TSTP Solution File: SEV451^1 by Leo-III---1.7.15

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.15
% Problem  : SEV451^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d THM

% Computer : n022.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 15:59:03 EDT 2024

% Result   : Theorem 2.99s 1.64s
% Output   : Refutation 2.99s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   14 (  12 unt;   0 typ;   0 def)
%            Number of atoms       :   51 (  15 equ;   0 cnn)
%            Maximal formula atoms :    2 (   3 avg)
%            Number of connectives :   83 (   4   ~;   2   |;   0   &;  77   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   4 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   13 (  13   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4 usr;   1 con; 0-4 aty)
%            Number of variables   :   32 (   0   ^  32   !;   0   ?;  32   :)

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

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

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

thf(skt1_type,type,
    skt1: $tType ).

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

thf(3,axiom,
    ! [TA: $tType,A: TA] : ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/UNIV\'' @ TA ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/IN_UNIV_') ).

thf(10,plain,
    ! [TA: $tType,A: TA] : ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/UNIV\'' @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(1,conjecture,
    ! [TA: $tType,A: TA > $o] :
      ( ( '\'const/sets/UNION\'' @ TA @ A @ ( '\'const/sets/UNIV\'' @ TA ) )
      = ( '\'const/sets/UNIV\'' @ TA ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/UNION_UNIV_1') ).

thf(2,negated_conjecture,
    ~ ! [TA: $tType,A: TA > $o] :
        ( ( '\'const/sets/UNION\'' @ TA @ A @ ( '\'const/sets/UNIV\'' @ TA ) )
        = ( '\'const/sets/UNIV\'' @ TA ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(7,plain,
    ~ ! [TA: $tType,A: TA > $o] :
        ( ( '\'const/sets/UNION\'' @ TA @ A @ ( '\'const/sets/UNIV\'' @ TA ) )
        = ( '\'const/sets/UNIV\'' @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(8,plain,
    ( ( '\'const/sets/UNION\'' @ skt1 @ sk1 @ ( '\'const/sets/UNIV\'' @ skt1 ) )
   != ( '\'const/sets/UNIV\'' @ skt1 ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(9,plain,
    ( ( '\'const/sets/UNION\'' @ skt1 @ sk1 @ ( '\'const/sets/UNIV\'' @ skt1 ) )
   != ( '\'const/sets/UNIV\'' @ skt1 ) ),
    inference(lifteq,[status(thm)],[8]) ).

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

thf(12,plain,
    ! [TA: $tType,A: TA > $o,B: TA] :
      ( ( '\'const/sets/IN\'' @ TA @ B @ A )
      = ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(6,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/sandbox/benchmark/theBenchmark.p','thm/sets/EXTENSION_') ).

thf(18,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)],[6]) ).

thf(5,axiom,
    ! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
      ( ( '\'const/sets/IN\'' @ TA @ C @ ( '\'const/sets/UNION\'' @ TA @ A @ B ) )
      = ( ( '\'const/sets/IN\'' @ TA @ C @ A )
        | ( '\'const/sets/IN\'' @ TA @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/IN_UNION_') ).

thf(15,plain,
    ! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
      ( ( '\'const/sets/IN\'' @ TA @ C @ ( '\'const/sets/UNION\'' @ TA @ A @ B ) )
      = ( ( '\'const/sets/IN\'' @ TA @ C @ A )
        | ( '\'const/sets/IN\'' @ TA @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(22,plain,
    $false,
    inference(e,[status(thm)],[10,9,12,7,18,15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEV451^1 : TPTP v8.2.0. Released v7.0.0.
% 0.03/0.12  % Command  : run_Leo-III %s %d THM
% 0.12/0.34  % Computer : n022.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % 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 18:47:10 EDT 2024
% 0.12/0.34  % CPUTime  : 
% 0.94/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.23/0.96  % [INFO] 	 Parsing done (97ms). 
% 1.23/0.97  % [INFO] 	 Running in sequential loop mode. 
% 1.63/1.16  % [INFO] 	 eprover registered as external prover. 
% 1.63/1.17  % [INFO] 	 Scanning for conjecture ... 
% 1.73/1.22  % [INFO] 	 Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ... 
% 1.84/1.24  % [INFO] 	 Axiom selection finished. Selected 4 axioms (removed 0 axioms). 
% 1.85/1.25  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.85/1.25  % [INFO] 	 Type checking passed. 
% 1.85/1.25  % [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 ... 
% 2.99/1.64  % External prover 'e' found a proof!
% 2.99/1.64  % [INFO] 	 Killing All external provers ... 
% 2.99/1.64  % Time passed: 1108ms (effective reasoning time: 672ms)
% 2.99/1.64  % 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)>
% 2.99/1.64  % Axioms used in derivation (4): thm/sets/IN_UNIV_, thm/sets/IN_, thm/sets/EXTENSION_, thm/sets/IN_UNION_
% 2.99/1.64  % No. of inferences in proof: 14
% 2.99/1.64  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1108 ms resp. 672 ms w/o parsing
% 2.99/1.67  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.99/1.67  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------