TSTP Solution File: SEV463^1 by Leo-III---1.7.15

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.15
% Problem  : SEV463^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d THM

% Computer : n026.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 15:59:06 EDT 2024

% Result   : Theorem 8.50s 2.90s
% Output   : Refutation 8.50s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   16 (  16 unt;   0 typ;   0 def)
%            Number of atoms       :   60 (  15 equ;   0 cnn)
%            Maximal formula atoms :    1 (   3 avg)
%            Number of connectives :  124 (   4   ~;   0   |;   0   &; 111   @)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   33 (  33   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   6 usr;   1 con; 0-3 aty)
%            Number of variables   :   44 (   0   ^  44   !;   0   ?;  44   :)

% 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/INTERS\'_type',type,
    '\'const/sets/INTERS\'': 
      !>[TA: $tType] : ( ( ( TA > $o ) > $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(sk2_type,type,
    sk2: ( skt1 > $o ) > $o ).

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

thf(1,conjecture,
    ! [TA: $tType,A: TA > $o,B: ( TA > $o ) > $o] :
      ( ( '\'const/sets/SUBSET\'' @ TA @ A @ ( '\'const/sets/INTERS\'' @ TA @ B ) )
      = ( ! [C: TA > $o] :
            ( ( '\'const/sets/IN\'' @ ( TA > $o ) @ C @ B )
           => ( '\'const/sets/SUBSET\'' @ TA @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/SUBSET_INTERS_') ).

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

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

thf(8,plain,
    ( ( '\'const/sets/SUBSET\'' @ skt1 @ sk1 @ ( '\'const/sets/INTERS\'' @ skt1 @ sk2 ) )
   != ( ! [A: skt1 > $o] :
          ( ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ A @ sk2 )
         => ( '\'const/sets/SUBSET\'' @ skt1 @ sk1 @ A ) ) ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(9,plain,
    ( ( '\'const/sets/SUBSET\'' @ skt1 @ sk1 @ ( '\'const/sets/INTERS\'' @ skt1 @ sk2 ) )
   != ( ! [A: skt1 > $o] :
          ( ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ A @ sk2 )
         => ( '\'const/sets/SUBSET\'' @ skt1 @ sk1 @ A ) ) ) ),
    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(13,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(11,plain,
    ! [TA: $tType,A: TA] :
      ( ( '\'const/trivia/I\'' @ TA @ A )
      = A ),
    inference(cnf,[status(esa)],[10]) ).

thf(12,plain,
    ! [TA: $tType,A: TA] :
      ( ( '\'const/trivia/I\'' @ TA @ A )
      = A ),
    inference(lifteq,[status(thm)],[11]) ).

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

thf(16,plain,
    ! [TA: $tType,A: ( TA > $o ) > $o,B: TA] :
      ( ( '\'const/sets/IN\'' @ TA @ B @ ( '\'const/sets/INTERS\'' @ TA @ A ) )
      = ( ! [C: TA > $o] :
            ( ( '\'const/sets/IN\'' @ ( TA > $o ) @ C @ A )
           => ( '\'const/sets/IN\'' @ TA @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(6,axiom,
    ! [TA: $tType,A: TA > $o,B: TA > $o] :
      ( ( '\'const/sets/SUBSET\'' @ TA @ 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/SUBSET_') ).

thf(19,plain,
    ! [TA: $tType,A: TA > $o,B: TA > $o] :
      ( ( '\'const/sets/SUBSET\'' @ TA @ 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(488,plain,
    $false,
    inference(e,[status(thm)],[10,9,13,12,7,16,19]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : SEV463^1 : TPTP v8.2.0. Released v7.0.0.
% 0.04/0.13  % Command  : run_Leo-III %s %d THM
% 0.13/0.35  % Computer : n026.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Fri Jun 21 18:27:10 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 1.07/0.96  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.32/1.07  % [INFO] 	 Parsing done (114ms). 
% 1.32/1.08  % [INFO] 	 Running in sequential loop mode. 
% 1.74/1.31  % [INFO] 	 eprover registered as external prover. 
% 1.74/1.31  % [INFO] 	 Scanning for conjecture ... 
% 2.01/1.37  % [INFO] 	 Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ... 
% 2.01/1.39  % [INFO] 	 Axiom selection finished. Selected 4 axioms (removed 0 axioms). 
% 2.01/1.41  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.01/1.41  % [INFO] 	 Type checking passed. 
% 2.01/1.41  % [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 ... 
% 8.50/2.90  % External prover 'e' found a proof!
% 8.50/2.90  % [INFO] 	 Killing All external provers ... 
% 8.50/2.90  % Time passed: 2334ms (effective reasoning time: 1812ms)
% 8.50/2.90  % 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)>
% 8.50/2.90  % Axioms used in derivation (4): thm/trivia/I_THM_, thm/sets/IN_, thm/sets/IN_INTERS_, thm/sets/SUBSET_
% 8.50/2.90  % No. of inferences in proof: 16
% 8.50/2.90  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2334 ms resp. 1812 ms w/o parsing
% 8.50/2.92  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.50/2.92  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------