TSTP Solution File: SWV320-2 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SWV320-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n029.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 : Thu Sep 29 15:11:08 EDT 2022

% Result   : Unsatisfiable 0.13s 0.39s
% Output   : Proof 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   26
% Syntax   : Number of formulae    :   37 (   9 unt;  14 typ;   0 def)
%            Number of atoms       :   84 (   0 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  113 (  54   ~;  50   |;   0   &)
%                                         (   9 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of FOOLs       :    2 (   2 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   6   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :   13 (  13 usr;   8 con; 0-2 aty)
%            Number of variables   :   34 (  30   !;   0   ?;  34   :)

% Comments : 
%------------------------------------------------------------------------------
tff(c_in_type,type,
    c_in: ( $i * $i * $i ) > $o ).

tff(tc_List_Olist_type,type,
    tc_List_Olist: $i > $i ).

tff(tc_Event_Oevent_type,type,
    tc_Event_Oevent: $i ).

tff(c_OtwayRees_Ootway_type,type,
    c_OtwayRees_Ootway: $i ).

tff(tc_Message_Omsg_type,type,
    tc_Message_Omsg: $i ).

tff(c_Message_Oparts_type,type,
    c_Message_Oparts: $i > $i ).

tff(c_Event_Oknows_type,type,
    c_Event_Oknows: ( $i * $i ) > $i ).

tff(c_Message_Oagent_OSpy_type,type,
    c_Message_Oagent_OSpy: $i ).

tff(c_Message_Omsg_OKey_type,type,
    c_Message_Omsg_OKey: $i > $i ).

tff(c_Public_OshrK_type,type,
    c_Public_OshrK: $i > $i ).

tff(tc_Message_Oagent_type,type,
    tc_Message_Oagent: $i ).

tff(c_Event_Obad_type,type,
    c_Event_Obad: $i ).

tff(v_A_type,type,
    v_A: $i ).

tff(v_evs_type,type,
    v_evs: $i ).

tff(1,plain,
    ^ [V_A: $i,V_evs: $i] :
      refl(
        ( ( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
          | ~ c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
          | ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) )
      <=> ( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
          | ~ c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
          | ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [V_A: $i,V_evs: $i] :
        ( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
        | ~ c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
        | ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) )
  <=> ! [V_A: $i,V_evs: $i] :
        ( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
        | ~ c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
        | ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ( ! [V_A: $i,V_evs: $i] :
        ( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
        | ~ c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
        | ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) )
  <=> ! [V_A: $i,V_evs: $i] :
        ( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
        | ~ c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
        | ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,plain,
    ^ [V_A: $i,V_evs: $i] :
      rewrite(
        ( ( ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent))
          | ~ c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
          | c_in(V_A,c_Event_Obad,tc_Message_Oagent) )
      <=> ( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
          | ~ c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
          | ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ) )),
    inference(bind,[status(th)],]) ).

tff(5,plain,
    ( ! [V_A: $i,V_evs: $i] :
        ( ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent))
        | ~ c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
        | c_in(V_A,c_Event_Obad,tc_Message_Oagent) )
  <=> ! [V_A: $i,V_evs: $i] :
        ( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
        | ~ c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
        | ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ) ),
    inference(quant_intro,[status(thm)],[4]) ).

tff(6,axiom,
    ! [V_A: $i,V_evs: $i] :
      ( ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent))
      | ~ c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
      | c_in(V_A,c_Event_Obad,tc_Message_Oagent) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OtwayRees_OSpy__see__shrK_0) ).

tff(7,plain,
    ! [V_A: $i,V_evs: $i] :
      ( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
      | ~ c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
      | ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ),
    inference(modus_ponens,[status(thm)],[6,5]) ).

tff(8,plain,
    ! [V_A: $i,V_evs: $i] :
      ( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
      | ~ c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
      | ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ),
    inference(modus_ponens,[status(thm)],[7,3]) ).

tff(9,plain,
    ! [V_A: $i,V_evs: $i] :
      ( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
      | ~ c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
      | ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ),
    inference(skolemize,[status(sab)],[8]) ).

tff(10,plain,
    ! [V_A: $i,V_evs: $i] :
      ( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
      | ~ c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
      | ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ),
    inference(modus_ponens,[status(thm)],[9,2]) ).

tff(11,plain,
    ( ~ c_in(v_A,c_Event_Obad,tc_Message_Oagent)
  <=> ~ c_in(v_A,c_Event_Obad,tc_Message_Oagent) ),
    inference(rewrite,[status(thm)],]) ).

tff(12,axiom,
    ~ c_in(v_A,c_Event_Obad,tc_Message_Oagent),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).

tff(13,plain,
    ~ c_in(v_A,c_Event_Obad,tc_Message_Oagent),
    inference(modus_ponens,[status(thm)],[12,11]) ).

tff(14,plain,
    ( c_in(v_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent))
  <=> c_in(v_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ),
    inference(rewrite,[status(thm)],]) ).

tff(15,axiom,
    c_in(v_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

tff(16,plain,
    c_in(v_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)),
    inference(modus_ponens,[status(thm)],[15,14]) ).

tff(17,plain,
    ( c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
  <=> c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) ),
    inference(rewrite,[status(thm)],]) ).

tff(18,axiom,
    c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

tff(19,plain,
    c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg),
    inference(modus_ponens,[status(thm)],[18,17]) ).

tff(20,plain,
    ( ( ~ ! [V_A: $i,V_evs: $i] :
            ( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
            | ~ c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
            | ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) )
      | c_in(v_A,c_Event_Obad,tc_Message_Oagent)
      | ~ c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
      | ~ c_in(v_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) )
  <=> ( ~ ! [V_A: $i,V_evs: $i] :
            ( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
            | ~ c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
            | ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) )
      | c_in(v_A,c_Event_Obad,tc_Message_Oagent)
      | ~ c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
      | ~ c_in(v_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(21,plain,
    ( ~ ! [V_A: $i,V_evs: $i] :
          ( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
          | ~ c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
          | ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) )
    | c_in(v_A,c_Event_Obad,tc_Message_Oagent)
    | ~ c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
    | ~ c_in(v_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(22,plain,
    ( ~ ! [V_A: $i,V_evs: $i] :
          ( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
          | ~ c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
          | ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) )
    | c_in(v_A,c_Event_Obad,tc_Message_Oagent)
    | ~ c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
    | ~ c_in(v_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ),
    inference(modus_ponens,[status(thm)],[21,20]) ).

tff(23,plain,
    $false,
    inference(unit_resolution,[status(thm)],[22,19,16,13,10]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SWV320-2 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n029.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 : Sun Sep  4 02:35:00 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34  Usage: tptp [options] [-file:]file
% 0.13/0.34    -h, -?       prints this message.
% 0.13/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.34    -m, -model   generate model.
% 0.13/0.34    -p, -proof   generate proof.
% 0.13/0.34    -c, -core    generate unsat core of named formulas.
% 0.13/0.34    -st, -statistics display statistics.
% 0.13/0.34    -t:timeout   set timeout (in second).
% 0.13/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34    -<param>:<value> configuration parameter and value.
% 0.13/0.34    -o:<output-file> file to place output in.
% 0.13/0.39  % SZS status Unsatisfiable
% 0.13/0.39  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------