TSTP Solution File: SET062+4 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SET062+4 : TPTP v8.2.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n028.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 03:05:09 EDT 2024

% Result   : Theorem 5.37s 2.64s
% Output   : Refutation 5.37s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   23 (  12 unt;   5 typ;   0 def)
%            Number of atoms       :   35 (   1 equ;   0 cnn)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :   94 (   9   ~;   3   |;   2   &;  70   @)
%                                         (   1 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   29 (   0   ^  28   !;   1   ?;  29   :)

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

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

thf(member_type,type,
    member: $i > $i > $o ).

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

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

thf(1,conjecture,
    ! [A: $i] : ( subset @ empty_set @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI15) ).

thf(2,negated_conjecture,
    ~ ! [A: $i] : ( subset @ empty_set @ A ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(14,plain,
    ~ ! [A: $i] : ( subset @ empty_set @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(15,plain,
    ~ ( subset @ empty_set @ sk1 ),
    inference(cnf,[status(esa)],[14]) ).

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

thf(16,plain,
    ! [A: $i,B: $i] :
      ( ( ( subset @ A @ B )
       => ! [C: $i] :
            ( ( member @ C @ A )
           => ( member @ C @ B ) ) )
      & ( ! [C: $i] :
            ( ( member @ C @ A )
           => ( member @ C @ B ) )
       => ( subset @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(17,plain,
    ( ! [A: $i,B: $i] :
        ( ( subset @ A @ B )
       => ! [C: $i] :
            ( ( member @ C @ A )
           => ( member @ C @ B ) ) )
    & ! [A: $i,B: $i] :
        ( ! [C: $i] :
            ( ( member @ C @ A )
           => ( member @ C @ B ) )
       => ( subset @ A @ B ) ) ),
    inference(miniscope,[status(thm)],[16]) ).

thf(18,plain,
    ! [B: $i,A: $i] :
      ( ( member @ ( sk2 @ B @ A ) @ A )
      | ( subset @ A @ B ) ),
    inference(cnf,[status(esa)],[17]) ).

thf(21,plain,
    ! [B: $i,A: $i] :
      ( ( member @ ( sk2 @ B @ A ) @ A )
      | ( subset @ A @ B ) ),
    inference(simp,[status(thm)],[18]) ).

thf(8,axiom,
    ! [A: $i] :
      ~ ( member @ A @ empty_set ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set) ).

thf(47,plain,
    ! [A: $i] :
      ~ ( member @ A @ empty_set ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(48,plain,
    ~ ? [A: $i] : ( member @ A @ empty_set ),
    inference(miniscope,[status(thm)],[47]) ).

thf(49,plain,
    ! [A: $i] :
      ~ ( member @ A @ empty_set ),
    inference(cnf,[status(esa)],[48]) ).

thf(183,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( subset @ A @ B )
      | ( ( member @ ( sk2 @ B @ A ) @ A )
       != ( member @ C @ empty_set ) ) ),
    inference(paramod_ordered,[status(thm)],[21,49]) ).

thf(184,plain,
    ! [A: $i] : ( subset @ empty_set @ A ),
    inference(pattern_uni,[status(thm)],[183:[bind(A,$thf( empty_set )),bind(B,$thf( D )),bind(C,$thf( sk2 @ D @ empty_set ))]]) ).

thf(190,plain,
    ! [A: $i] : ( subset @ empty_set @ A ),
    inference(simp,[status(thm)],[184]) ).

thf(194,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[15,190]) ).

thf(195,plain,
    $false,
    inference(simp,[status(thm)],[194]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : SET062+4 : TPTP v8.2.0. Released v2.2.0.
% 0.10/0.12  % Command  : run_Leo-III %s %d
% 0.11/0.32  % Computer : n028.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Mon May 20 12:10:38 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 0.95/0.93  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.35/1.10  % [INFO] 	 Parsing done (169ms). 
% 1.35/1.11  % [INFO] 	 Running in sequential loop mode. 
% 1.78/1.45  % [INFO] 	 nitpick registered as external prover. 
% 1.78/1.46  % [INFO] 	 Scanning for conjecture ... 
% 2.08/1.54  % [INFO] 	 Found a conjecture (or negated_conjecture) and 11 axioms. Running axiom selection ... 
% 2.08/1.57  % [INFO] 	 Axiom selection finished. Selected 11 axioms (removed 0 axioms). 
% 2.08/1.60  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.08/1.61  % [INFO] 	 Type checking passed. 
% 2.30/1.61  % [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 ... 
% 5.37/2.63  % [INFO] 	 Killing All external provers ... 
% 5.37/2.63  % Time passed: 2161ms (effective reasoning time: 1515ms)
% 5.37/2.63  % 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)>
% 5.37/2.63  % Axioms used in derivation (2): subset, empty_set
% 5.37/2.63  % No. of inferences in proof: 18
% 5.37/2.64  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2161 ms resp. 1515 ms w/o parsing
% 5.37/2.66  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.37/2.66  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------