TSTP Solution File: NLP001^17 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : NLP001^17 : TPTP v8.2.0. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n005.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 00:58:24 EDT 2024

% Result   : Theorem 3.99s 1.96s
% Output   : Refutation 4.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   31
% Syntax   : Number of formulae    :   38 (   9 unt;  22 typ;   4 def)
%            Number of atoms       :  354 (   4 equ;   0 cnn)
%            Maximal formula atoms :  128 (  22 avg)
%            Number of connectives :  671 (   2   ~;   0   |;  75   &; 587   @)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   31 (   9 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   58 (  58   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   23 (  21 usr;   2 con; 0-3 aty)
%            Number of variables   :   76 (  41   ^  16   !;  19   ?;  76   :)

% 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(eiw_di_type,type,
    eiw_di: $i > mworld > $o ).

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(chevy_type,type,
    chevy: $i > mworld > $o ).

thf(dirty_type,type,
    dirty: $i > mworld > $o ).

thf(barrel_type,type,
    barrel: $i > $i > mworld > $o ).

thf(hollywood_type,type,
    hollywood: $i > mworld > $o ).

thf(city_type,type,
    city: $i > mworld > $o ).

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

thf(old_type,type,
    old: $i > mworld > $o ).

thf(down_type,type,
    down: $i > $i > mworld > $o ).

thf(way_type,type,
    way: $i > mworld > $o ).

thf(white_type,type,
    white: $i > mworld > $o ).

thf(car_type,type,
    car: $i > mworld > $o ).

thf(street_type,type,
    street: $i > mworld > $o ).

thf(event_type,type,
    event: $i > mworld > $o ).

thf(lonely_type,type,
    lonely: $i > mworld > $o ).

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

thf(53,plain,
    ! [A: mworld,B: mworld,C: $i] :
      ( ( ( eiw_di @ C @ A )
        & ( mrel @ A @ B ) )
     => ( 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(49,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(1,conjecture,
    ( mlocal
    @ ( mand
      @ ( mimplies
        @ ( mexists_di
          @ ^ [A: $i] :
              ( mexists_di
              @ ^ [B: $i] :
                  ( mexists_di
                  @ ^ [C: $i] :
                      ( mexists_di
                      @ ^ [D: $i] : ( mand @ ( hollywood @ A ) @ ( mand @ ( city @ A ) @ ( mand @ ( event @ B ) @ ( mand @ ( street @ C ) @ ( mand @ ( way @ C ) @ ( mand @ ( lonely @ C ) @ ( mand @ ( chevy @ D ) @ ( mand @ ( car @ D ) @ ( mand @ ( white @ D ) @ ( mand @ ( dirty @ D ) @ ( mand @ ( old @ D ) @ ( mand @ ( barrel @ B @ D ) @ ( mand @ ( down @ B @ C ) @ ( in @ B @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
        @ ( mexists_di
          @ ^ [A: $i] :
              ( mexists_di
              @ ^ [B: $i] :
                  ( mexists_di
                  @ ^ [C: $i] :
                      ( mexists_di
                      @ ^ [D: $i] : ( mand @ ( hollywood @ A ) @ ( mand @ ( city @ A ) @ ( mand @ ( event @ B ) @ ( mand @ ( chevy @ C ) @ ( mand @ ( car @ C ) @ ( mand @ ( white @ C ) @ ( mand @ ( dirty @ C ) @ ( mand @ ( old @ C ) @ ( mand @ ( street @ D ) @ ( mand @ ( way @ D ) @ ( mand @ ( lonely @ D ) @ ( mand @ ( barrel @ B @ C ) @ ( mand @ ( down @ B @ D ) @ ( in @ B @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      @ ( mimplies
        @ ( mexists_di
          @ ^ [A: $i] :
              ( mexists_di
              @ ^ [B: $i] :
                  ( mexists_di
                  @ ^ [C: $i] :
                      ( mexists_di
                      @ ^ [D: $i] : ( mand @ ( hollywood @ A ) @ ( mand @ ( city @ A ) @ ( mand @ ( event @ B ) @ ( mand @ ( chevy @ C ) @ ( mand @ ( car @ C ) @ ( mand @ ( white @ C ) @ ( mand @ ( dirty @ C ) @ ( mand @ ( old @ C ) @ ( mand @ ( street @ D ) @ ( mand @ ( way @ D ) @ ( mand @ ( lonely @ D ) @ ( mand @ ( barrel @ B @ C ) @ ( mand @ ( down @ B @ D ) @ ( in @ B @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
        @ ( mexists_di
          @ ^ [A: $i] :
              ( mexists_di
              @ ^ [B: $i] :
                  ( mexists_di
                  @ ^ [C: $i] :
                      ( mexists_di
                      @ ^ [D: $i] : ( mand @ ( hollywood @ A ) @ ( mand @ ( city @ A ) @ ( mand @ ( event @ B ) @ ( mand @ ( street @ C ) @ ( mand @ ( way @ C ) @ ( mand @ ( lonely @ C ) @ ( mand @ ( chevy @ D ) @ ( mand @ ( car @ D ) @ ( mand @ ( white @ D ) @ ( mand @ ( dirty @ D ) @ ( mand @ ( old @ D ) @ ( mand @ ( barrel @ B @ D ) @ ( mand @ ( down @ B @ C ) @ ( in @ B @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

thf(2,negated_conjecture,
    ~ ( mlocal
      @ ( mand
        @ ( mimplies
          @ ( mexists_di
            @ ^ [A: $i] :
                ( mexists_di
                @ ^ [B: $i] :
                    ( mexists_di
                    @ ^ [C: $i] :
                        ( mexists_di
                        @ ^ [D: $i] : ( mand @ ( hollywood @ A ) @ ( mand @ ( city @ A ) @ ( mand @ ( event @ B ) @ ( mand @ ( street @ C ) @ ( mand @ ( way @ C ) @ ( mand @ ( lonely @ C ) @ ( mand @ ( chevy @ D ) @ ( mand @ ( car @ D ) @ ( mand @ ( white @ D ) @ ( mand @ ( dirty @ D ) @ ( mand @ ( old @ D ) @ ( mand @ ( barrel @ B @ D ) @ ( mand @ ( down @ B @ C ) @ ( in @ B @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          @ ( mexists_di
            @ ^ [A: $i] :
                ( mexists_di
                @ ^ [B: $i] :
                    ( mexists_di
                    @ ^ [C: $i] :
                        ( mexists_di
                        @ ^ [D: $i] : ( mand @ ( hollywood @ A ) @ ( mand @ ( city @ A ) @ ( mand @ ( event @ B ) @ ( mand @ ( chevy @ C ) @ ( mand @ ( car @ C ) @ ( mand @ ( white @ C ) @ ( mand @ ( dirty @ C ) @ ( mand @ ( old @ C ) @ ( mand @ ( street @ D ) @ ( mand @ ( way @ D ) @ ( mand @ ( lonely @ D ) @ ( mand @ ( barrel @ B @ C ) @ ( mand @ ( down @ B @ D ) @ ( in @ B @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
        @ ( mimplies
          @ ( mexists_di
            @ ^ [A: $i] :
                ( mexists_di
                @ ^ [B: $i] :
                    ( mexists_di
                    @ ^ [C: $i] :
                        ( mexists_di
                        @ ^ [D: $i] : ( mand @ ( hollywood @ A ) @ ( mand @ ( city @ A ) @ ( mand @ ( event @ B ) @ ( mand @ ( chevy @ C ) @ ( mand @ ( car @ C ) @ ( mand @ ( white @ C ) @ ( mand @ ( dirty @ C ) @ ( mand @ ( old @ C ) @ ( mand @ ( street @ D ) @ ( mand @ ( way @ D ) @ ( mand @ ( lonely @ D ) @ ( mand @ ( barrel @ B @ C ) @ ( mand @ ( down @ B @ D ) @ ( in @ B @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          @ ( mexists_di
            @ ^ [A: $i] :
                ( mexists_di
                @ ^ [B: $i] :
                    ( mexists_di
                    @ ^ [C: $i] :
                        ( mexists_di
                        @ ^ [D: $i] : ( mand @ ( hollywood @ A ) @ ( mand @ ( city @ A ) @ ( mand @ ( event @ B ) @ ( mand @ ( street @ C ) @ ( mand @ ( way @ C ) @ ( mand @ ( lonely @ C ) @ ( mand @ ( chevy @ D ) @ ( mand @ ( car @ D ) @ ( mand @ ( white @ D ) @ ( mand @ ( dirty @ D ) @ ( mand @ ( old @ D ) @ ( mand @ ( barrel @ B @ D ) @ ( mand @ ( down @ B @ C ) @ ( in @ B @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(7,plain,
    ~ ( ( ? [A: $i] :
            ( ( eiw_di @ A @ mactual )
            & ? [B: $i] :
                ( ( eiw_di @ B @ mactual )
                & ? [C: $i] :
                    ( ( eiw_di @ C @ mactual )
                    & ? [D: $i] :
                        ( ( eiw_di @ D @ mactual )
                        & ( hollywood @ A @ mactual )
                        & ( city @ A @ mactual )
                        & ( event @ B @ mactual )
                        & ( street @ C @ mactual )
                        & ( way @ C @ mactual )
                        & ( lonely @ C @ mactual )
                        & ( chevy @ D @ mactual )
                        & ( car @ D @ mactual )
                        & ( white @ D @ mactual )
                        & ( dirty @ D @ mactual )
                        & ( old @ D @ mactual )
                        & ( barrel @ B @ D @ mactual )
                        & ( down @ B @ C @ mactual )
                        & ( in @ B @ A @ mactual ) ) ) ) )
       => ? [A: $i] :
            ( ( eiw_di @ A @ mactual )
            & ? [B: $i] :
                ( ( eiw_di @ B @ mactual )
                & ? [C: $i] :
                    ( ( eiw_di @ C @ mactual )
                    & ? [D: $i] :
                        ( ( eiw_di @ D @ mactual )
                        & ( hollywood @ A @ mactual )
                        & ( city @ A @ mactual )
                        & ( event @ B @ mactual )
                        & ( chevy @ C @ mactual )
                        & ( car @ C @ mactual )
                        & ( white @ C @ mactual )
                        & ( dirty @ C @ mactual )
                        & ( old @ C @ mactual )
                        & ( street @ D @ mactual )
                        & ( way @ D @ mactual )
                        & ( lonely @ D @ mactual )
                        & ( barrel @ B @ C @ mactual )
                        & ( down @ B @ D @ mactual )
                        & ( in @ B @ A @ mactual ) ) ) ) ) )
      & ( ? [A: $i] :
            ( ( eiw_di @ A @ mactual )
            & ? [B: $i] :
                ( ( eiw_di @ B @ mactual )
                & ? [C: $i] :
                    ( ( eiw_di @ C @ mactual )
                    & ? [D: $i] :
                        ( ( eiw_di @ D @ mactual )
                        & ( hollywood @ A @ mactual )
                        & ( city @ A @ mactual )
                        & ( event @ B @ mactual )
                        & ( chevy @ C @ mactual )
                        & ( car @ C @ mactual )
                        & ( white @ C @ mactual )
                        & ( dirty @ C @ mactual )
                        & ( old @ C @ mactual )
                        & ( street @ D @ mactual )
                        & ( way @ D @ mactual )
                        & ( lonely @ D @ mactual )
                        & ( barrel @ B @ C @ mactual )
                        & ( down @ B @ D @ mactual )
                        & ( in @ B @ A @ mactual ) ) ) ) )
       => ? [A: $i] :
            ( ( eiw_di @ A @ mactual )
            & ? [B: $i] :
                ( ( eiw_di @ B @ mactual )
                & ? [C: $i] :
                    ( ( eiw_di @ C @ mactual )
                    & ? [D: $i] :
                        ( ( eiw_di @ D @ mactual )
                        & ( hollywood @ A @ mactual )
                        & ( city @ A @ mactual )
                        & ( event @ B @ mactual )
                        & ( street @ C @ mactual )
                        & ( way @ C @ mactual )
                        & ( lonely @ C @ mactual )
                        & ( chevy @ D @ mactual )
                        & ( car @ D @ mactual )
                        & ( white @ D @ mactual )
                        & ( dirty @ D @ mactual )
                        & ( old @ D @ mactual )
                        & ( barrel @ B @ D @ mactual )
                        & ( down @ B @ C @ mactual )
                        & ( in @ B @ A @ mactual ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

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

thf(51,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(47,plain,
    ! [A: mworld] : ( mrel @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(55,plain,
    $false,
    inference(e,[status(thm)],[53,49,7,51,47]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : NLP001^17 : TPTP v8.2.0. Released v8.1.0.
% 0.16/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n005.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Sun May 19 22:05:24 EDT 2024
% 0.22/0.37  % CPUTime  : 
% 0.97/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.28/1.00  % [INFO] 	 Parsing done (134ms). 
% 1.28/1.01  % [INFO] 	 Running in sequential loop mode. 
% 1.79/1.22  % [INFO] 	 eprover registered as external prover. 
% 1.79/1.22  % [INFO] 	 cvc4 registered as external prover. 
% 1.79/1.22  % [INFO] 	 Scanning for conjecture ... 
% 2.16/1.32  % [INFO] 	 Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ... 
% 2.16/1.35  % [INFO] 	 Axiom selection finished. Selected 4 axioms (removed 0 axioms). 
% 2.31/1.36  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.31/1.36  % [INFO] 	 Type checking passed. 
% 2.31/1.36  % [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 ... 
% 3.99/1.95  % External prover 'e' found a proof!
% 3.99/1.95  % [INFO] 	 Killing All external provers ... 
% 3.99/1.95  % Time passed: 1424ms (effective reasoning time: 939ms)
% 3.99/1.95  % 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)>
% 3.99/1.95  % Axioms used in derivation (4): eiw_di_cumul, mrel_euclidean, eiw_di_nonempty, mrel_reflexive
% 3.99/1.95  % No. of inferences in proof: 12
% 3.99/1.96  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1424 ms resp. 939 ms w/o parsing
% 4.18/2.01  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.18/2.01  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------