TSTP Solution File: SET596+3 by Leo-III-SAT---1.7.10

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.10
% Problem  : SET596+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n002.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  7 10:50:00 EDT 2024

% Result   : Theorem 5.11s 2.33s
% Output   : Refutation 5.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   31 (  11 unt;   6 typ;   0 def)
%            Number of atoms       :   44 (  17 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  139 (  12   ~;   6   |;   3   &; 110   @)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :   32 (   0   ^  32   !;   0   ?;  32   :)

% 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 )
        & ( ( intersection @ B @ C )
          = empty_set ) )
     => ( ( intersection @ A @ C )
        = empty_set ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th55) ).

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

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

thf(15,plain,
    ( ( intersection @ sk2 @ sk3 )
    = empty_set ),
    inference(cnf,[status(esa)],[13]) ).

thf(18,plain,
    ( ( intersection @ sk2 @ sk3 )
    = empty_set ),
    inference(lifteq,[status(thm)],[15]) ).

thf(16,plain,
    subset @ sk1 @ sk2,
    inference(cnf,[status(esa)],[13]) ).

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

thf(22,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( subset @ A @ B )
     => ( subset @ ( intersection @ A @ C ) @ ( intersection @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(23,plain,
    ! [A: $i,B: $i] :
      ( ( subset @ A @ B )
     => ! [C: $i] : ( subset @ ( intersection @ A @ C ) @ ( intersection @ B @ C ) ) ),
    inference(miniscope,[status(thm)],[22]) ).

thf(24,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( subset @ A @ B )
      | ( subset @ ( intersection @ A @ C ) @ ( intersection @ B @ C ) ) ),
    inference(cnf,[status(esa)],[23]) ).

thf(216,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( subset @ ( intersection @ A @ C ) @ ( intersection @ B @ C ) )
      | ( ( subset @ sk1 @ sk2 )
       != ( subset @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[16,24]) ).

thf(217,plain,
    ! [A: $i] : ( subset @ ( intersection @ sk1 @ A ) @ ( intersection @ sk2 @ A ) ),
    inference(pattern_uni,[status(thm)],[216:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).

thf(243,plain,
    ! [A: $i] : ( subset @ ( intersection @ sk1 @ A ) @ ( intersection @ sk2 @ A ) ),
    inference(simp,[status(thm)],[217]) ).

thf(266,plain,
    ! [A: $i] :
      ( ( subset @ ( intersection @ sk1 @ A ) @ empty_set )
      | ( ( intersection @ sk2 @ sk3 )
       != ( intersection @ sk2 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[18,243]) ).

thf(267,plain,
    subset @ ( intersection @ sk1 @ sk3 ) @ empty_set,
    inference(pattern_uni,[status(thm)],[266:[bind(A,$thf( sk3 ))]]) ).

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

thf(20,plain,
    ! [A: $i] :
      ( ~ ( subset @ A @ empty_set )
      | ( A = empty_set ) ),
    inference(cnf,[status(esa)],[19]) ).

thf(21,plain,
    ! [A: $i] :
      ( ( A = empty_set )
      | ~ ( subset @ A @ empty_set ) ),
    inference(lifteq,[status(thm)],[20]) ).

thf(14,plain,
    ( ( intersection @ sk1 @ sk3 )
   != empty_set ),
    inference(cnf,[status(esa)],[13]) ).

thf(17,plain,
    ( ( intersection @ sk1 @ sk3 )
   != empty_set ),
    inference(lifteq,[status(thm)],[14]) ).

thf(91,plain,
    ! [A: $i] :
      ( ~ ( subset @ A @ empty_set )
      | ( A
       != ( intersection @ sk1 @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[21,17]) ).

thf(92,plain,
    ~ ( subset @ ( intersection @ sk1 @ sk3 ) @ empty_set ),
    inference(pattern_uni,[status(thm)],[91:[bind(A,$thf( intersection @ sk1 @ sk3 ))]]) ).

thf(296,plain,
    $false,
    inference(rewrite,[status(thm)],[267,92]) ).

thf(297,plain,
    $false,
    inference(simp,[status(thm)],[296]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SET596+3 : TPTP v8.1.2. Released v2.2.0.
% 0.06/0.14  % Command  : run_Leo-III %s %d
% 0.13/0.34  % Computer : n002.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Mon May  6 20:45:09 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 0.79/0.83  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.09/0.97  % [INFO] 	 Parsing done (135ms). 
% 1.09/0.97  % [INFO] 	 Running in sequential loop mode. 
% 1.50/1.24  % [INFO] 	 nitpick registered as external prover. 
% 1.50/1.24  % [INFO] 	 Scanning for conjecture ... 
% 1.81/1.32  % [INFO] 	 Found a conjecture and 10 axioms. Running axiom selection ... 
% 1.88/1.35  % [INFO] 	 Axiom selection finished. Selected 10 axioms (removed 0 axioms). 
% 1.88/1.37  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 1.88/1.37  % [INFO] 	 Type checking passed. 
% 1.88/1.37  % [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 ... 
% 5.11/2.33  % [INFO] 	 Killing All external provers ... 
% 5.11/2.33  % Time passed: 1845ms (effective reasoning time: 1349ms)
% 5.11/2.33  % 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)>
% 5.11/2.33  % Axioms used in derivation (2): intersection_of_subset, subset_of_empty_set_is_empty_set
% 5.11/2.33  % No. of inferences in proof: 25
% 5.11/2.33  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1845 ms resp. 1349 ms w/o parsing
% 5.11/2.36  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.11/2.36  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------