TSTP Solution File: SWV314-2 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SWV314-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n011.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 15:11:06 EDT 2022

% Result   : Unsatisfiable 0.14s 0.39s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   42
% Syntax   : Number of formulae    :   56 (  15 unt;  24 typ;   0 def)
%            Number of atoms       :  258 (   0 equ)
%            Maximal formula atoms :   24 (   8 avg)
%            Number of connectives :  345 ( 139   ~; 185   |;   0   &)
%                                         (  21 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   6 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of FOOLs       :   20 (  20 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   20 (  11   >;   9   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :   23 (  23 usr;  13 con; 0-3 aty)
%            Number of variables   :  102 (  90   !;   0   ?; 102   :)

% 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(c_List_Oset_type,type,
    c_List_Oset: ( $i * $i ) > $i ).

tff(c_Event_Oevent_OSays_type,type,
    c_Event_Oevent_OSays: ( $i * $i * $i ) > $i ).

tff(c_Message_Omsg_OMPair_type,type,
    c_Message_Omsg_OMPair: ( $i * $i ) > $i ).

tff(c_Message_Omsg_OCrypt_type,type,
    c_Message_Omsg_OCrypt: ( $i * $i ) > $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(c_Message_Oagent_OServer_type,type,
    c_Message_Oagent_OServer: $i ).

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

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

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

tff(c_Event_Oevent_ONotes_type,type,
    c_Event_Oevent_ONotes: ( $i * $i ) > $i ).

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

tff(v_K_type,type,
    v_K: $i ).

tff(v_B_type,type,
    v_B: $i ).

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

tff(v_NB_type,type,
    v_NB: $i ).

tff(v_NA_type,type,
    v_NA: $i ).

tff(1,plain,
    ^ [V_NA: $i,V_NB: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
      refl(
        ( ( c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
          | c_in(V_A,c_Event_Obad,tc_Message_Oagent)
          | c_in(V_B,c_Event_Obad,tc_Message_Oagent)
          | ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
          | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
          | ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) )
      <=> ( c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
          | c_in(V_A,c_Event_Obad,tc_Message_Oagent)
          | c_in(V_B,c_Event_Obad,tc_Message_Oagent)
          | ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
          | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
          | ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [V_NA: $i,V_NB: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
        ( c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
        | c_in(V_A,c_Event_Obad,tc_Message_Oagent)
        | c_in(V_B,c_Event_Obad,tc_Message_Oagent)
        | ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
        | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
        | ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) )
  <=> ! [V_NA: $i,V_NB: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
        ( c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
        | c_in(V_A,c_Event_Obad,tc_Message_Oagent)
        | c_in(V_B,c_Event_Obad,tc_Message_Oagent)
        | ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
        | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
        | ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ( ! [V_NA: $i,V_NB: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
        ( c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
        | c_in(V_A,c_Event_Obad,tc_Message_Oagent)
        | c_in(V_B,c_Event_Obad,tc_Message_Oagent)
        | ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
        | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
        | ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) )
  <=> ! [V_NA: $i,V_NB: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
        ( c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
        | c_in(V_A,c_Event_Obad,tc_Message_Oagent)
        | c_in(V_B,c_Event_Obad,tc_Message_Oagent)
        | ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
        | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
        | ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,plain,
    ^ [V_NA: $i,V_NB: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              trans(
                monotonicity(
                  rewrite(
                    ( ( ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent))
                      | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
                      | ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
                  <=> ( ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
                      | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
                      | ~ 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))
                    | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
                    | ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
                    | c_in(V_B,c_Event_Obad,tc_Message_Oagent) )
                <=> ( ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
                    | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
                    | ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent))
                    | c_in(V_B,c_Event_Obad,tc_Message_Oagent) ) )),
                rewrite(
                  ( ( ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
                    | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
                    | ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent))
                    | c_in(V_B,c_Event_Obad,tc_Message_Oagent) )
                <=> ( c_in(V_B,c_Event_Obad,tc_Message_Oagent)
                    | ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
                    | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
                    | ~ 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))
                  | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
                  | ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
                  | c_in(V_B,c_Event_Obad,tc_Message_Oagent) )
              <=> ( c_in(V_B,c_Event_Obad,tc_Message_Oagent)
                  | ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
                  | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
                  | ~ 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))
                | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
                | ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
                | c_in(V_B,c_Event_Obad,tc_Message_Oagent)
                | c_in(V_A,c_Event_Obad,tc_Message_Oagent) )
            <=> ( c_in(V_B,c_Event_Obad,tc_Message_Oagent)
                | ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
                | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
                | ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent))
                | c_in(V_A,c_Event_Obad,tc_Message_Oagent) ) )),
            rewrite(
              ( ( c_in(V_B,c_Event_Obad,tc_Message_Oagent)
                | ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
                | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
                | ~ 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(V_A,c_Event_Obad,tc_Message_Oagent)
                | c_in(V_B,c_Event_Obad,tc_Message_Oagent)
                | ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
                | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
                | ~ 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))
              | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
              | ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
              | c_in(V_B,c_Event_Obad,tc_Message_Oagent)
              | c_in(V_A,c_Event_Obad,tc_Message_Oagent) )
          <=> ( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
              | c_in(V_B,c_Event_Obad,tc_Message_Oagent)
              | ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
              | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
              | ~ 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))
            | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
            | ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
            | c_in(V_B,c_Event_Obad,tc_Message_Oagent)
            | c_in(V_A,c_Event_Obad,tc_Message_Oagent)
            | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) )
        <=> ( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
            | c_in(V_B,c_Event_Obad,tc_Message_Oagent)
            | ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
            | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
            | ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent))
            | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) ) )),
        rewrite(
          ( ( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
            | c_in(V_B,c_Event_Obad,tc_Message_Oagent)
            | ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
            | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
            | ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent))
            | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) )
        <=> ( c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
            | c_in(V_A,c_Event_Obad,tc_Message_Oagent)
            | c_in(V_B,c_Event_Obad,tc_Message_Oagent)
            | ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
            | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
            | ~ 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))
          | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
          | ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
          | c_in(V_B,c_Event_Obad,tc_Message_Oagent)
          | c_in(V_A,c_Event_Obad,tc_Message_Oagent)
          | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) )
      <=> ( c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
          | c_in(V_A,c_Event_Obad,tc_Message_Oagent)
          | c_in(V_B,c_Event_Obad,tc_Message_Oagent)
          | ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
          | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
          | ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ) )),
    inference(bind,[status(th)],]) ).

tff(5,plain,
    ( ! [V_NA: $i,V_NB: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
        ( ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent))
        | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
        | ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
        | c_in(V_B,c_Event_Obad,tc_Message_Oagent)
        | c_in(V_A,c_Event_Obad,tc_Message_Oagent)
        | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) )
  <=> ! [V_NA: $i,V_NB: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
        ( c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
        | c_in(V_A,c_Event_Obad,tc_Message_Oagent)
        | c_in(V_B,c_Event_Obad,tc_Message_Oagent)
        | ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
        | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
        | ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ) ),
    inference(quant_intro,[status(thm)],[4]) ).

tff(6,axiom,
    ! [V_NA: $i,V_NB: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
      ( ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent))
      | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
      | ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
      | c_in(V_B,c_Event_Obad,tc_Message_Oagent)
      | c_in(V_A,c_Event_Obad,tc_Message_Oagent)
      | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OtwayRees_Osecrecy__lemma__dest_0) ).

tff(7,plain,
    ! [V_NA: $i,V_NB: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
      ( c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
      | c_in(V_A,c_Event_Obad,tc_Message_Oagent)
      | c_in(V_B,c_Event_Obad,tc_Message_Oagent)
      | ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
      | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
      | ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ),
    inference(modus_ponens,[status(thm)],[6,5]) ).

tff(8,plain,
    ! [V_NA: $i,V_NB: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
      ( c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
      | c_in(V_A,c_Event_Obad,tc_Message_Oagent)
      | c_in(V_B,c_Event_Obad,tc_Message_Oagent)
      | ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
      | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
      | ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ),
    inference(modus_ponens,[status(thm)],[7,3]) ).

tff(9,plain,
    ! [V_NA: $i,V_NB: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
      ( c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
      | c_in(V_A,c_Event_Obad,tc_Message_Oagent)
      | c_in(V_B,c_Event_Obad,tc_Message_Oagent)
      | ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
      | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
      | ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ),
    inference(skolemize,[status(sab)],[8]) ).

tff(10,plain,
    ! [V_NA: $i,V_NB: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
      ( c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
      | c_in(V_A,c_Event_Obad,tc_Message_Oagent)
      | c_in(V_B,c_Event_Obad,tc_Message_Oagent)
      | ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
      | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
      | ~ 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(c_Message_Omsg_OKey(v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
  <=> c_in(c_Message_Omsg_OKey(v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) ),
    inference(rewrite,[status(thm)],]) ).

tff(12,axiom,
    c_in(c_Message_Omsg_OKey(v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).

tff(13,plain,
    c_in(c_Message_Omsg_OKey(v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg),
    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/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).

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(v_B,c_Event_Obad,tc_Message_Oagent)
  <=> ~ c_in(v_B,c_Event_Obad,tc_Message_Oagent) ),
    inference(rewrite,[status(thm)],]) ).

tff(18,axiom,
    ~ c_in(v_B,c_Event_Obad,tc_Message_Oagent),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).

tff(19,plain,
    ~ c_in(v_B,c_Event_Obad,tc_Message_Oagent),
    inference(modus_ponens,[status(thm)],[18,17]) ).

tff(20,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(21,axiom,
    ~ c_in(v_A,c_Event_Obad,tc_Message_Oagent),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

tff(22,plain,
    ~ c_in(v_A,c_Event_Obad,tc_Message_Oagent),
    inference(modus_ponens,[status(thm)],[21,20]) ).

tff(23,plain,
    ( ~ c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_NB,c_Message_Omsg_OKey(v_K)))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)
  <=> ~ c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_NB,c_Message_Omsg_OKey(v_K)))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent) ),
    inference(rewrite,[status(thm)],]) ).

tff(24,axiom,
    ~ c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_NB,c_Message_Omsg_OKey(v_K)))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

tff(25,plain,
    ~ c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_NB,c_Message_Omsg_OKey(v_K)))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent),
    inference(modus_ponens,[status(thm)],[24,23]) ).

tff(26,plain,
    ( c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_B,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OKey(v_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(v_NB,c_Message_Omsg_OKey(v_K)))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)
  <=> c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_B,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OKey(v_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(v_NB,c_Message_Omsg_OKey(v_K)))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent) ),
    inference(rewrite,[status(thm)],]) ).

tff(27,axiom,
    c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_B,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OKey(v_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(v_NB,c_Message_Omsg_OKey(v_K)))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

tff(28,plain,
    c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_B,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OKey(v_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(v_NB,c_Message_Omsg_OKey(v_K)))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent),
    inference(modus_ponens,[status(thm)],[27,26]) ).

tff(29,plain,
    ( ( ~ ! [V_NA: $i,V_NB: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
            ( c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
            | c_in(V_A,c_Event_Obad,tc_Message_Oagent)
            | c_in(V_B,c_Event_Obad,tc_Message_Oagent)
            | ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
            | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
            | ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) )
      | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_NB,c_Message_Omsg_OKey(v_K)))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)
      | c_in(v_A,c_Event_Obad,tc_Message_Oagent)
      | c_in(v_B,c_Event_Obad,tc_Message_Oagent)
      | ~ c_in(c_Message_Omsg_OKey(v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
      | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_B,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OKey(v_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(v_NB,c_Message_Omsg_OKey(v_K)))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)
      | ~ c_in(v_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) )
  <=> ( ~ ! [V_NA: $i,V_NB: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
            ( c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
            | c_in(V_A,c_Event_Obad,tc_Message_Oagent)
            | c_in(V_B,c_Event_Obad,tc_Message_Oagent)
            | ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
            | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
            | ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) )
      | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_NB,c_Message_Omsg_OKey(v_K)))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)
      | c_in(v_A,c_Event_Obad,tc_Message_Oagent)
      | c_in(v_B,c_Event_Obad,tc_Message_Oagent)
      | ~ c_in(c_Message_Omsg_OKey(v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
      | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_B,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OKey(v_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(v_NB,c_Message_Omsg_OKey(v_K)))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)
      | ~ c_in(v_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(30,plain,
    ( ~ ! [V_NA: $i,V_NB: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
          ( c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
          | c_in(V_A,c_Event_Obad,tc_Message_Oagent)
          | c_in(V_B,c_Event_Obad,tc_Message_Oagent)
          | ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
          | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
          | ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) )
    | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_NB,c_Message_Omsg_OKey(v_K)))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)
    | c_in(v_A,c_Event_Obad,tc_Message_Oagent)
    | c_in(v_B,c_Event_Obad,tc_Message_Oagent)
    | ~ c_in(c_Message_Omsg_OKey(v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
    | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_B,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OKey(v_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(v_NB,c_Message_Omsg_OKey(v_K)))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)
    | ~ c_in(v_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(31,plain,
    ( ~ ! [V_NA: $i,V_NB: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
          ( c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
          | c_in(V_A,c_Event_Obad,tc_Message_Oagent)
          | c_in(V_B,c_Event_Obad,tc_Message_Oagent)
          | ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
          | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
          | ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) )
    | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_NB,c_Message_Omsg_OKey(v_K)))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)
    | c_in(v_A,c_Event_Obad,tc_Message_Oagent)
    | c_in(v_B,c_Event_Obad,tc_Message_Oagent)
    | ~ c_in(c_Message_Omsg_OKey(v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
    | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_B,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OKey(v_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(v_NB,c_Message_Omsg_OKey(v_K)))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)
    | ~ c_in(v_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ),
    inference(modus_ponens,[status(thm)],[30,29]) ).

tff(32,plain,
    $false,
    inference(unit_resolution,[status(thm)],[31,28,25,22,19,16,13,10]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SWV314-2 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34  % Computer : n011.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Sun Sep  4 02:19:59 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.14/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34  Usage: tptp [options] [-file:]file
% 0.14/0.34    -h, -?       prints this message.
% 0.14/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.14/0.34    -m, -model   generate model.
% 0.14/0.34    -p, -proof   generate proof.
% 0.14/0.34    -c, -core    generate unsat core of named formulas.
% 0.14/0.34    -st, -statistics display statistics.
% 0.14/0.34    -t:timeout   set timeout (in second).
% 0.14/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.14/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34    -<param>:<value> configuration parameter and value.
% 0.14/0.34    -o:<output-file> file to place output in.
% 0.14/0.39  % SZS status Unsatisfiable
% 0.14/0.39  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------