TSTP Solution File: SEV486^1 by Leo-III---1.7.15

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.15
% Problem  : SEV486^1 : 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 15:59:09 EDT 2024

% Result   : Theorem 3.02s 1.68s
% Output   : Refutation 3.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    3
% Syntax   : Number of formulae    :    8 (   3 unt;   0 typ;   0 def)
%            Number of atoms       :   29 (   4 equ;   0 cnn)
%            Maximal formula atoms :    4 (   3 avg)
%            Number of connectives :   70 (   2   ~;   0   |;   2   &;  66   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   8 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   6 usr;   1 con; 0-4 aty)
%            Number of variables   :   21 (   5   ^  11   !;   5   ?;  21   :)

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

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

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

thf('\'const/arith/<\'_type',type,
    '\'const/arith/<\'': '\'type/nums/num\'' > '\'type/nums/num\'' > $o ).

thf(1,conjecture,
    ! [A: '\'type/nums/num\''] :
      ( '\'const/sets/FINITE\'' @ '\'type/nums/num\''
      @ ( '\'const/sets/GSPEC\'' @ '\'type/nums/num\''
        @ ^ [B: '\'type/nums/num\''] :
          ? [C: '\'type/nums/num\''] : ( '\'const/sets/SETSPEC\'' @ '\'type/nums/num\'' @ B @ ( '\'const/arith/<\'' @ C @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/FINITE_NUMSEG_LT_') ).

thf(2,negated_conjecture,
    ~ ! [A: '\'type/nums/num\''] :
        ( '\'const/sets/FINITE\'' @ '\'type/nums/num\''
        @ ( '\'const/sets/GSPEC\'' @ '\'type/nums/num\''
          @ ^ [B: '\'type/nums/num\''] :
            ? [C: '\'type/nums/num\''] : ( '\'const/sets/SETSPEC\'' @ '\'type/nums/num\'' @ B @ ( '\'const/arith/<\'' @ C @ A ) @ C ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(5,plain,
    ~ ! [A: '\'type/nums/num\''] :
        ( '\'const/sets/FINITE\'' @ '\'type/nums/num\''
        @ ( '\'const/sets/GSPEC\'' @ '\'type/nums/num\''
          @ ^ [B: '\'type/nums/num\''] :
            ? [C: '\'type/nums/num\''] : ( '\'const/sets/SETSPEC\'' @ '\'type/nums/num\'' @ B @ ( '\'const/arith/<\'' @ C @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(3,axiom,
    ! [A: '\'type/nums/num\''] :
      ( '\'const/sets/HAS_SIZE\'' @ '\'type/nums/num\''
      @ ( '\'const/sets/GSPEC\'' @ '\'type/nums/num\''
        @ ^ [B: '\'type/nums/num\''] :
          ? [C: '\'type/nums/num\''] : ( '\'const/sets/SETSPEC\'' @ '\'type/nums/num\'' @ B @ ( '\'const/arith/<\'' @ C @ A ) @ C ) )
      @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/HAS_SIZE_NUMSEG_LT_') ).

thf(7,plain,
    ! [A: '\'type/nums/num\''] :
      ( '\'const/sets/HAS_SIZE\'' @ '\'type/nums/num\''
      @ ( '\'const/sets/GSPEC\'' @ '\'type/nums/num\''
        @ ^ [B: '\'type/nums/num\''] :
          ? [C: '\'type/nums/num\''] : ( '\'const/sets/SETSPEC\'' @ '\'type/nums/num\'' @ B @ ( '\'const/arith/<\'' @ C @ A ) @ C ) )
      @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(4,axiom,
    ! [TA: $tType,A: TA > $o,B: '\'type/nums/num\''] :
      ( ( '\'const/sets/HAS_SIZE\'' @ TA @ A @ B )
      = ( ( '\'const/sets/FINITE\'' @ TA @ A )
        & ( ( '\'const/sets/CARD\'' @ TA @ A )
          = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/HAS_SIZE_') ).

thf(9,plain,
    ! [TA: $tType,A: TA > $o,B: '\'type/nums/num\''] :
      ( ( '\'const/sets/HAS_SIZE\'' @ TA @ A @ B )
      = ( ( '\'const/sets/FINITE\'' @ TA @ A )
        & ( ( '\'const/sets/CARD\'' @ TA @ A )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(12,plain,
    $false,
    inference(e,[status(thm)],[5,7,9]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEV486^1 : TPTP v8.2.0. Released v7.0.0.
% 0.03/0.12  % Command  : run_Leo-III %s %d THM
% 0.12/0.33  % Computer : n021.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Fri Jun 21 18:49:55 EDT 2024
% 0.12/0.34  % CPUTime  : 
% 0.97/0.89  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.23/1.00  % [INFO] 	 Parsing done (108ms). 
% 1.23/1.01  % [INFO] 	 Running in sequential loop mode. 
% 1.61/1.21  % [INFO] 	 eprover registered as external prover. 
% 1.61/1.21  % [INFO] 	 Scanning for conjecture ... 
% 1.82/1.26  % [INFO] 	 Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ... 
% 1.82/1.28  % [INFO] 	 Axiom selection finished. Selected 2 axioms (removed 0 axioms). 
% 1.82/1.29  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.82/1.29  % [INFO] 	 Type checking passed. 
% 1.82/1.29  % [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 ... 
% 3.02/1.67  % External prover 'e' found a proof!
% 3.02/1.67  % [INFO] 	 Killing All external provers ... 
% 3.02/1.68  % Time passed: 1124ms (effective reasoning time: 664ms)
% 3.02/1.68  % 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)>
% 3.02/1.68  % Axioms used in derivation (2): thm/sets/HAS_SIZE_NUMSEG_LT_, thm/sets/HAS_SIZE_
% 3.02/1.68  % No. of inferences in proof: 8
% 3.02/1.68  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1124 ms resp. 664 ms w/o parsing
% 3.22/1.70  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.22/1.70  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------