TSTP Solution File: SET044^23 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SET044^23 : TPTP v8.2.0. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n007.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 03:01:07 EDT 2024

% Result   : Theorem 2.83s 1.66s
% Output   : Refutation 2.83s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   29 (  11 unt;  11 typ;   6 def)
%            Number of atoms       :   73 (   9 equ;   0 cnn)
%            Maximal formula atoms :   15 (   4 avg)
%            Number of connectives :  134 (   5   ~;   0   |;   7   &; 112   @)
%                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   5 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   40 (  40   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (  10 usr;   2 con; 0-3 aty)
%            Number of variables   :   48 (  23   ^  20   !;   5   ?;  48   :)

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

thf(mrel_type,type,
    mrel: mworld > mworld > $o ).

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(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(mexists_di_type,type,
    mexists_di: ( $i > mworld > $o ) > mworld > $o ).

thf(mexists_di_def,definition,
    ( mexists_di
    = ( ^ [A: $i > mworld > $o,B: mworld] :
        ? [C: $i] :
          ( ( eiw_di @ C @ B )
          & ( A @ C @ B ) ) ) ) ).

thf(element_type,type,
    element: $i > $i > mworld > $o ).

thf(5,axiom,
    ! [A: mworld] :
    ? [B: $i] : ( eiw_di @ B @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eiw_di_nonempty) ).

thf(20,plain,
    ! [A: mworld] :
    ? [B: $i] : ( eiw_di @ B @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(6,axiom,
    ! [A: mworld,B: mworld,C: $i] :
      ( ( ( eiw_di @ C @ A )
        & ( mrel @ B @ A ) )
     => ( eiw_di @ C @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eiw_di_decr) ).

thf(22,plain,
    ! [A: mworld,B: mworld,C: $i] :
      ( ( ( eiw_di @ C @ A )
        & ( mrel @ B @ A ) )
     => ( eiw_di @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(1,conjecture,
    ( mlocal
    @ ( mimplies
      @ ( mexists_di
        @ ^ [A: $i] :
            ( mforall_di
            @ ^ [B: $i] : ( mequiv @ ( element @ B @ A ) @ ( element @ B @ B ) ) ) )
      @ ( mnot
        @ ( mforall_di
          @ ^ [A: $i] :
              ( mexists_di
              @ ^ [B: $i] :
                  ( mforall_di
                  @ ^ [C: $i] : ( mequiv @ ( element @ C @ B ) @ ( mnot @ ( element @ C @ A ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel40) ).

thf(2,negated_conjecture,
    ~ ( mlocal
      @ ( mimplies
        @ ( mexists_di
          @ ^ [A: $i] :
              ( mforall_di
              @ ^ [B: $i] : ( mequiv @ ( element @ B @ A ) @ ( element @ B @ B ) ) ) )
        @ ( mnot
          @ ( mforall_di
            @ ^ [A: $i] :
                ( mexists_di
                @ ^ [B: $i] :
                    ( mforall_di
                    @ ^ [C: $i] : ( mequiv @ ( element @ C @ B ) @ ( mnot @ ( element @ C @ A ) ) ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(7,plain,
    ~ ( ? [A: $i] :
          ( ( eiw_di @ A @ mactual )
          & ! [B: $i] :
              ( ( eiw_di @ B @ mactual )
             => ( ( element @ B @ A @ mactual )
                = ( element @ B @ B @ mactual ) ) ) )
     => ~ ! [A: $i] :
            ( ( eiw_di @ A @ mactual )
           => ? [B: $i] :
                ( ( eiw_di @ B @ mactual )
                & ! [C: $i] :
                    ( ( eiw_di @ C @ mactual )
                   => ( ( element @ C @ B @ mactual )
                      = ( ~ ( element @ C @ A @ mactual ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,axiom,
    ! [A: mworld,B: mworld,C: mworld] :
      ( ( ( mrel @ A @ C )
        & ( mrel @ A @ B ) )
     => ( mrel @ C @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_euclidean) ).

thf(18,plain,
    ! [A: mworld,B: mworld,C: mworld] :
      ( ( ( mrel @ A @ C )
        & ( mrel @ A @ B ) )
     => ( mrel @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(3,axiom,
    ! [A: mworld] : ( mrel @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).

thf(16,plain,
    ! [A: mworld] : ( mrel @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(24,plain,
    $false,
    inference(e,[status(thm)],[20,22,7,18,16]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET044^23 : TPTP v8.2.0. Released v8.1.0.
% 0.12/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n007.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Mon May 20 11:59:09 EDT 2024
% 0.16/0.36  % CPUTime  : 
% 0.97/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.18/0.99  % [INFO] 	 Parsing done (128ms). 
% 1.18/1.00  % [INFO] 	 Running in sequential loop mode. 
% 1.80/1.22  % [INFO] 	 eprover registered as external prover. 
% 1.80/1.22  % [INFO] 	 cvc4 registered as external prover. 
% 1.80/1.22  % [INFO] 	 Scanning for conjecture ... 
% 1.85/1.30  % [INFO] 	 Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ... 
% 2.09/1.32  % [INFO] 	 Axiom selection finished. Selected 4 axioms (removed 0 axioms). 
% 2.09/1.33  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.09/1.33  % [INFO] 	 Type checking passed. 
% 2.09/1.33  % [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 ... 
% 2.83/1.66  % External prover 'e' found a proof!
% 2.83/1.66  % [INFO] 	 Killing All external provers ... 
% 2.83/1.66  % Time passed: 1135ms (effective reasoning time: 658ms)
% 2.83/1.66  % 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)>
% 2.83/1.66  % Axioms used in derivation (4): eiw_di_nonempty, eiw_di_decr, mrel_euclidean, mrel_reflexive
% 2.83/1.66  % No. of inferences in proof: 12
% 2.83/1.66  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1135 ms resp. 658 ms w/o parsing
% 2.83/1.70  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.83/1.70  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------