TSTP Solution File: SET926^20 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SET926^20 : TPTP v8.2.0. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n025.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 03:07:23 EDT 2024

% Result   : Theorem 45.69s 7.74s
% Output   : Refutation 45.73s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   45 (  13 unt;  15 typ;   5 def)
%            Number of atoms       :  110 (  19 equ;   0 cnn)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives :  321 (  28   ~;  21   |;   0   &; 265   @)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   38 (  38   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  14 usr;   6 con; 0-3 aty)
%            Number of variables   :   40 (  19   ^  21   !;   0   ?;  40   :)

% Comments : 
%------------------------------------------------------------------------------
thf(mworld_type,type,
    mworld: $tType ).

thf(mactual_type,type,
    mactual: mworld ).

thf(mlocal_type,type,
    mlocal: ( mworld > $o ) > $o ).

thf(mlocal_def,definition,
    ( mlocal
    = ( ^ [A: mworld > $o] : ( A @ mactual ) ) ) ).

thf(mnot_type,type,
    mnot: ( mworld > $o ) > mworld > $o ).

thf(mnot_def,definition,
    ( mnot
    = ( ^ [A: mworld > $o,B: mworld] :
          ~ ( A @ B ) ) ) ).

thf(mor_type,type,
    mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).

thf(mor_def,definition,
    ( mor
    = ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
          ( ( A @ C )
          | ( B @ C ) ) ) ) ).

thf(mequiv_type,type,
    mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).

thf(mequiv_def,definition,
    ( mequiv
    = ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
          ( ( A @ C )
          = ( B @ C ) ) ) ) ).

thf(eiw_di_type,type,
    eiw_di: $i > mworld > $o ).

thf(mforall_di_type,type,
    mforall_di: ( $i > mworld > $o ) > mworld > $o ).

thf(mforall_di_def,definition,
    ( mforall_di
    = ( ^ [A: $i > mworld > $o,B: mworld] :
        ! [C: $i] :
          ( ( eiw_di @ C @ B )
         => ( A @ C @ B ) ) ) ) ).

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

thf(qmltpeq_type,type,
    qmltpeq: $i > $i > mworld > $o ).

thf(in_type,type,
    in: $i > $i > mworld > $o ).

thf(singleton_type,type,
    singleton: $i > $i ).

thf(set_difference_type,type,
    set_difference: $i > $i > $i ).

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

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

thf(1,conjecture,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] : ( mor @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set ) @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_zfmisc_1) ).

thf(2,negated_conjecture,
    ~ ( mlocal
      @ ( mforall_di
        @ ^ [A: $i] :
            ( mforall_di
            @ ^ [B: $i] : ( mor @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set ) @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(21,plain,
    ~ ! [A: $i] :
        ( ( eiw_di @ A @ mactual )
       => ! [B: $i] :
            ( ( eiw_di @ B @ mactual )
           => ( ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set @ mactual )
              | ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) @ mactual ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(25,plain,
    eiw_di @ sk1 @ mactual,
    inference(cnf,[status(esa)],[21]) ).

thf(24,plain,
    eiw_di @ sk2 @ mactual,
    inference(cnf,[status(esa)],[21]) ).

thf(18,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set ) @ ( in @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l36_zfmisc_1) ).

thf(58,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ( ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set @ mactual )
            = ( in @ A @ B @ mactual ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(59,plain,
    ! [B: $i,A: $i] :
      ( ~ ( eiw_di @ A @ mactual )
      | ~ ( eiw_di @ B @ mactual )
      | ( ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set @ mactual )
        = ( in @ A @ B @ mactual ) ) ),
    inference(cnf,[status(esa)],[58]) ).

thf(60,plain,
    ! [B: $i,A: $i] :
      ( ( ( in @ A @ B @ mactual )
        = ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set @ mactual ) )
      | ~ ( eiw_di @ A @ mactual )
      | ~ ( eiw_di @ B @ mactual ) ),
    inference(lifteq,[status(thm)],[59]) ).

thf(2594,plain,
    ! [B: $i,A: $i] :
      ( ( ( in @ A @ B @ mactual )
        = ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set @ mactual ) )
      | ~ ( eiw_di @ A @ mactual )
      | ( ( eiw_di @ sk2 @ mactual )
       != ( eiw_di @ B @ mactual ) ) ),
    inference(paramod_ordered,[status(thm)],[24,60]) ).

thf(2595,plain,
    ! [A: $i] :
      ( ( ( in @ A @ sk2 @ mactual )
        = ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ sk2 ) @ empty_set @ mactual ) )
      | ~ ( eiw_di @ A @ mactual ) ),
    inference(pattern_uni,[status(thm)],[2594:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).

thf(4128,plain,
    ! [A: $i] :
      ( ( ( in @ A @ sk2 @ mactual )
        = ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ sk2 ) @ empty_set @ mactual ) )
      | ( ( eiw_di @ sk1 @ mactual )
       != ( eiw_di @ A @ mactual ) ) ),
    inference(paramod_ordered,[status(thm)],[25,2595]) ).

thf(4129,plain,
    ( ( in @ sk1 @ sk2 @ mactual )
    = ( qmltpeq @ ( set_difference @ ( singleton @ sk1 ) @ sk2 ) @ empty_set @ mactual ) ),
    inference(pattern_uni,[status(thm)],[4128:[bind(A,$thf( sk1 ))]]) ).

thf(23,plain,
    ~ ( qmltpeq @ ( set_difference @ ( singleton @ sk1 ) @ sk2 ) @ empty_set @ mactual ),
    inference(cnf,[status(esa)],[21]) ).

thf(16,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) ) @ ( mnot @ ( in @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l34_zfmisc_1) ).

thf(53,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ( ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) @ mactual )
            = ( ~ ( in @ A @ B @ mactual ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(54,plain,
    ! [B: $i,A: $i] :
      ( ~ ( eiw_di @ A @ mactual )
      | ~ ( eiw_di @ B @ mactual )
      | ( ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) @ mactual )
        = ( ~ ( in @ A @ B @ mactual ) ) ) ),
    inference(cnf,[status(esa)],[53]) ).

thf(55,plain,
    ! [B: $i,A: $i] :
      ( ( ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) @ mactual )
        = ( ~ ( in @ A @ B @ mactual ) ) )
      | ~ ( eiw_di @ A @ mactual )
      | ~ ( eiw_di @ B @ mactual ) ),
    inference(lifteq,[status(thm)],[54]) ).

thf(22,plain,
    ~ ( qmltpeq @ ( set_difference @ ( singleton @ sk1 ) @ sk2 ) @ ( singleton @ sk1 ) @ mactual ),
    inference(cnf,[status(esa)],[21]) ).

thf(1694,plain,
    ! [B: $i,A: $i] :
      ( ~ ( eiw_di @ A @ mactual )
      | ~ ( eiw_di @ B @ mactual )
      | ( in @ A @ B @ mactual )
      | ( ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) @ mactual )
       != ( qmltpeq @ ( set_difference @ ( singleton @ sk1 ) @ sk2 ) @ ( singleton @ sk1 ) @ mactual ) ) ),
    inference(paramod_ordered,[status(thm)],[55,22]) ).

thf(1695,plain,
    ( ~ ( eiw_di @ sk1 @ mactual )
    | ~ ( eiw_di @ sk2 @ mactual )
    | ( in @ sk1 @ sk2 @ mactual ) ),
    inference(pattern_uni,[status(thm)],[1694:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).

thf(2091,plain,
    ( ~ $true
    | ~ $true
    | ( in @ sk1 @ sk2 @ mactual ) ),
    inference(rewrite,[status(thm)],[1695,24,25]) ).

thf(2092,plain,
    in @ sk1 @ sk2 @ mactual,
    inference(simp,[status(thm)],[2091]) ).

thf(4319,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[4129,23,2092]) ).

thf(4320,plain,
    $false,
    inference(simp,[status(thm)],[4319]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.15  % Problem  : SET926^20 : TPTP v8.2.0. Released v8.1.0.
% 0.17/0.18  % Command  : run_Leo-III %s %d
% 0.18/0.40  % Computer : n025.cluster.edu
% 0.18/0.40  % Model    : x86_64 x86_64
% 0.18/0.40  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.40  % Memory   : 8042.1875MB
% 0.18/0.40  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.18/0.40  % CPULimit : 300
% 0.18/0.40  % WCLimit  : 300
% 0.18/0.40  % DateTime : Mon May 20 11:05:54 EDT 2024
% 0.18/0.40  % CPUTime  : 
% 1.01/0.92  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.45/1.09  % [INFO] 	 Parsing done (167ms). 
% 1.45/1.09  % [INFO] 	 Running in sequential loop mode. 
% 2.03/1.37  % [INFO] 	 nitpick registered as external prover. 
% 2.03/1.37  % [INFO] 	 Scanning for conjecture ... 
% 2.35/1.46  % [INFO] 	 Found a conjecture (or negated_conjecture) and 18 axioms. Running axiom selection ... 
% 2.52/1.51  % [INFO] 	 Axiom selection finished. Selected 18 axioms (removed 0 axioms). 
% 2.52/1.53  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.52/1.54  % [INFO] 	 Type checking passed. 
% 2.52/1.54  % [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 ... 
% 45.69/7.73  % [INFO] 	 Killing All external provers ... 
% 45.69/7.74  % Time passed: 7171ms (effective reasoning time: 6635ms)
% 45.69/7.74  % 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)>
% 45.69/7.74  % Axioms used in derivation (2): l36_zfmisc_1, l34_zfmisc_1
% 45.69/7.74  % No. of inferences in proof: 25
% 45.69/7.74  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 7171 ms resp. 6635 ms w/o parsing
% 45.73/7.80  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 45.73/7.81  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------