TSTP Solution File: SET019^4 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SET019^4 : TPTP v8.2.0. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n016.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 03:04:53 EDT 2024

% Result   : Theorem 14.91s 4.38s
% Output   : Refutation 15.07s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   35 (  12 unt;  12 typ;   5 def)
%            Number of atoms       :   91 (  15 equ;   0 cnn)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  200 (  12   ~;   8   |;  10   &; 163   @)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   38 (  38   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  11 usr;   5 con; 0-3 aty)
%            Number of variables   :   31 (  18   ^  13   !;   0   ?;  31   :)

% 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(equal_set_type,type,
    equal_set: $i > $i > mworld > $o ).

thf(subset_type,type,
    subset: $i > $i > mworld > $o ).

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

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

thf(1,conjecture,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] : ( mimplies @ ( mand @ ( subset @ A @ B ) @ ( subset @ B @ A ) ) @ ( equal_set @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI02) ).

thf(2,negated_conjecture,
    ~ ( mlocal
      @ ( mforall_di
        @ ^ [A: $i] :
            ( mforall_di
            @ ^ [B: $i] : ( mimplies @ ( mand @ ( subset @ A @ B ) @ ( subset @ B @ A ) ) @ ( equal_set @ A @ B ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(38,plain,
    ~ ! [A: $i] :
        ( ( eiw_di @ A @ mactual )
       => ! [B: $i] :
            ( ( eiw_di @ B @ mactual )
           => ( ( ( subset @ A @ B @ mactual )
                & ( subset @ B @ A @ mactual ) )
             => ( equal_set @ A @ B @ mactual ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(43,plain,
    eiw_di @ sk1 @ mactual,
    inference(cnf,[status(esa)],[38]) ).

thf(41,plain,
    eiw_di @ sk2 @ mactual,
    inference(cnf,[status(esa)],[38]) ).

thf(8,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] : ( mequiv @ ( equal_set @ A @ B ) @ ( mand @ ( subset @ A @ B ) @ ( subset @ B @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set_0) ).

thf(56,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ( ( equal_set @ A @ B @ mactual )
            = ( ( subset @ A @ B @ mactual )
              & ( subset @ B @ A @ mactual ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(57,plain,
    ! [B: $i,A: $i] :
      ( ~ ( eiw_di @ A @ mactual )
      | ~ ( eiw_di @ B @ mactual )
      | ( ( equal_set @ A @ B @ mactual )
        = ( ( subset @ A @ B @ mactual )
          & ( subset @ B @ A @ mactual ) ) ) ),
    inference(cnf,[status(esa)],[56]) ).

thf(58,plain,
    ! [B: $i,A: $i] :
      ( ( ( equal_set @ A @ B @ mactual )
        = ( ( subset @ A @ B @ mactual )
          & ( subset @ B @ A @ mactual ) ) )
      | ~ ( eiw_di @ A @ mactual )
      | ~ ( eiw_di @ B @ mactual ) ),
    inference(lifteq,[status(thm)],[57]) ).

thf(481,plain,
    ! [B: $i,A: $i] :
      ( ( ( equal_set @ A @ B @ mactual )
        = ( ( subset @ A @ B @ mactual )
          & ( subset @ B @ A @ mactual ) ) )
      | ~ ( eiw_di @ A @ mactual )
      | ( ( eiw_di @ sk2 @ mactual )
       != ( eiw_di @ B @ mactual ) ) ),
    inference(paramod_ordered,[status(thm)],[41,58]) ).

thf(482,plain,
    ! [A: $i] :
      ( ( ( equal_set @ A @ sk2 @ mactual )
        = ( ( subset @ A @ sk2 @ mactual )
          & ( subset @ sk2 @ A @ mactual ) ) )
      | ~ ( eiw_di @ A @ mactual ) ),
    inference(pattern_uni,[status(thm)],[481:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).

thf(1241,plain,
    ! [A: $i] :
      ( ( ( equal_set @ A @ sk2 @ mactual )
        = ( ( subset @ A @ sk2 @ mactual )
          & ( subset @ sk2 @ A @ mactual ) ) )
      | ( ( eiw_di @ sk1 @ mactual )
       != ( eiw_di @ A @ mactual ) ) ),
    inference(paramod_ordered,[status(thm)],[43,482]) ).

thf(1242,plain,
    ( ( equal_set @ sk1 @ sk2 @ mactual )
    = ( ( subset @ sk1 @ sk2 @ mactual )
      & ( subset @ sk2 @ sk1 @ mactual ) ) ),
    inference(pattern_uni,[status(thm)],[1241:[bind(A,$thf( sk1 ))]]) ).

thf(39,plain,
    subset @ sk1 @ sk2 @ mactual,
    inference(cnf,[status(esa)],[38]) ).

thf(40,plain,
    subset @ sk2 @ sk1 @ mactual,
    inference(cnf,[status(esa)],[38]) ).

thf(42,plain,
    ~ ( equal_set @ sk1 @ sk2 @ mactual ),
    inference(cnf,[status(esa)],[38]) ).

thf(1349,plain,
    ~ ( $true
      & $true ),
    inference(rewrite,[status(thm)],[1242,39,40,42]) ).

thf(1350,plain,
    $false,
    inference(simp,[status(thm)],[1349]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SET019^4 : TPTP v8.2.0. Released v8.1.0.
% 0.06/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.35  % Computer : n016.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Mon May 20 11:23:24 EDT 2024
% 0.15/0.35  % CPUTime  : 
% 1.01/0.96  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.59/1.17  % [INFO] 	 Parsing done (211ms). 
% 1.59/1.18  % [INFO] 	 Running in sequential loop mode. 
% 2.08/1.44  % [INFO] 	 nitpick registered as external prover. 
% 2.08/1.45  % [INFO] 	 Scanning for conjecture ... 
% 2.33/1.59  % [INFO] 	 Found a conjecture (or negated_conjecture) and 35 axioms. Running axiom selection ... 
% 2.52/1.68  % [INFO] 	 Axiom selection finished. Selected 35 axioms (removed 0 axioms). 
% 2.72/1.75  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.72/1.76  % [INFO] 	 Type checking passed. 
% 2.72/1.76  % [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 ... 
% 14.91/4.37  % [INFO] 	 Killing All external provers ... 
% 14.91/4.37  % Time passed: 3864ms (effective reasoning time: 3185ms)
% 14.91/4.37  % 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)>
% 14.91/4.37  % Axioms used in derivation (1): equal_set_0
% 14.91/4.37  % No. of inferences in proof: 18
% 14.91/4.38  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3864 ms resp. 3185 ms w/o parsing
% 15.07/4.44  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 15.07/4.44  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------