TSTP Solution File: PUZ130_1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : PUZ130_1 : TPTP v8.1.0. Released v5.5.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n004.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 : Sun Sep 18 14:11:31 EDT 2022

% Result   : Theorem 0.14s 0.33s
% Output   : Proof 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   41 (  14 unt;   8 typ;   0 def)
%            Number of atoms       :   76 (   8 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   75 (  34   ~;  24   |;   0   &)
%                                         (  14 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of FOOLs       :    2 (   2 fml;   0 var)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    7 (   5   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   8 usr;   5 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-1 aty)
%            Number of variables   :   34 (  30   !;   0   ?;  34   :)

% Comments : 
%------------------------------------------------------------------------------
tff(hates_type,type,
    hates: ( human * human ) > $o ).

tff(owner_of_type,type,
    owner_of: animal > human ).

tff(dog_to_animal_type,type,
    dog_to_animal: dog > animal ).

tff(odie_type,type,
    odie: dog ).

tff(cat_to_animal_type,type,
    cat_to_animal: cat > animal ).

tff(garfield_type,type,
    garfield: cat ).

tff(jon_type,type,
    jon: human ).

tff(chased_type,type,
    chased: ( dog * cat ) > $o ).

tff(1,plain,
    ( ( jon = owner_of(dog_to_animal(odie)) )
  <=> ( owner_of(cat_to_animal(garfield)) = owner_of(dog_to_animal(odie)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,plain,
    ( ( jon = owner_of(dog_to_animal(odie)) )
  <=> ( jon = owner_of(dog_to_animal(odie)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(3,axiom,
    jon = owner_of(dog_to_animal(odie)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',jon_owns_odie) ).

tff(4,plain,
    jon = owner_of(dog_to_animal(odie)),
    inference(modus_ponens,[status(thm)],[3,2]) ).

tff(5,plain,
    owner_of(cat_to_animal(garfield)) = owner_of(dog_to_animal(odie)),
    inference(modus_ponens,[status(thm)],[4,1]) ).

tff(6,plain,
    owner_of(dog_to_animal(odie)) = owner_of(cat_to_animal(garfield)),
    inference(symmetry,[status(thm)],[5]) ).

tff(7,plain,
    ( hates(owner_of(cat_to_animal(garfield)),owner_of(dog_to_animal(odie)))
  <=> hates(owner_of(cat_to_animal(garfield)),owner_of(cat_to_animal(garfield))) ),
    inference(monotonicity,[status(thm)],[6]) ).

tff(8,plain,
    ( hates(owner_of(cat_to_animal(garfield)),owner_of(cat_to_animal(garfield)))
  <=> hates(owner_of(cat_to_animal(garfield)),owner_of(dog_to_animal(odie))) ),
    inference(symmetry,[status(thm)],[7]) ).

tff(9,plain,
    ( ~ hates(owner_of(cat_to_animal(garfield)),owner_of(cat_to_animal(garfield)))
  <=> ~ hates(owner_of(cat_to_animal(garfield)),owner_of(dog_to_animal(odie))) ),
    inference(monotonicity,[status(thm)],[8]) ).

tff(10,plain,
    ( ~ hates(jon,jon)
  <=> ~ hates(owner_of(cat_to_animal(garfield)),owner_of(cat_to_animal(garfield))) ),
    inference(rewrite,[status(thm)],]) ).

tff(11,plain,
    ( ~ hates(jon,jon)
  <=> ~ hates(jon,jon) ),
    inference(rewrite,[status(thm)],]) ).

tff(12,axiom,
    ~ hates(jon,jon),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',jon_hates_jon) ).

tff(13,plain,
    ~ hates(jon,jon),
    inference(modus_ponens,[status(thm)],[12,11]) ).

tff(14,plain,
    ~ hates(owner_of(cat_to_animal(garfield)),owner_of(cat_to_animal(garfield))),
    inference(modus_ponens,[status(thm)],[13,10]) ).

tff(15,plain,
    ~ hates(owner_of(cat_to_animal(garfield)),owner_of(dog_to_animal(odie))),
    inference(modus_ponens,[status(thm)],[14,9]) ).

tff(16,plain,
    ( chased(odie,garfield)
  <=> chased(odie,garfield) ),
    inference(rewrite,[status(thm)],]) ).

tff(17,axiom,
    chased(odie,garfield),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',odie_chased_garfield) ).

tff(18,plain,
    chased(odie,garfield),
    inference(modus_ponens,[status(thm)],[17,16]) ).

tff(19,plain,
    ^ [C: cat,D: dog] :
      refl(
        ( ( ~ chased(D,C)
          | hates(owner_of(cat_to_animal(C)),owner_of(dog_to_animal(D))) )
      <=> ( ~ chased(D,C)
          | hates(owner_of(cat_to_animal(C)),owner_of(dog_to_animal(D))) ) )),
    inference(bind,[status(th)],]) ).

tff(20,plain,
    ( ! [C: cat,D: dog] :
        ( ~ chased(D,C)
        | hates(owner_of(cat_to_animal(C)),owner_of(dog_to_animal(D))) )
  <=> ! [C: cat,D: dog] :
        ( ~ chased(D,C)
        | hates(owner_of(cat_to_animal(C)),owner_of(dog_to_animal(D))) ) ),
    inference(quant_intro,[status(thm)],[19]) ).

tff(21,plain,
    ( ! [C: cat,D: dog] :
        ( ~ chased(D,C)
        | hates(owner_of(cat_to_animal(C)),owner_of(dog_to_animal(D))) )
  <=> ! [C: cat,D: dog] :
        ( ~ chased(D,C)
        | hates(owner_of(cat_to_animal(C)),owner_of(dog_to_animal(D))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(22,plain,
    ^ [C: cat,D: dog] :
      rewrite(
        ( ( chased(D,C)
         => hates(owner_of(cat_to_animal(C)),owner_of(dog_to_animal(D))) )
      <=> ( ~ chased(D,C)
          | hates(owner_of(cat_to_animal(C)),owner_of(dog_to_animal(D))) ) )),
    inference(bind,[status(th)],]) ).

tff(23,plain,
    ( ! [C: cat,D: dog] :
        ( chased(D,C)
       => hates(owner_of(cat_to_animal(C)),owner_of(dog_to_animal(D))) )
  <=> ! [C: cat,D: dog] :
        ( ~ chased(D,C)
        | hates(owner_of(cat_to_animal(C)),owner_of(dog_to_animal(D))) ) ),
    inference(quant_intro,[status(thm)],[22]) ).

tff(24,axiom,
    ! [C: cat,D: dog] :
      ( chased(D,C)
     => hates(owner_of(cat_to_animal(C)),owner_of(dog_to_animal(D))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dog_chase_cat) ).

tff(25,plain,
    ! [C: cat,D: dog] :
      ( ~ chased(D,C)
      | hates(owner_of(cat_to_animal(C)),owner_of(dog_to_animal(D))) ),
    inference(modus_ponens,[status(thm)],[24,23]) ).

tff(26,plain,
    ! [C: cat,D: dog] :
      ( ~ chased(D,C)
      | hates(owner_of(cat_to_animal(C)),owner_of(dog_to_animal(D))) ),
    inference(modus_ponens,[status(thm)],[25,21]) ).

tff(27,plain,
    ! [C: cat,D: dog] :
      ( ~ chased(D,C)
      | hates(owner_of(cat_to_animal(C)),owner_of(dog_to_animal(D))) ),
    inference(skolemize,[status(sab)],[26]) ).

tff(28,plain,
    ! [C: cat,D: dog] :
      ( ~ chased(D,C)
      | hates(owner_of(cat_to_animal(C)),owner_of(dog_to_animal(D))) ),
    inference(modus_ponens,[status(thm)],[27,20]) ).

tff(29,plain,
    ( ( ~ ! [C: cat,D: dog] :
            ( ~ chased(D,C)
            | hates(owner_of(cat_to_animal(C)),owner_of(dog_to_animal(D))) )
      | ~ chased(odie,garfield)
      | hates(owner_of(cat_to_animal(garfield)),owner_of(dog_to_animal(odie))) )
  <=> ( ~ ! [C: cat,D: dog] :
            ( ~ chased(D,C)
            | hates(owner_of(cat_to_animal(C)),owner_of(dog_to_animal(D))) )
      | ~ chased(odie,garfield)
      | hates(owner_of(cat_to_animal(garfield)),owner_of(dog_to_animal(odie))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(30,plain,
    ( ~ ! [C: cat,D: dog] :
          ( ~ chased(D,C)
          | hates(owner_of(cat_to_animal(C)),owner_of(dog_to_animal(D))) )
    | ~ chased(odie,garfield)
    | hates(owner_of(cat_to_animal(garfield)),owner_of(dog_to_animal(odie))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(31,plain,
    ( ~ ! [C: cat,D: dog] :
          ( ~ chased(D,C)
          | hates(owner_of(cat_to_animal(C)),owner_of(dog_to_animal(D))) )
    | ~ chased(odie,garfield)
    | hates(owner_of(cat_to_animal(garfield)),owner_of(dog_to_animal(odie))) ),
    inference(modus_ponens,[status(thm)],[30,29]) ).

tff(32,plain,
    hates(owner_of(cat_to_animal(garfield)),owner_of(dog_to_animal(odie))),
    inference(unit_resolution,[status(thm)],[31,28,18]) ).

tff(33,plain,
    $false,
    inference(unit_resolution,[status(thm)],[32,15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : PUZ130_1 : TPTP v8.1.0. Released v5.5.0.
% 0.00/0.09  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.09/0.29  % Computer : n004.cluster.edu
% 0.09/0.29  % Model    : x86_64 x86_64
% 0.09/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29  % Memory   : 8042.1875MB
% 0.09/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29  % CPULimit : 300
% 0.09/0.29  % WCLimit  : 300
% 0.09/0.29  % DateTime : Fri Sep  2 18:59:34 EDT 2022
% 0.09/0.29  % CPUTime  : 
% 0.09/0.30  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.09/0.30  Usage: tptp [options] [-file:]file
% 0.09/0.30    -h, -?       prints this message.
% 0.09/0.30    -smt2        print SMT-LIB2 benchmark.
% 0.09/0.30    -m, -model   generate model.
% 0.09/0.30    -p, -proof   generate proof.
% 0.09/0.30    -c, -core    generate unsat core of named formulas.
% 0.09/0.30    -st, -statistics display statistics.
% 0.09/0.30    -t:timeout   set timeout (in second).
% 0.09/0.30    -smt2status  display status in smt2 format instead of SZS.
% 0.09/0.30    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.09/0.30    -<param>:<value> configuration parameter and value.
% 0.09/0.30    -o:<output-file> file to place output in.
% 0.14/0.33  % SZS status Theorem
% 0.14/0.33  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------