TSTP Solution File: NLP266^23 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : NLP266^23 : TPTP v8.2.0. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n020.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 00:59:27 EDT 2024

% Result   : Theorem 52.68s 9.21s
% Output   : Refutation 52.68s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   32
% Syntax   : Number of formulae    :   42 (  11 unt;  18 typ;   6 def)
%            Number of atoms       :  129 (   6 equ;   0 cnn)
%            Maximal formula atoms :   18 (   5 avg)
%            Number of connectives :  265 (   2   ~;   0   |;  19   &; 221   @)
%                                         (   0 <=>;  23  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   8 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   55 (  55   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   19 (  17 usr;   4 con; 0-4 aty)
%            Number of variables   :   71 (  30   ^  31   !;  10   ?;  71   :)

% 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(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(mbox_type,type,
    mbox: ( mworld > $o ) > mworld > $o ).

thf(mbox_def,definition,
    ( mbox
    = ( ^ [A: mworld > $o,B: mworld] :
        ! [C: mworld] :
          ( ( mrel @ B @ C )
         => ( A @ 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(u_type,type,
    u: $i ).

thf(one_type,type,
    one: $i ).

thf(number_type,type,
    number: $i > $i > mworld > $o ).

thf(string_type,type,
    string: $i > mworld > $o ).

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

thf(do_type,type,
    do: $i > $i > $i > mworld > $o ).

thf(entry_box_type,type,
    entry_box: $i > mworld > $o ).

thf(userid_type,type,
    userid: $i > $i > mworld > $o ).

thf(1,conjecture,
    ( mlocal
    @ ( mbox
      @ ( mexists_di
        @ ^ [A: $i] :
            ( mexists_di
            @ ^ [B: $i] :
                ( mexists_di
                @ ^ [C: $i] :
                    ( mexists_di
                    @ ^ [D: $i] :
                        ( mand @ ( mbox @ ( mand @ ( userid @ u @ A ) @ ( mand @ ( entry_box @ B ) @ ( number @ B @ one ) ) ) )
                        @ ( mbox
                          @ ( mforall_di
                            @ ^ [E: $i] : ( mimplies @ ( do @ D @ C @ E ) @ ( in @ A @ B @ E ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).

thf(2,negated_conjecture,
    ~ ( mlocal
      @ ( mbox
        @ ( mexists_di
          @ ^ [A: $i] :
              ( mexists_di
              @ ^ [B: $i] :
                  ( mexists_di
                  @ ^ [C: $i] :
                      ( mexists_di
                      @ ^ [D: $i] :
                          ( mand @ ( mbox @ ( mand @ ( userid @ u @ A ) @ ( mand @ ( entry_box @ B ) @ ( number @ B @ one ) ) ) )
                          @ ( mbox
                            @ ( mforall_di
                              @ ^ [E: $i] : ( mimplies @ ( do @ D @ C @ E ) @ ( in @ A @ B @ E ) ) ) ) ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(10,plain,
    ~ ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ? [B: $i] :
            ( ( eiw_di @ B @ A )
            & ? [C: $i] :
                ( ( eiw_di @ C @ A )
                & ? [D: $i] :
                    ( ( eiw_di @ D @ A )
                    & ? [E: $i] :
                        ( ( eiw_di @ E @ A )
                        & ! [F: mworld] :
                            ( ( mrel @ A @ F )
                           => ( ( userid @ u @ B @ F )
                              & ( entry_box @ C @ F )
                              & ( number @ C @ one @ F ) ) )
                        & ! [F: mworld] :
                            ( ( mrel @ A @ F )
                           => ! [G: $i] :
                                ( ( eiw_di @ G @ F )
                               => ( ( do @ E @ D @ G @ F )
                                 => ( in @ B @ C @ G @ F ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

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

thf(24,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(4,axiom,
    ! [A: mworld,B: mworld,C: mworld] :
      ( ( ( mrel @ A @ C )
        & ( mrel @ A @ B ) )
     => ( mrel @ C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_euclidean) ).

thf(20,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(9,axiom,
    ( mlocal
    @ ( mbox
      @ ( mforall_di
        @ ^ [A: $i] :
            ( mforall_di
            @ ^ [B: $i] :
                ( mforall_di
                @ ^ [C: $i] :
                    ( mimplies @ ( mand @ ( string @ B ) @ ( entry_box @ C ) )
                    @ ( mexists_di
                      @ ^ [D: $i] :
                          ( mbox
                          @ ( mforall_di
                            @ ^ [E: $i] : ( mimplies @ ( do @ A @ D @ E ) @ ( in @ B @ C @ E ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).

thf(34,plain,
    ! [A: mworld] :
      ( ( mrel @ mactual @ A )
     => ! [B: $i] :
          ( ( eiw_di @ B @ A )
         => ! [C: $i] :
              ( ( eiw_di @ C @ A )
             => ! [D: $i] :
                  ( ( eiw_di @ D @ A )
                 => ( ( ( string @ C @ A )
                      & ( entry_box @ D @ A ) )
                   => ? [E: $i] :
                        ( ( eiw_di @ E @ A )
                        & ! [F: mworld] :
                            ( ( mrel @ A @ F )
                           => ! [G: $i] :
                                ( ( eiw_di @ G @ F )
                               => ( ( do @ B @ E @ G @ F )
                                 => ( in @ C @ D @ G @ F ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

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

thf(22,plain,
    ! [A: mworld] :
    ? [B: $i] : ( eiw_di @ B @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

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

thf(18,plain,
    ! [A: mworld] : ( mrel @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(7,axiom,
    ( mlocal
    @ ( mbox
      @ ( mexists_di
        @ ^ [A: $i] : ( mbox @ ( mand @ ( userid @ u @ A ) @ ( string @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).

thf(26,plain,
    ! [A: mworld] :
      ( ( mrel @ mactual @ A )
     => ? [B: $i] :
          ( ( eiw_di @ B @ A )
          & ! [C: mworld] :
              ( ( mrel @ A @ C )
             => ( ( userid @ u @ B @ C )
                & ( string @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(8,axiom,
    ( mlocal
    @ ( mexists_di
      @ ^ [A: $i] : ( mbox @ ( mand @ ( entry_box @ A ) @ ( number @ A @ one ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).

thf(30,plain,
    ? [A: $i] :
      ( ( eiw_di @ A @ mactual )
      & ! [B: mworld] :
          ( ( mrel @ mactual @ B )
         => ( ( entry_box @ A @ B )
            & ( number @ A @ one @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(18288,plain,
    $false,
    inference(e,[status(thm)],[10,24,20,34,22,18,26,30]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : NLP266^23 : TPTP v8.2.0. Released v8.1.0.
% 0.06/0.15  % Command  : run_Leo-III %s %d
% 0.14/0.36  % Computer : n020.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Sun May 19 21:38:54 EDT 2024
% 0.14/0.36  % CPUTime  : 
% 0.89/0.90  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.29/1.03  % [INFO] 	 Parsing done (124ms). 
% 1.29/1.03  % [INFO] 	 Running in sequential loop mode. 
% 1.81/1.24  % [INFO] 	 eprover registered as external prover. 
% 1.81/1.24  % [INFO] 	 cvc4 registered as external prover. 
% 1.81/1.25  % [INFO] 	 Scanning for conjecture ... 
% 1.97/1.32  % [INFO] 	 Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ... 
% 1.97/1.35  % [INFO] 	 Axiom selection finished. Selected 7 axioms (removed 0 axioms). 
% 2.20/1.36  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.20/1.36  % [INFO] 	 Type checking passed. 
% 2.20/1.36  % [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 ... 
% 52.68/9.20  % External prover 'e' found a proof!
% 52.68/9.20  % [INFO] 	 Killing All external provers ... 
% 52.68/9.20  % Time passed: 8668ms (effective reasoning time: 8166ms)
% 52.68/9.20  % 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)>
% 52.68/9.21  % Axioms used in derivation (7): mrel_euclidean, mrel_reflexive, ax1, eiw_di_nonempty, ax2, ax3, eiw_di_decr
% 52.68/9.21  % No. of inferences in proof: 18
% 52.68/9.21  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 8668 ms resp. 8166 ms w/o parsing
% 52.68/9.24  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 52.68/9.24  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------