TSTP Solution File: SEV472^1 by Leo-III---1.7.15

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.15
% Problem  : SEV472^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d THM

% 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 Jun 24 15:59:07 EDT 2024

% Result   : Theorem 3.63s 2.20s
% Output   : Refutation 3.86s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   11 (   3 unt;   0 typ;   0 def)
%            Number of atoms       :   34 (   2 equ;   0 cnn)
%            Maximal formula atoms :    5 (   3 avg)
%            Number of connectives :  102 (   2   ~;   0   |;   7   &;  88   @)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (  10 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   14 (  14   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7 usr;   1 con; 0-4 aty)
%            Number of variables   :   35 (   5   ^  25   !;   5   ?;  35   :)

% Comments : 
%------------------------------------------------------------------------------
thf('\'const/trivia/I\'_type',type,
    '\'const/trivia/I\'': 
      !>[TA: $tType] : ( TA > TA ) ).

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/IN\'_type',type,
    '\'const/sets/IN\'': 
      !>[TA: $tType] : ( TA > ( 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(skt1_type,type,
    skt1: $tType ).

thf(sk1_type,type,
    sk1: skt1 > $o ).

thf(5,axiom,
    ! [TA: $tType,A: TA > $o,B: TA > $o] :
      ( '\'const/sets/SUBSET\'' @ TA
      @ ( '\'const/sets/GSPEC\'' @ TA
        @ ^ [C: TA] :
          ? [D: TA] :
            ( '\'const/sets/SETSPEC\'' @ TA @ C
            @ ( ( '\'const/sets/IN\'' @ TA @ D @ A )
              & ( B @ D ) )
            @ D ) )
      @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/SUBSET_RESTRICT_') ).

thf(14,plain,
    ! [TA: $tType,A: TA > $o,B: TA > $o] :
      ( '\'const/sets/SUBSET\'' @ TA
      @ ( '\'const/sets/GSPEC\'' @ TA
        @ ^ [C: TA] :
          ? [D: TA] :
            ( '\'const/sets/SETSPEC\'' @ TA @ C
            @ ( ( '\'const/sets/IN\'' @ TA @ D @ A )
              & ( B @ D ) )
            @ D ) )
      @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(1,conjecture,
    ! [TA: $tType,A: TA > $o,B: TA > $o] :
      ( ( '\'const/sets/FINITE\'' @ TA @ A )
     => ( '\'const/sets/FINITE\'' @ TA
        @ ( '\'const/sets/GSPEC\'' @ TA
          @ ^ [C: TA] :
            ? [D: TA] :
              ( '\'const/sets/SETSPEC\'' @ TA @ C
              @ ( ( '\'const/sets/IN\'' @ TA @ D @ A )
                & ( B @ D ) )
              @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/FINITE_RESTRICT_') ).

thf(2,negated_conjecture,
    ~ ! [TA: $tType,A: TA > $o,B: TA > $o] :
        ( ( '\'const/sets/FINITE\'' @ TA @ A )
       => ( '\'const/sets/FINITE\'' @ TA
          @ ( '\'const/sets/GSPEC\'' @ TA
            @ ^ [C: TA] :
              ? [D: TA] :
                ( '\'const/sets/SETSPEC\'' @ TA @ C
                @ ( ( '\'const/sets/IN\'' @ TA @ D @ A )
                  & ( B @ D ) )
                @ D ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(6,plain,
    ~ ! [TA: $tType,A: TA > $o,B: TA > $o] :
        ( ( '\'const/sets/FINITE\'' @ TA @ A )
       => ( '\'const/sets/FINITE\'' @ TA
          @ ( '\'const/sets/GSPEC\'' @ TA
            @ ^ [C: TA] :
              ? [D: TA] :
                ( '\'const/sets/SETSPEC\'' @ TA @ C
                @ ( ( '\'const/sets/IN\'' @ TA @ D @ A )
                  & ( B @ D ) )
                @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(3,axiom,
    ! [TA: $tType,A: TA] :
      ( ( '\'const/trivia/I\'' @ TA @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/trivia/I_THM_') ).

thf(9,plain,
    ! [TA: $tType,A: TA] :
      ( ( '\'const/trivia/I\'' @ TA @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(4,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(12,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)],[4]) ).

thf(8,plain,
    '\'const/sets/FINITE\'' @ skt1 @ sk1,
    inference(cnf,[status(esa)],[6]) ).

thf(21,plain,
    $false,
    inference(e,[status(thm)],[14,6,9,12,8]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10  % Problem  : SEV472^1 : TPTP v8.2.0. Released v7.0.0.
% 0.03/0.10  % Command  : run_Leo-III %s %d THM
% 0.10/0.30  % Computer : n029.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit : 300
% 0.10/0.30  % WCLimit  : 300
% 0.10/0.30  % DateTime : Fri Jun 21 19:14:40 EDT 2024
% 0.10/0.30  % CPUTime  : 
% 0.89/0.90  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.24/1.03  % [INFO] 	 Parsing done (134ms). 
% 1.24/1.05  % [INFO] 	 Running in sequential loop mode. 
% 1.69/1.35  % [INFO] 	 eprover registered as external prover. 
% 1.69/1.35  % [INFO] 	 Scanning for conjecture ... 
% 1.81/1.42  % [INFO] 	 Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ... 
% 1.98/1.45  % [INFO] 	 Axiom selection finished. Selected 3 axioms (removed 0 axioms). 
% 1.98/1.46  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.98/1.46  % [INFO] 	 Type checking passed. 
% 1.98/1.47  % [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 ... 
% 3.63/2.20  % External prover 'e' found a proof!
% 3.63/2.20  % [INFO] 	 Killing All external provers ... 
% 3.63/2.20  % Time passed: 1733ms (effective reasoning time: 1147ms)
% 3.63/2.20  % 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)>
% 3.63/2.20  % Axioms used in derivation (3): thm/sets/SUBSET_RESTRICT_, thm/trivia/I_THM_, thm/sets/FINITE_SUBSET_
% 3.63/2.20  % No. of inferences in proof: 11
% 3.63/2.20  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1733 ms resp. 1147 ms w/o parsing
% 3.86/2.25  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.86/2.25  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------