TSTP Solution File: SET055^12 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SET055^12 : TPTP v8.2.0. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n027.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 03:05:06 EDT 2024

% Result   : Theorem 99.26s 17.15s
% Output   : Refutation 99.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   47 (  10 unt;  13 typ;   5 def)
%            Number of atoms       :  127 (  14 equ;   0 cnn)
%            Maximal formula atoms :    9 (   3 avg)
%            Number of connectives :  347 (  46   ~;  31   |;   6   &; 247   @)
%                                         (   0 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   41 (  41   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   15 (  12 usr;   5 con; 0-3 aty)
%            Number of variables   :   42 (  19   ^  23   !;   0   ?;  42   :)

% 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(mand_type,type,
    mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).

thf(mand_def,definition,
    ( mand
    = ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
          ( ( A @ C )
          & ( B @ C ) ) ) ) ).

thf(mimplies_type,type,
    mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).

thf(mimplies_def,definition,
    ( mimplies
    = ( ^ [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(qmltpeq_type,type,
    qmltpeq: $i > $i > mworld > $o ).

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

thf(subclass_type,type,
    subclass: $i > $i > mworld > $o ).

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

thf(sk199_type,type,
    sk199: $i ).

thf(57,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] :
              ( mequiv @ ( subclass @ A @ B )
              @ ( mforall_di
                @ ^ [C: $i] : ( mimplies @ ( member @ C @ A ) @ ( member @ C @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_defn) ).

thf(217,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ( ( subclass @ A @ B @ mactual )
            = ( ! [C: $i] :
                  ( ( eiw_di @ C @ mactual )
                 => ( ( member @ C @ A @ mactual )
                   => ( member @ C @ B @ mactual ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(218,plain,
    ! [B: $i,A: $i] :
      ( ~ ( eiw_di @ A @ mactual )
      | ~ ( eiw_di @ B @ mactual )
      | ( ( subclass @ A @ B @ mactual )
        = ( ! [C: $i] :
              ( ( eiw_di @ C @ mactual )
             => ( ( member @ C @ A @ mactual )
               => ( member @ C @ B @ mactual ) ) ) ) ) ),
    inference(cnf,[status(esa)],[217]) ).

thf(219,plain,
    ! [B: $i,A: $i] :
      ( ( ( subclass @ A @ B @ mactual )
        = ( ! [C: $i] :
              ( ( eiw_di @ C @ mactual )
             => ( ( member @ C @ A @ mactual )
               => ( member @ C @ B @ mactual ) ) ) ) )
      | ~ ( eiw_di @ A @ mactual )
      | ~ ( eiw_di @ B @ mactual ) ),
    inference(lifteq,[status(thm)],[218]) ).

thf(9,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] : ( mequiv @ ( qmltpeq @ A @ B ) @ ( mand @ ( subclass @ A @ B ) @ ( subclass @ B @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality) ).

thf(103,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ( ( qmltpeq @ A @ B @ mactual )
            = ( ( subclass @ A @ B @ mactual )
              & ( subclass @ B @ A @ mactual ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(104,plain,
    ! [B: $i,A: $i] :
      ( ~ ( eiw_di @ A @ mactual )
      | ~ ( eiw_di @ B @ mactual )
      | ( ( qmltpeq @ A @ B @ mactual )
        = ( ( subclass @ A @ B @ mactual )
          & ( subclass @ B @ A @ mactual ) ) ) ),
    inference(cnf,[status(esa)],[103]) ).

thf(105,plain,
    ! [B: $i,A: $i] :
      ( ( ( qmltpeq @ A @ B @ mactual )
        = ( ( subclass @ A @ B @ mactual )
          & ( subclass @ B @ A @ mactual ) ) )
      | ~ ( eiw_di @ A @ mactual )
      | ~ ( eiw_di @ B @ mactual ) ),
    inference(lifteq,[status(thm)],[104]) ).

thf(1,conjecture,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] : ( qmltpeq @ A @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_0) ).

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

thf(87,plain,
    ~ ! [A: $i] :
        ( ( eiw_di @ A @ mactual )
       => ( qmltpeq @ A @ A @ mactual ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(88,plain,
    ~ ( qmltpeq @ sk1 @ sk1 @ mactual ),
    inference(cnf,[status(esa)],[87]) ).

thf(1373,plain,
    ! [B: $i,A: $i] :
      ( ~ ( eiw_di @ A @ mactual )
      | ~ ( eiw_di @ B @ mactual )
      | ~ ( ( subclass @ A @ B @ mactual )
          & ( subclass @ B @ A @ mactual ) )
      | ( ( qmltpeq @ A @ B @ mactual )
       != ( qmltpeq @ sk1 @ sk1 @ mactual ) ) ),
    inference(paramod_ordered,[status(thm)],[105,88]) ).

thf(1374,plain,
    ( ~ ( eiw_di @ sk1 @ mactual )
    | ~ ( eiw_di @ sk1 @ mactual )
    | ~ ( ( subclass @ sk1 @ sk1 @ mactual )
        & ( subclass @ sk1 @ sk1 @ mactual ) ) ),
    inference(pattern_uni,[status(thm)],[1373:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).

thf(1488,plain,
    ( ~ ( subclass @ sk1 @ sk1 @ mactual )
    | ~ ( subclass @ sk1 @ sk1 @ mactual )
    | ~ ( eiw_di @ sk1 @ mactual )
    | ~ ( eiw_di @ sk1 @ mactual ) ),
    inference(cnf,[status(esa)],[1374]) ).

thf(1489,plain,
    ( ~ ( subclass @ sk1 @ sk1 @ mactual )
    | ~ ( eiw_di @ sk1 @ mactual ) ),
    inference(simp,[status(thm)],[1488]) ).

thf(89,plain,
    eiw_di @ sk1 @ mactual,
    inference(cnf,[status(esa)],[87]) ).

thf(1528,plain,
    ( ~ ( subclass @ sk1 @ sk1 @ mactual )
    | ~ $true ),
    inference(rewrite,[status(thm)],[1489,89]) ).

thf(1529,plain,
    ~ ( subclass @ sk1 @ sk1 @ mactual ),
    inference(simp,[status(thm)],[1528]) ).

thf(32201,plain,
    ! [B: $i,A: $i] :
      ( ~ ( eiw_di @ A @ mactual )
      | ~ ( eiw_di @ B @ mactual )
      | ~ ! [C: $i] :
            ( ( eiw_di @ C @ mactual )
           => ( ( member @ C @ A @ mactual )
             => ( member @ C @ B @ mactual ) ) )
      | ( ( subclass @ A @ B @ mactual )
       != ( subclass @ sk1 @ sk1 @ mactual ) ) ),
    inference(paramod_ordered,[status(thm)],[219,1529]) ).

thf(32202,plain,
    ( ~ ( eiw_di @ sk1 @ mactual )
    | ~ ( eiw_di @ sk1 @ mactual )
    | ~ ! [A: $i] :
          ( ( eiw_di @ A @ mactual )
         => ( ( member @ A @ sk1 @ mactual )
           => ( member @ A @ sk1 @ mactual ) ) ) ),
    inference(pattern_uni,[status(thm)],[32201:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).

thf(32614,plain,
    ( ( member @ sk199 @ sk1 @ mactual )
    | ~ ( eiw_di @ sk1 @ mactual )
    | ~ ( eiw_di @ sk1 @ mactual ) ),
    inference(cnf,[status(esa)],[32202]) ).

thf(32617,plain,
    ( ( member @ sk199 @ sk1 @ mactual )
    | ~ ( eiw_di @ sk1 @ mactual ) ),
    inference(simp,[status(thm)],[32614]) ).

thf(32613,plain,
    ( ~ ( member @ sk199 @ sk1 @ mactual )
    | ~ ( eiw_di @ sk1 @ mactual )
    | ~ ( eiw_di @ sk1 @ mactual ) ),
    inference(cnf,[status(esa)],[32202]) ).

thf(32616,plain,
    ( ~ ( member @ sk199 @ sk1 @ mactual )
    | ~ ( eiw_di @ sk1 @ mactual ) ),
    inference(simp,[status(thm)],[32613]) ).

thf(35081,plain,
    ( ~ ( member @ sk199 @ sk1 @ mactual )
    | ~ $true ),
    inference(rewrite,[status(thm)],[32616,89]) ).

thf(35082,plain,
    ~ ( member @ sk199 @ sk1 @ mactual ),
    inference(simp,[status(thm)],[35081]) ).

thf(35880,plain,
    ( $false
    | ~ $true ),
    inference(rewrite,[status(thm)],[32617,89,35082]) ).

thf(35881,plain,
    $false,
    inference(simp,[status(thm)],[35880]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : SET055^12 : TPTP v8.2.0. Released v8.1.0.
% 0.11/0.14  % Command  : run_Leo-III %s %d
% 0.14/0.35  % Computer : n027.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Mon May 20 12:18:23 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.93/0.83  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.40/1.04  % [INFO] 	 Parsing done (204ms). 
% 1.40/1.05  % [INFO] 	 Running in sequential loop mode. 
% 2.03/1.24  % [INFO] 	 nitpick registered as external prover. 
% 2.03/1.25  % [INFO] 	 Scanning for conjecture ... 
% 2.19/1.34  % [INFO] 	 Found a conjecture (or negated_conjecture) and 85 axioms. Running axiom selection ... 
% 2.60/1.40  % [INFO] 	 Axiom selection finished. Selected 84 axioms (removed 1 axioms). 
% 2.81/1.47  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.81/1.48  % [INFO] 	 Type checking passed. 
% 2.81/1.48  % [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 ... 
% 99.26/17.14  % [INFO] 	 Killing All external provers ... 
% 99.26/17.15  % Time passed: 16639ms (effective reasoning time: 16093ms)
% 99.26/17.15  % 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)>
% 99.26/17.15  % Axioms used in derivation (2): subclass_defn, extensionality
% 99.26/17.15  % No. of inferences in proof: 29
% 99.26/17.15  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 16639 ms resp. 16093 ms w/o parsing
% 99.26/17.19  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 99.26/17.19  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------