TSTP Solution File: SWB018+1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SWB018+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n021.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 Sep 20 08:31:49 EDT 2022

% Result   : Theorem 0.78s 0.76s
% Output   : Proof 0.78s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   31
% Syntax   : Number of formulae    :   67 (  17 unt;   8 typ;   0 def)
%            Number of atoms       :  243 (  19 equ)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :  275 ( 108   ~;  89   |;  17   &)
%                                         (  58 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :   17 (  17 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   2   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   6 con; 0-0 aty)
%            Number of variables   :  140 ( 124   !;   0   ?; 140   :)

% Comments : 
%------------------------------------------------------------------------------
tff(iext_type,type,
    iext: ( $i * $i * $i ) > $o ).

tff(uri_ex_u_type,type,
    uri_ex_u: $i ).

tff(uri_owl_sameAs_type,type,
    uri_owl_sameAs: $i ).

tff(uri_ex_w_type,type,
    uri_ex_w: $i ).

tff(uri_ex_Person_type,type,
    uri_ex_Person: $i ).

tff(uri_rdfs_domain_type,type,
    uri_rdfs_domain: $i ).

tff(icext_type,type,
    icext: ( $i * $i ) > $o ).

tff(uri_rdf_type_type,type,
    uri_rdf_type: $i ).

tff(1,plain,
    ^ [X: $i,Y: $i] :
      refl(
        ( ( iext(uri_owl_sameAs,X,Y)
        <=> ( X = Y ) )
      <=> ( iext(uri_owl_sameAs,X,Y)
        <=> ( X = Y ) ) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [X: $i,Y: $i] :
        ( iext(uri_owl_sameAs,X,Y)
      <=> ( X = Y ) )
  <=> ! [X: $i,Y: $i] :
        ( iext(uri_owl_sameAs,X,Y)
      <=> ( X = Y ) ) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ( ! [X: $i,Y: $i] :
        ( iext(uri_owl_sameAs,X,Y)
      <=> ( X = Y ) )
  <=> ! [X: $i,Y: $i] :
        ( iext(uri_owl_sameAs,X,Y)
      <=> ( X = Y ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,axiom,
    ! [X: $i,Y: $i] :
      ( iext(uri_owl_sameAs,X,Y)
    <=> ( X = Y ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax',owl_eqdis_sameas) ).

tff(5,plain,
    ! [X: $i,Y: $i] :
      ( iext(uri_owl_sameAs,X,Y)
    <=> ( X = Y ) ),
    inference(modus_ponens,[status(thm)],[4,3]) ).

tff(6,plain,
    ! [X: $i,Y: $i] :
      ( iext(uri_owl_sameAs,X,Y)
    <=> ( X = Y ) ),
    inference(skolemize,[status(sab)],[5]) ).

tff(7,plain,
    ! [X: $i,Y: $i] :
      ( iext(uri_owl_sameAs,X,Y)
    <=> ( X = Y ) ),
    inference(modus_ponens,[status(thm)],[6,2]) ).

tff(8,plain,
    ( ~ ! [X: $i,Y: $i] :
          ( iext(uri_owl_sameAs,X,Y)
        <=> ( X = Y ) )
    | ( iext(uri_owl_sameAs,uri_ex_w,uri_ex_u)
    <=> ( uri_ex_w = uri_ex_u ) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(9,plain,
    ( iext(uri_owl_sameAs,uri_ex_w,uri_ex_u)
  <=> ( uri_ex_w = uri_ex_u ) ),
    inference(unit_resolution,[status(thm)],[8,7]) ).

tff(10,plain,
    ( iext(uri_owl_sameAs,uri_ex_w,uri_ex_u)
  <=> iext(uri_owl_sameAs,uri_ex_w,uri_ex_u) ),
    inference(rewrite,[status(thm)],]) ).

tff(11,axiom,
    ( iext(uri_rdfs_domain,uri_owl_sameAs,uri_ex_Person)
    & iext(uri_owl_sameAs,uri_ex_w,uri_ex_u) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',testcase_premise_fullish_018_Modified_Logical_Vocabulary_Semantics) ).

tff(12,plain,
    iext(uri_owl_sameAs,uri_ex_w,uri_ex_u),
    inference(and_elim,[status(thm)],[11]) ).

tff(13,plain,
    iext(uri_owl_sameAs,uri_ex_w,uri_ex_u),
    inference(modus_ponens,[status(thm)],[12,10]) ).

tff(14,plain,
    ( ~ ( iext(uri_owl_sameAs,uri_ex_w,uri_ex_u)
      <=> ( uri_ex_w = uri_ex_u ) )
    | ~ iext(uri_owl_sameAs,uri_ex_w,uri_ex_u)
    | ( uri_ex_w = uri_ex_u ) ),
    inference(tautology,[status(thm)],]) ).

tff(15,plain,
    ( ~ ( iext(uri_owl_sameAs,uri_ex_w,uri_ex_u)
      <=> ( uri_ex_w = uri_ex_u ) )
    | ( uri_ex_w = uri_ex_u ) ),
    inference(unit_resolution,[status(thm)],[14,13]) ).

tff(16,plain,
    uri_ex_w = uri_ex_u,
    inference(unit_resolution,[status(thm)],[15,9]) ).

tff(17,plain,
    uri_ex_u = uri_ex_w,
    inference(symmetry,[status(thm)],[16]) ).

tff(18,plain,
    ( iext(uri_owl_sameAs,uri_ex_u,uri_ex_u)
  <=> iext(uri_owl_sameAs,uri_ex_w,uri_ex_u) ),
    inference(monotonicity,[status(thm)],[17]) ).

tff(19,plain,
    ( iext(uri_owl_sameAs,uri_ex_w,uri_ex_u)
  <=> iext(uri_owl_sameAs,uri_ex_u,uri_ex_u) ),
    inference(symmetry,[status(thm)],[18]) ).

tff(20,plain,
    iext(uri_owl_sameAs,uri_ex_u,uri_ex_u),
    inference(modus_ponens,[status(thm)],[13,19]) ).

tff(21,plain,
    ^ [X: $i,C: $i] :
      refl(
        ( ( iext(uri_rdf_type,X,C)
        <=> icext(C,X) )
      <=> ( iext(uri_rdf_type,X,C)
        <=> icext(C,X) ) )),
    inference(bind,[status(th)],]) ).

tff(22,plain,
    ( ! [X: $i,C: $i] :
        ( iext(uri_rdf_type,X,C)
      <=> icext(C,X) )
  <=> ! [X: $i,C: $i] :
        ( iext(uri_rdf_type,X,C)
      <=> icext(C,X) ) ),
    inference(quant_intro,[status(thm)],[21]) ).

tff(23,plain,
    ( ! [X: $i,C: $i] :
        ( iext(uri_rdf_type,X,C)
      <=> icext(C,X) )
  <=> ! [X: $i,C: $i] :
        ( iext(uri_rdf_type,X,C)
      <=> icext(C,X) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(24,axiom,
    ! [X: $i,C: $i] :
      ( iext(uri_rdf_type,X,C)
    <=> icext(C,X) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax',rdfs_cext_def) ).

tff(25,plain,
    ! [X: $i,C: $i] :
      ( iext(uri_rdf_type,X,C)
    <=> icext(C,X) ),
    inference(modus_ponens,[status(thm)],[24,23]) ).

tff(26,plain,
    ! [X: $i,C: $i] :
      ( iext(uri_rdf_type,X,C)
    <=> icext(C,X) ),
    inference(skolemize,[status(sab)],[25]) ).

tff(27,plain,
    ! [X: $i,C: $i] :
      ( iext(uri_rdf_type,X,C)
    <=> icext(C,X) ),
    inference(modus_ponens,[status(thm)],[26,22]) ).

tff(28,plain,
    ( ~ ! [X: $i,C: $i] :
          ( iext(uri_rdf_type,X,C)
        <=> icext(C,X) )
    | ( iext(uri_rdf_type,uri_ex_u,uri_ex_Person)
    <=> icext(uri_ex_Person,uri_ex_u) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(29,plain,
    ( iext(uri_rdf_type,uri_ex_u,uri_ex_Person)
  <=> icext(uri_ex_Person,uri_ex_u) ),
    inference(unit_resolution,[status(thm)],[28,27]) ).

tff(30,plain,
    ( ~ iext(uri_rdf_type,uri_ex_u,uri_ex_Person)
  <=> ~ iext(uri_rdf_type,uri_ex_u,uri_ex_Person) ),
    inference(rewrite,[status(thm)],]) ).

tff(31,axiom,
    ~ iext(uri_rdf_type,uri_ex_u,uri_ex_Person),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',testcase_conclusion_fullish_018_Modified_Logical_Vocabulary_Semantics) ).

tff(32,plain,
    ~ iext(uri_rdf_type,uri_ex_u,uri_ex_Person),
    inference(modus_ponens,[status(thm)],[31,30]) ).

tff(33,plain,
    ( ~ ( iext(uri_rdf_type,uri_ex_u,uri_ex_Person)
      <=> icext(uri_ex_Person,uri_ex_u) )
    | iext(uri_rdf_type,uri_ex_u,uri_ex_Person)
    | ~ icext(uri_ex_Person,uri_ex_u) ),
    inference(tautology,[status(thm)],]) ).

tff(34,plain,
    ( ~ ( iext(uri_rdf_type,uri_ex_u,uri_ex_Person)
      <=> icext(uri_ex_Person,uri_ex_u) )
    | ~ icext(uri_ex_Person,uri_ex_u) ),
    inference(unit_resolution,[status(thm)],[33,32]) ).

tff(35,plain,
    ~ icext(uri_ex_Person,uri_ex_u),
    inference(unit_resolution,[status(thm)],[34,29]) ).

tff(36,plain,
    ( iext(uri_rdfs_domain,uri_owl_sameAs,uri_ex_Person)
  <=> iext(uri_rdfs_domain,uri_owl_sameAs,uri_ex_Person) ),
    inference(rewrite,[status(thm)],]) ).

tff(37,plain,
    iext(uri_rdfs_domain,uri_owl_sameAs,uri_ex_Person),
    inference(and_elim,[status(thm)],[11]) ).

tff(38,plain,
    iext(uri_rdfs_domain,uri_owl_sameAs,uri_ex_Person),
    inference(modus_ponens,[status(thm)],[37,36]) ).

tff(39,plain,
    ^ [P: $i,C: $i,X: $i,Y: $i] :
      refl(
        ( ( icext(C,X)
          | ~ iext(P,X,Y)
          | ~ iext(uri_rdfs_domain,P,C) )
      <=> ( icext(C,X)
          | ~ iext(P,X,Y)
          | ~ iext(uri_rdfs_domain,P,C) ) )),
    inference(bind,[status(th)],]) ).

tff(40,plain,
    ( ! [P: $i,C: $i,X: $i,Y: $i] :
        ( icext(C,X)
        | ~ iext(P,X,Y)
        | ~ iext(uri_rdfs_domain,P,C) )
  <=> ! [P: $i,C: $i,X: $i,Y: $i] :
        ( icext(C,X)
        | ~ iext(P,X,Y)
        | ~ iext(uri_rdfs_domain,P,C) ) ),
    inference(quant_intro,[status(thm)],[39]) ).

tff(41,plain,
    ^ [P: $i,C: $i,X: $i,Y: $i] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              rewrite(
                ( ( iext(uri_rdfs_domain,P,C)
                  & iext(P,X,Y) )
              <=> ~ ( ~ iext(uri_rdfs_domain,P,C)
                    | ~ iext(P,X,Y) ) )),
              ( ~ ( iext(uri_rdfs_domain,P,C)
                  & iext(P,X,Y) )
            <=> ~ ~ ( ~ iext(uri_rdfs_domain,P,C)
                    | ~ iext(P,X,Y) ) )),
            rewrite(
              ( ~ ~ ( ~ iext(uri_rdfs_domain,P,C)
                    | ~ iext(P,X,Y) )
            <=> ( ~ iext(uri_rdfs_domain,P,C)
                | ~ iext(P,X,Y) ) )),
            ( ~ ( iext(uri_rdfs_domain,P,C)
                & iext(P,X,Y) )
          <=> ( ~ iext(uri_rdfs_domain,P,C)
              | ~ iext(P,X,Y) ) )),
          ( ( ~ ( iext(uri_rdfs_domain,P,C)
                & iext(P,X,Y) )
            | icext(C,X) )
        <=> ( ~ iext(uri_rdfs_domain,P,C)
            | ~ iext(P,X,Y)
            | icext(C,X) ) )),
        rewrite(
          ( ( ~ iext(uri_rdfs_domain,P,C)
            | ~ iext(P,X,Y)
            | icext(C,X) )
        <=> ( icext(C,X)
            | ~ iext(P,X,Y)
            | ~ iext(uri_rdfs_domain,P,C) ) )),
        ( ( ~ ( iext(uri_rdfs_domain,P,C)
              & iext(P,X,Y) )
          | icext(C,X) )
      <=> ( icext(C,X)
          | ~ iext(P,X,Y)
          | ~ iext(uri_rdfs_domain,P,C) ) )),
    inference(bind,[status(th)],]) ).

tff(42,plain,
    ( ! [P: $i,C: $i,X: $i,Y: $i] :
        ( ~ ( iext(uri_rdfs_domain,P,C)
            & iext(P,X,Y) )
        | icext(C,X) )
  <=> ! [P: $i,C: $i,X: $i,Y: $i] :
        ( icext(C,X)
        | ~ iext(P,X,Y)
        | ~ iext(uri_rdfs_domain,P,C) ) ),
    inference(quant_intro,[status(thm)],[41]) ).

tff(43,plain,
    ( ! [P: $i,C: $i,X: $i,Y: $i] :
        ( ~ ( iext(uri_rdfs_domain,P,C)
            & iext(P,X,Y) )
        | icext(C,X) )
  <=> ! [P: $i,C: $i,X: $i,Y: $i] :
        ( ~ ( iext(uri_rdfs_domain,P,C)
            & iext(P,X,Y) )
        | icext(C,X) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(44,plain,
    ^ [P: $i,C: $i,X: $i,Y: $i] :
      rewrite(
        ( ( ( iext(uri_rdfs_domain,P,C)
            & iext(P,X,Y) )
         => icext(C,X) )
      <=> ( ~ ( iext(uri_rdfs_domain,P,C)
              & iext(P,X,Y) )
          | icext(C,X) ) )),
    inference(bind,[status(th)],]) ).

tff(45,plain,
    ( ! [P: $i,C: $i,X: $i,Y: $i] :
        ( ( iext(uri_rdfs_domain,P,C)
          & iext(P,X,Y) )
       => icext(C,X) )
  <=> ! [P: $i,C: $i,X: $i,Y: $i] :
        ( ~ ( iext(uri_rdfs_domain,P,C)
            & iext(P,X,Y) )
        | icext(C,X) ) ),
    inference(quant_intro,[status(thm)],[44]) ).

tff(46,axiom,
    ! [P: $i,C: $i,X: $i,Y: $i] :
      ( ( iext(uri_rdfs_domain,P,C)
        & iext(P,X,Y) )
     => icext(C,X) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax',rdfs_domain_main) ).

tff(47,plain,
    ! [P: $i,C: $i,X: $i,Y: $i] :
      ( ~ ( iext(uri_rdfs_domain,P,C)
          & iext(P,X,Y) )
      | icext(C,X) ),
    inference(modus_ponens,[status(thm)],[46,45]) ).

tff(48,plain,
    ! [P: $i,C: $i,X: $i,Y: $i] :
      ( ~ ( iext(uri_rdfs_domain,P,C)
          & iext(P,X,Y) )
      | icext(C,X) ),
    inference(modus_ponens,[status(thm)],[47,43]) ).

tff(49,plain,
    ! [P: $i,C: $i,X: $i,Y: $i] :
      ( ~ ( iext(uri_rdfs_domain,P,C)
          & iext(P,X,Y) )
      | icext(C,X) ),
    inference(skolemize,[status(sab)],[48]) ).

tff(50,plain,
    ! [P: $i,C: $i,X: $i,Y: $i] :
      ( icext(C,X)
      | ~ iext(P,X,Y)
      | ~ iext(uri_rdfs_domain,P,C) ),
    inference(modus_ponens,[status(thm)],[49,42]) ).

tff(51,plain,
    ! [P: $i,C: $i,X: $i,Y: $i] :
      ( icext(C,X)
      | ~ iext(P,X,Y)
      | ~ iext(uri_rdfs_domain,P,C) ),
    inference(modus_ponens,[status(thm)],[50,40]) ).

tff(52,plain,
    ( ( ~ ! [P: $i,C: $i,X: $i,Y: $i] :
            ( icext(C,X)
            | ~ iext(P,X,Y)
            | ~ iext(uri_rdfs_domain,P,C) )
      | icext(uri_ex_Person,uri_ex_u)
      | ~ iext(uri_rdfs_domain,uri_owl_sameAs,uri_ex_Person)
      | ~ iext(uri_owl_sameAs,uri_ex_u,uri_ex_u) )
  <=> ( ~ ! [P: $i,C: $i,X: $i,Y: $i] :
            ( icext(C,X)
            | ~ iext(P,X,Y)
            | ~ iext(uri_rdfs_domain,P,C) )
      | icext(uri_ex_Person,uri_ex_u)
      | ~ iext(uri_rdfs_domain,uri_owl_sameAs,uri_ex_Person)
      | ~ iext(uri_owl_sameAs,uri_ex_u,uri_ex_u) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(53,plain,
    ( ( icext(uri_ex_Person,uri_ex_u)
      | ~ iext(uri_owl_sameAs,uri_ex_u,uri_ex_u)
      | ~ iext(uri_rdfs_domain,uri_owl_sameAs,uri_ex_Person) )
  <=> ( icext(uri_ex_Person,uri_ex_u)
      | ~ iext(uri_rdfs_domain,uri_owl_sameAs,uri_ex_Person)
      | ~ iext(uri_owl_sameAs,uri_ex_u,uri_ex_u) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(54,plain,
    ( ( ~ ! [P: $i,C: $i,X: $i,Y: $i] :
            ( icext(C,X)
            | ~ iext(P,X,Y)
            | ~ iext(uri_rdfs_domain,P,C) )
      | icext(uri_ex_Person,uri_ex_u)
      | ~ iext(uri_owl_sameAs,uri_ex_u,uri_ex_u)
      | ~ iext(uri_rdfs_domain,uri_owl_sameAs,uri_ex_Person) )
  <=> ( ~ ! [P: $i,C: $i,X: $i,Y: $i] :
            ( icext(C,X)
            | ~ iext(P,X,Y)
            | ~ iext(uri_rdfs_domain,P,C) )
      | icext(uri_ex_Person,uri_ex_u)
      | ~ iext(uri_rdfs_domain,uri_owl_sameAs,uri_ex_Person)
      | ~ iext(uri_owl_sameAs,uri_ex_u,uri_ex_u) ) ),
    inference(monotonicity,[status(thm)],[53]) ).

tff(55,plain,
    ( ( ~ ! [P: $i,C: $i,X: $i,Y: $i] :
            ( icext(C,X)
            | ~ iext(P,X,Y)
            | ~ iext(uri_rdfs_domain,P,C) )
      | icext(uri_ex_Person,uri_ex_u)
      | ~ iext(uri_owl_sameAs,uri_ex_u,uri_ex_u)
      | ~ iext(uri_rdfs_domain,uri_owl_sameAs,uri_ex_Person) )
  <=> ( ~ ! [P: $i,C: $i,X: $i,Y: $i] :
            ( icext(C,X)
            | ~ iext(P,X,Y)
            | ~ iext(uri_rdfs_domain,P,C) )
      | icext(uri_ex_Person,uri_ex_u)
      | ~ iext(uri_rdfs_domain,uri_owl_sameAs,uri_ex_Person)
      | ~ iext(uri_owl_sameAs,uri_ex_u,uri_ex_u) ) ),
    inference(transitivity,[status(thm)],[54,52]) ).

tff(56,plain,
    ( ~ ! [P: $i,C: $i,X: $i,Y: $i] :
          ( icext(C,X)
          | ~ iext(P,X,Y)
          | ~ iext(uri_rdfs_domain,P,C) )
    | icext(uri_ex_Person,uri_ex_u)
    | ~ iext(uri_owl_sameAs,uri_ex_u,uri_ex_u)
    | ~ iext(uri_rdfs_domain,uri_owl_sameAs,uri_ex_Person) ),
    inference(quant_inst,[status(thm)],]) ).

tff(57,plain,
    ( ~ ! [P: $i,C: $i,X: $i,Y: $i] :
          ( icext(C,X)
          | ~ iext(P,X,Y)
          | ~ iext(uri_rdfs_domain,P,C) )
    | icext(uri_ex_Person,uri_ex_u)
    | ~ iext(uri_rdfs_domain,uri_owl_sameAs,uri_ex_Person)
    | ~ iext(uri_owl_sameAs,uri_ex_u,uri_ex_u) ),
    inference(modus_ponens,[status(thm)],[56,55]) ).

tff(58,plain,
    ~ iext(uri_owl_sameAs,uri_ex_u,uri_ex_u),
    inference(unit_resolution,[status(thm)],[57,51,38,35]) ).

tff(59,plain,
    $false,
    inference(unit_resolution,[status(thm)],[58,20]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWB018+1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n021.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Sat Sep  3 19:30:00 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35  Usage: tptp [options] [-file:]file
% 0.13/0.35    -h, -?       prints this message.
% 0.13/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.35    -m, -model   generate model.
% 0.13/0.35    -p, -proof   generate proof.
% 0.13/0.35    -c, -core    generate unsat core of named formulas.
% 0.13/0.35    -st, -statistics display statistics.
% 0.13/0.35    -t:timeout   set timeout (in second).
% 0.13/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35    -<param>:<value> configuration parameter and value.
% 0.13/0.35    -o:<output-file> file to place output in.
% 0.78/0.76  % SZS status Theorem
% 0.78/0.76  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------