TSTP Solution File: SET002^3 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SET002^3 : TPTP v8.2.0. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n022.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 03:04:45 EDT 2024

% Result   : Theorem 6.18s 2.82s
% Output   : Refutation 6.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   33 (  17 unt;  11 typ;   4 def)
%            Number of atoms       :   82 (  20 equ;   0 cnn)
%            Maximal formula atoms :    9 (   3 avg)
%            Number of connectives :  181 (   9   ~;   6   |;   0   &; 166   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   31 (  31   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (  10 usr;   4 con; 0-3 aty)
%            Number of variables   :   41 (  17   ^  24   !;   0   ?;  41   :)

% 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(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(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] : ( A @ C @ B ) ) ) ).

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

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

thf(union_type,type,
    union: $i > $i > $i ).

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

thf(sk10_type,type,
    sk10: $i ).

thf(8,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] :
              ( mequiv @ ( qmltpeq @ A @ B )
              @ ( mforall_di
                @ ^ [C: $i] : ( mequiv @ ( member @ C @ A ) @ ( member @ C @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).

thf(34,plain,
    ! [A: $i,B: $i] :
      ( ( qmltpeq @ A @ B @ mactual )
      = ( ! [C: $i] :
            ( ( member @ C @ A @ mactual )
            = ( member @ C @ B @ mactual ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(35,plain,
    ! [B: $i,A: $i] :
      ( ( qmltpeq @ A @ B @ mactual )
      = ( ! [C: $i] :
            ( ( member @ C @ A @ mactual )
            = ( member @ C @ B @ mactual ) ) ) ),
    inference(cnf,[status(esa)],[34]) ).

thf(36,plain,
    ! [B: $i,A: $i] :
      ( ( qmltpeq @ A @ B @ mactual )
      = ( ! [C: $i] :
            ( ( member @ C @ A @ mactual )
            = ( member @ C @ B @ mactual ) ) ) ),
    inference(lifteq,[status(thm)],[35]) ).

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

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

thf(19,plain,
    ~ ! [A: $i] : ( qmltpeq @ ( union @ A @ A ) @ A @ mactual ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(20,plain,
    ~ ( qmltpeq @ ( union @ sk1 @ sk1 ) @ sk1 @ mactual ),
    inference(cnf,[status(esa)],[19]) ).

thf(154,plain,
    ! [B: $i,A: $i] :
      ( ~ ! [C: $i] :
            ( ( member @ C @ A @ mactual )
            = ( member @ C @ B @ mactual ) )
      | ( ( qmltpeq @ A @ B @ mactual )
       != ( qmltpeq @ ( union @ sk1 @ sk1 ) @ sk1 @ mactual ) ) ),
    inference(paramod_ordered,[status(thm)],[36,20]) ).

thf(155,plain,
    ~ ! [A: $i] :
        ( ( member @ A @ ( union @ sk1 @ sk1 ) @ mactual )
        = ( member @ A @ sk1 @ mactual ) ),
    inference(pattern_uni,[status(thm)],[154:[bind(A,$thf( union @ sk1 @ sk1 )),bind(B,$thf( sk1 ))]]) ).

thf(204,plain,
    ( ( member @ sk10 @ ( union @ sk1 @ sk1 ) @ mactual )
   != ( member @ sk10 @ sk1 @ mactual ) ),
    inference(cnf,[status(esa)],[155]) ).

thf(205,plain,
    ( ( member @ sk10 @ ( union @ sk1 @ sk1 ) @ mactual )
   != ( member @ sk10 @ sk1 @ mactual ) ),
    inference(lifteq,[status(thm)],[204]) ).

thf(5,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] :
              ( mforall_di
              @ ^ [C: $i] : ( mequiv @ ( member @ C @ ( union @ A @ B ) ) @ ( mor @ ( member @ C @ A ) @ ( member @ C @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).

thf(25,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( member @ C @ ( union @ A @ B ) @ mactual )
      = ( ( member @ C @ A @ mactual )
        | ( member @ C @ B @ mactual ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(26,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( member @ C @ ( union @ A @ B ) @ mactual )
      = ( ( member @ C @ A @ mactual )
        | ( member @ C @ B @ mactual ) ) ),
    inference(cnf,[status(esa)],[25]) ).

thf(27,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( member @ C @ ( union @ A @ B ) @ mactual )
      = ( ( member @ C @ A @ mactual )
        | ( member @ C @ B @ mactual ) ) ),
    inference(lifteq,[status(thm)],[26]) ).

thf(255,plain,
    ( ( ( member @ sk10 @ sk1 @ mactual )
      | ( member @ sk10 @ sk1 @ mactual ) )
   != ( member @ sk10 @ sk1 @ mactual ) ),
    inference(rewrite,[status(thm)],[205,27]) ).

thf(256,plain,
    $false,
    inference(simp,[status(thm)],[255]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET002^3 : TPTP v8.2.0. Released v8.1.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.14/0.35  % Computer : n022.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 13:06:39 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 1.01/0.98  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.33/1.13  % [INFO] 	 Parsing done (147ms). 
% 1.51/1.14  % [INFO] 	 Running in sequential loop mode. 
% 1.96/1.38  % [INFO] 	 nitpick registered as external prover. 
% 1.96/1.39  % [INFO] 	 Scanning for conjecture ... 
% 2.20/1.48  % [INFO] 	 Found a conjecture (or negated_conjecture) and 17 axioms. Running axiom selection ... 
% 2.34/1.55  % [INFO] 	 Axiom selection finished. Selected 16 axioms (removed 1 axioms). 
% 2.40/1.59  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.40/1.60  % [INFO] 	 Type checking passed. 
% 2.40/1.60  % [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 ... 
% 6.18/2.81  % [INFO] 	 Killing All external provers ... 
% 6.18/2.82  % Time passed: 2315ms (effective reasoning time: 1669ms)
% 6.18/2.82  % 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)>
% 6.18/2.82  % Axioms used in derivation (2): equal_member_defn, union_defn
% 6.18/2.82  % No. of inferences in proof: 18
% 6.18/2.82  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2315 ms resp. 1669 ms w/o parsing
% 6.18/2.88  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.18/2.88  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------