     => ( '\'const/sets/FINITE\'' @ TA @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(1,conjecture,
    '\'const/sets/INFINITE\'' @ '\'type/realax/real\'' @ ( '\'const/sets/UNIV\'' @ '\'type/realax/real\'' ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/real_INFINITE_') ).

thf(2,negated_conjecture,
    ~ ( '\'const/sets/INFINITE\'' @ '\'type/realax/real\'' @ ( '\'const/sets/UNIV\'' @ '\'type/realax/real\'' ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(7,plain,
    ~ ( '\'const/sets/INFINITE\'' @ '\'type/realax/real\'' @ ( '\'const/sets/UNIV\'' @ '\'type/realax/real\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,axiom,
    ! [TA: $tType,A: TA > $o] : ( '\'const/sets/SUBSET\'' @ TA @ A @ ( '\'const/sets/UNIV\'' @ TA ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/SUBSET_UNIV_') ).

thf(11,plain,
    ! [TA: $tType,A: TA > $o] : ( '\'const/sets/SUBSET\'' @ TA @ A @ ( '\'const/sets/UNIV\'' @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(3,axiom,
    ! [A: '\'type/realax/real\''] :
      ~ ( '\'const/sets/FINITE\'' @ '\'type/realax/real\''
        @ ( '\'const/sets/GSPEC\'' @ '\'type/realax/real\''
          @ ^ [B: '\'type/realax/real\''] :
            ? [C: '\'type/realax/real\''] : ( '\'const/sets/SETSPEC\'' @ '\'type/realax/real\'' @ B @ ( '\'const/realax/real_le\'' @ A @ C ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/FINITE_REAL_INTERVAL_1') ).

thf(8,plain,
    ! [A: '\'type/realax/real\''] :
      ~ ( '\'const/sets/FINITE\'' @ '\'type/realax/real\''
        @ ( '\'const/sets/GSPEC\'' @ '\'type/realax/real\''
          @ ^ [B: '\'type/realax/real\''] :
            ? [C: '\'type/realax/real\''] : ( '\'const/sets/SETSPEC\'' @ '\'type/realax/real\'' @ B @ ( '\'const/realax/real_le\'' @ A @ C ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(6,axiom,
    ! [TA: $tType,A: TA > $o] :
      ( ( '\'const/sets/INFINITE\'' @ TA @ A )
      = ( ~ ( '\'const/sets/FINITE\'' @ TA @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/INFINITE_') ).

thf(15,plain,
    ! [TA: $tType,A: TA > $o] :
      ( ( '\'const/sets/INFINITE\'' @ TA @ A )
      = ( ~ ( '\'const/sets/FINITE\'' @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(18,plain,
    $false,
    inference(e,[status(thm)],[13,7,11,8,15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem  : ANA068^1 : TPTP v8.1.2. Released v7.0.0.
% 0.11/0.16  % Command  : run_Leo-III %s %d
% 0.17/0.38  % Computer : n009.cluster.edu
% 0.17/0.38  % Model    : x86_64 x86_64
% 0.17/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38  % Memory   : 8042.1875MB
% 0.17/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38  % CPULimit : 300
% 0.17/0.38  % WCLimit  : 300
% 0.17/0.38  % DateTime : Mon May  6 12:46:24 EDT 2024
% 0.17/0.38  % CPUTime  : 
% 0.89/0.84  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.24/0.95  % [INFO] 	 Parsing done (110ms). 
% 1.24/0.96  % [INFO] 	 Running in sequential loop mode. 
% 1.66/1.16  % [INFO] 	 eprover registered as external prover. 
% 1.66/1.16  % [INFO] 	 cvc4 registered as external prover. 
% 1.66/1.17  % [INFO] 	 Scanning for conjecture ... 
% 1.77/1.21  % [INFO] 	 Found a conjecture and 4 axioms. Running axiom selection ... 
% 1.77/1.23  % [INFO] 	 Axiom selection finished. Selected 4 axioms (removed 0 axioms). 
% 1.77/1.24  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.77/1.25  % [INFO] 	 Type checking passed. 
% 1.77/1.25  % [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 ... 
% 3.49/1.68  % External prover 'e' found a proof!
% 3.49/1.68  % [INFO] 	 Killing All external provers ... 
% 3.49/1.68  % Time passed: 1139ms (effective reasoning time: 719ms)
% 3.49/1.68  % 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)>
% 3.49/1.68  % Axioms used in derivation (4): thm/sets/FINITE_SUBSET_, thm/sets/SUBSET_UNIV_, thm/sets/FINITE_REAL_INTERVAL_1, thm/sets/INFINITE_
% 3.49/1.68  % No. of inferences in proof: 12
% 3.49/1.68  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1139 ms resp. 719 ms w/o parsing
% 3.49/1.71  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.49/1.71  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------