TSTP Solution File: SET592+3 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SET592+3 : TPTP v8.2.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% 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 : Tue May 21 03:06:21 EDT 2024

% Result   : Theorem 34.58s 6.56s
% Output   : Refutation 34.58s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   31 (   8 unt;   6 typ;   0 def)
%            Number of atoms       :   59 (  19 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  149 (  21   ~;  14   |;  10   &;  96   @)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   6 usr;   6 con; 0-2 aty)
%            Number of variables   :   31 (   0   ^  29   !;   2   ?;  31   :)

% Comments : 
%------------------------------------------------------------------------------
thf(subset_type,type,
    subset: $i > $i > $o ).

thf(intersection_type,type,
    intersection: $i > $i > $i ).

thf(empty_set_type,type,
    empty_set: $i ).

thf(sk1_type,type,
    sk1: $i ).

thf(sk2_type,type,
    sk2: $i ).

thf(sk3_type,type,
    sk3: $i ).

thf(1,conjecture,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( subset @ A @ B )
        & ( subset @ A @ C )
        & ( ( intersection @ B @ C )
          = empty_set ) )
     => ( A = empty_set ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th51) ).

thf(2,negated_conjecture,
    ~ ! [A: $i,B: $i,C: $i] :
        ( ( ( subset @ A @ B )
          & ( subset @ A @ C )
          & ( ( intersection @ B @ C )
            = empty_set ) )
       => ( A = empty_set ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(13,plain,
    ~ ! [A: $i,B: $i,C: $i] :
        ( ( ( subset @ A @ B )
          & ( subset @ A @ C )
          & ( ( intersection @ B @ C )
            = empty_set ) )
       => ( A = empty_set ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(14,plain,
    ~ ! [A: $i] :
        ( ? [B: $i] :
            ( ( subset @ A @ B )
            & ? [C: $i] :
                ( ( subset @ A @ C )
                & ( ( intersection @ B @ C )
                  = empty_set ) ) )
       => ( A = empty_set ) ),
    inference(miniscope,[status(thm)],[13]) ).

thf(17,plain,
    subset @ sk1 @ sk3,
    inference(cnf,[status(esa)],[14]) ).

thf(16,plain,
    ( ( intersection @ sk2 @ sk3 )
    = empty_set ),
    inference(cnf,[status(esa)],[14]) ).

thf(20,plain,
    ( ( intersection @ sk2 @ sk3 )
    = empty_set ),
    inference(lifteq,[status(thm)],[16]) ).

thf(4,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( subset @ A @ B )
        & ( subset @ A @ C ) )
     => ( subset @ A @ ( intersection @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_of_subsets) ).

thf(24,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( subset @ A @ B )
        & ( subset @ A @ C ) )
     => ( subset @ A @ ( intersection @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(25,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( subset @ A @ B )
      | ~ ( subset @ A @ C )
      | ( subset @ A @ ( intersection @ B @ C ) ) ),
    inference(cnf,[status(esa)],[24]) ).

thf(176,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( subset @ A @ B )
      | ~ ( subset @ A @ C )
      | ( subset @ A @ empty_set )
      | ( ( intersection @ sk2 @ sk3 )
       != ( intersection @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[20,25]) ).

thf(177,plain,
    ! [A: $i] :
      ( ~ ( subset @ A @ sk2 )
      | ~ ( subset @ A @ sk3 )
      | ( subset @ A @ empty_set ) ),
    inference(pattern_uni,[status(thm)],[176:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( sk3 ))]]) ).

thf(6142,plain,
    ! [A: $i] :
      ( ~ ( subset @ A @ sk2 )
      | ( subset @ A @ empty_set )
      | ( ( subset @ sk1 @ sk3 )
       != ( subset @ A @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[17,177]) ).

thf(6143,plain,
    ( ~ ( subset @ sk1 @ sk2 )
    | ( subset @ sk1 @ empty_set ) ),
    inference(pattern_uni,[status(thm)],[6142:[bind(A,$thf( sk1 ))]]) ).

thf(18,plain,
    subset @ sk1 @ sk2,
    inference(cnf,[status(esa)],[14]) ).

thf(3,axiom,
    ! [A: $i] :
      ( ( subset @ A @ empty_set )
     => ( A = empty_set ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_of_empty_set_is_empty_set) ).

thf(21,plain,
    ! [A: $i] :
      ( ( subset @ A @ empty_set )
     => ( A = empty_set ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(22,plain,
    ! [A: $i] :
      ( ~ ( subset @ A @ empty_set )
      | ( A = empty_set ) ),
    inference(cnf,[status(esa)],[21]) ).

thf(23,plain,
    ! [A: $i] :
      ( ( A = empty_set )
      | ~ ( subset @ A @ empty_set ) ),
    inference(lifteq,[status(thm)],[22]) ).

thf(15,plain,
    sk1 != empty_set,
    inference(cnf,[status(esa)],[14]) ).

thf(19,plain,
    sk1 != empty_set,
    inference(lifteq,[status(thm)],[15]) ).

thf(109,plain,
    ! [A: $i] :
      ( ~ ( subset @ A @ empty_set )
      | ( A != sk1 ) ),
    inference(paramod_ordered,[status(thm)],[23,19]) ).

thf(110,plain,
    ~ ( subset @ sk1 @ empty_set ),
    inference(pattern_uni,[status(thm)],[109:[bind(A,$thf( sk1 ))]]) ).

thf(6220,plain,
    ( ~ $true
    | $false ),
    inference(rewrite,[status(thm)],[6143,18,110]) ).

thf(6221,plain,
    $false,
    inference(simp,[status(thm)],[6220]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09  % Problem  : SET592+3 : TPTP v8.2.0. Released v2.2.0.
% 0.05/0.11  % Command  : run_Leo-III %s %d
% 0.11/0.31  % Computer : n021.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit : 300
% 0.11/0.31  % WCLimit  : 300
% 0.11/0.31  % DateTime : Mon May 20 12:09:09 EDT 2024
% 0.15/0.31  % CPUTime  : 
% 0.90/0.92  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.31/1.08  % [INFO] 	 Parsing done (161ms). 
% 1.31/1.09  % [INFO] 	 Running in sequential loop mode. 
% 1.69/1.44  % [INFO] 	 nitpick registered as external prover. 
% 1.69/1.45  % [INFO] 	 Scanning for conjecture ... 
% 2.00/1.54  % [INFO] 	 Found a conjecture (or negated_conjecture) and 10 axioms. Running axiom selection ... 
% 2.03/1.57  % [INFO] 	 Axiom selection finished. Selected 10 axioms (removed 0 axioms). 
% 2.03/1.59  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.03/1.60  % [INFO] 	 Type checking passed. 
% 2.03/1.60  % [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 ... 
% 34.58/6.55  % [INFO] 	 Killing All external provers ... 
% 34.58/6.56  % Time passed: 6100ms (effective reasoning time: 5455ms)
% 34.58/6.56  % 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)>
% 34.58/6.56  % Axioms used in derivation (2): intersection_of_subsets, subset_of_empty_set_is_empty_set
% 34.58/6.56  % No. of inferences in proof: 25
% 34.58/6.56  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6100 ms resp. 5455 ms w/o parsing
% 34.58/6.64  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 34.58/6.64  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------