%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : PUZ132+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n026.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  : 600s
% DateTime : Mon Jul 18 18:21:01 EDT 2022

% Result   : Theorem 0.13s 0.34s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   42 (  21 unt;   0 def)
%            Number of atoms       :   64 (   4 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   44 (  22   ~;  15   |;   2   &)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    8 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-1 aty)
%            Number of variables   :   12 (   0 sgn   9   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(capital_city_type,axiom,
    ! [A] :
      ( capital(A)
     => city(A) ) ).

fof(washington_type,axiom,
    capital(washington) ).

fof(usa_type,axiom,
    country(usa) ).

fof(crime_axiom,axiom,
    ! [X] :
      ( city(X)
     => has_crime(X) ) ).

fof(usa_capital_axiom,axiom,
    capital_city(usa) = washington ).

fof(beautiful_capital_axiom,axiom,
    ! [X] :
      ( country(X)
     => beautiful(capital_city(X)) ) ).

fof(washington_conjecture,conjecture,
    ( beautiful(washington)
    & has_crime(washington) ) ).

fof(subgoal_0,plain,
    beautiful(washington),
    inference(strip,[],[washington_conjecture]) ).

fof(subgoal_1,plain,
    ( beautiful(washington)
   => has_crime(washington) ),
    inference(strip,[],[washington_conjecture]) ).

fof(negate_0_0,plain,
    ~ beautiful(washington),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    country(usa),
    inference(canonicalize,[],[usa_type]) ).

fof(normalize_0_1,plain,
    ! [X] :
      ( ~ country(X)
      | beautiful(capital_city(X)) ),
    inference(canonicalize,[],[beautiful_capital_axiom]) ).

fof(normalize_0_2,plain,
    ! [X] :
      ( ~ country(X)
      | beautiful(capital_city(X)) ),
    inference(specialize,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    capital_city(usa) = washington,
    inference(canonicalize,[],[usa_capital_axiom]) ).

fof(normalize_0_4,plain,
    ~ beautiful(washington),
    inference(canonicalize,[],[negate_0_0]) ).

cnf(refute_0_0,plain,
    country(usa),
    inference(canonicalize,[],[normalize_0_0]) ).

cnf(refute_0_1,plain,
    ( ~ country(X)
    | beautiful(capital_city(X)) ),
    inference(canonicalize,[],[normalize_0_2]) ).

cnf(refute_0_2,plain,
    ( ~ country(usa)
    | beautiful(capital_city(usa)) ),
    inference(subst,[],[refute_0_1:[bind(X,$fot(usa))]]) ).

cnf(refute_0_3,plain,
    beautiful(capital_city(usa)),
    inference(resolve,[$cnf( country(usa) )],[refute_0_0,refute_0_2]) ).

cnf(refute_0_4,plain,
    capital_city(usa) = washington,
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_5,plain,
    ( capital_city(usa) != washington
    | ~ beautiful(capital_city(usa))
    | beautiful(washington) ),
    introduced(tautology,[equality,[$cnf( beautiful(capital_city(usa)) ),[0],$fot(washington)]]) ).

cnf(refute_0_6,plain,
    ( ~ beautiful(capital_city(usa))
    | beautiful(washington) ),
    inference(resolve,[$cnf( $equal(capital_city(usa),washington) )],[refute_0_4,refute_0_5]) ).

cnf(refute_0_7,plain,
    beautiful(washington),
    inference(resolve,[$cnf( beautiful(capital_city(usa)) )],[refute_0_3,refute_0_6]) ).

cnf(refute_0_8,plain,
    ~ beautiful(washington),
    inference(canonicalize,[],[normalize_0_4]) ).

cnf(refute_0_9,plain,
    $false,
    inference(resolve,[$cnf( beautiful(washington) )],[refute_0_7,refute_0_8]) ).

fof(negate_1_0,plain,
    ~ ( beautiful(washington)
     => has_crime(washington) ),
    inference(negate,[],[subgoal_1]) ).

fof(normalize_1_0,plain,
    capital(washington),
    inference(canonicalize,[],[washington_type]) ).

fof(normalize_1_1,plain,
    ! [A] :
      ( ~ capital(A)
      | city(A) ),
    inference(canonicalize,[],[capital_city_type]) ).

fof(normalize_1_2,plain,
    ! [A] :
      ( ~ capital(A)
      | city(A) ),
    inference(specialize,[],[normalize_1_1]) ).

fof(normalize_1_3,plain,
    ! [X] :
      ( ~ city(X)
      | has_crime(X) ),
    inference(canonicalize,[],[crime_axiom]) ).

fof(normalize_1_4,plain,
    ! [X] :
      ( ~ city(X)
      | has_crime(X) ),
    inference(specialize,[],[normalize_1_3]) ).

fof(normalize_1_5,plain,
    ( ~ has_crime(washington)
    & beautiful(washington) ),
    inference(canonicalize,[],[negate_1_0]) ).

fof(normalize_1_6,plain,
    ~ has_crime(washington),
    inference(conjunct,[],[normalize_1_5]) ).

cnf(refute_1_0,plain,
    capital(washington),
    inference(canonicalize,[],[normalize_1_0]) ).

cnf(refute_1_1,plain,
    ( ~ capital(A)
    | city(A) ),
    inference(canonicalize,[],[normalize_1_2]) ).

cnf(refute_1_2,plain,
    ( ~ capital(washington)
    | city(washington) ),
    inference(subst,[],[refute_1_1:[bind(A,$fot(washington))]]) ).

cnf(refute_1_3,plain,
    city(washington),
    inference(resolve,[$cnf( capital(washington) )],[refute_1_0,refute_1_2]) ).

cnf(refute_1_4,plain,
    ( ~ city(X)
    | has_crime(X) ),
    inference(canonicalize,[],[normalize_1_4]) ).

cnf(refute_1_5,plain,
    ( ~ city(washington)
    | has_crime(washington) ),
    inference(subst,[],[refute_1_4:[bind(X,$fot(washington))]]) ).

cnf(refute_1_6,plain,
    has_crime(washington),
    inference(resolve,[$cnf( city(washington) )],[refute_1_3,refute_1_5]) ).

cnf(refute_1_7,plain,
    ~ has_crime(washington),
    inference(canonicalize,[],[normalize_1_6]) ).

cnf(refute_1_8,plain,
    $false,
    inference(resolve,[$cnf( has_crime(washington) )],[refute_1_6,refute_1_7]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : PUZ132+1 : TPTP v8.1.0. Released v4.1.0.
% 0.06/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.33  % Computer : n026.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Sun May 29 02:30:24 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.34  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.34  
% 0.13/0.34  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.35  
%------------------------------------------------------------------------------