Z3---4.15.1.UNS-Prf.s

%------------------------------------------------------------------------------
% File     : Z3---4.15.1
% Problem  : SWV298-1 : TPTP v9.0.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_E %s %d THM

% Computer : n014.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 : Sat Jun 21 05:32:01 AM UTC 2025

% Result   : Unsatisfiable 0.60s 0.76s
% Output   : Proof 0.65s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   54
% Syntax   : Number of formulae    :  118 (  29 unt;   0 typ;   0 def)
%            Number of atoms       :  551 (  62 equ)
%            Maximal formula atoms :   20 (   4 avg)
%            Number of connectives :  765 ( 351   ~; 365   |;   0   &)
%                                         (  49 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Maximal term depth    :   11 (   2 avg)
%            Number of FOOLs       :   19 (  19 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :   25 (  25 usr;  14 con; 0-3 aty)
%            Number of variables   :  354 ( 331   !;   0   ?; 354   :)

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

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(v_evs3_type,type,
    v_evs3: $i ).

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

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

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

tff(c_Message_Omsg_OAgent_type,type,
    c_Message_Omsg_OAgent: $i > $i ).

tff(v_Ba_type,type,
    v_Ba: $i ).

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

tff(c_Message_Omsg_ONonce_type,type,
    c_Message_Omsg_ONonce: $i > $i ).

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

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

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

tff(c_Message_Oanalz_type,type,
    c_Message_Oanalz: $i > $i ).

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

tff(v_Aa_type,type,
    v_Aa: $i ).

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

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

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

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

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

tff(1,plain,
    ( c_in(c_Event_Oevent_OSays(v_Aa,c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))))))))),c_List_Oset(v_evs3,tc_Event_Oevent),tc_Event_Oevent)
  <=> c_in(c_Event_Oevent_OSays(v_Aa,c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))))))))),c_List_Oset(v_evs3,tc_Event_Oevent),tc_Event_Oevent) ),
    inference(rewrite,[status(thm)],[]) ).

tff(2,axiom,
    c_in(c_Event_Oevent_OSays(v_Aa,c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))))))))),c_List_Oset(v_evs3,tc_Event_Oevent),tc_Event_Oevent),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).

tff(3,plain,
    c_in(c_Event_Oevent_OSays(v_Aa,c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))))))))),c_List_Oset(v_evs3,tc_Event_Oevent),tc_Event_Oevent),
    inference(modus_ponens,[status(thm)],[2,1]) ).

tff(4,plain,
    ^ [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
      refl(( ( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
          | c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
      <=> ( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
          | c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ) )),
    inference(bind,[status(th)],[]) ).

tff(5,plain,
    ( ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
        ( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
        | c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
  <=> ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
        ( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
        | c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ) ),
    inference(quant_intro,[status(thm)],[4]) ).

tff(6,plain,
    ( ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
        ( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
        | c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
  <=> ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
        ( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
        | c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(7,axiom,
    ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
      ( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
      | c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV006-1.ax',cls_Event_OSays__imp__analz__Spy__dest_0) ).

tff(8,plain,
    ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
      ( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
      | c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ),
    inference(modus_ponens,[status(thm)],[7,6]) ).

tff(9,plain,
    ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
      ( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
      | c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ),
    inference(skolemize,[status(sab)],[8]) ).

tff(10,plain,
    ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
      ( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
      | c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ),
    inference(modus_ponens,[status(thm)],[9,5]) ).

tff(11,plain,
    ( ( ~ ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
            ( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
            | c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
      | ~ c_in(c_Event_Oevent_OSays(v_Aa,c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))))))))),c_List_Oset(v_evs3,tc_Event_Oevent),tc_Event_Oevent)
      | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba))))))))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) )
  <=> ( ~ ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
            ( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
            | c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
      | ~ c_in(c_Event_Oevent_OSays(v_Aa,c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))))))))),c_List_Oset(v_evs3,tc_Event_Oevent),tc_Event_Oevent)
      | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba))))))))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(12,plain,
    ( ~ ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
          ( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
          | c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
    | ~ c_in(c_Event_Oevent_OSays(v_Aa,c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))))))))),c_List_Oset(v_evs3,tc_Event_Oevent),tc_Event_Oevent)
    | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba))))))))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(13,plain,
    ( ~ ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
          ( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
          | c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
    | ~ c_in(c_Event_Oevent_OSays(v_Aa,c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))))))))),c_List_Oset(v_evs3,tc_Event_Oevent),tc_Event_Oevent)
    | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba))))))))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ),
    inference(modus_ponens,[status(thm)],[12,11]) ).

tff(14,plain,
    c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba))))))))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg),
    inference(unit_resolution,[status(thm)],[13,10,3]) ).

tff(15,plain,
    ^ [V_c: $i,V_H: $i] :
      refl(( ( ~ c_in(V_c,c_Message_Oanalz(V_H),tc_Message_Omsg)
          | c_in(V_c,c_Message_Oparts(V_H),tc_Message_Omsg) )
      <=> ( ~ c_in(V_c,c_Message_Oanalz(V_H),tc_Message_Omsg)
          | c_in(V_c,c_Message_Oparts(V_H),tc_Message_Omsg) ) )),
    inference(bind,[status(th)],[]) ).

tff(16,plain,
    ( ! [V_c: $i,V_H: $i] :
        ( ~ c_in(V_c,c_Message_Oanalz(V_H),tc_Message_Omsg)
        | c_in(V_c,c_Message_Oparts(V_H),tc_Message_Omsg) )
  <=> ! [V_c: $i,V_H: $i] :
        ( ~ c_in(V_c,c_Message_Oanalz(V_H),tc_Message_Omsg)
        | c_in(V_c,c_Message_Oparts(V_H),tc_Message_Omsg) ) ),
    inference(quant_intro,[status(thm)],[15]) ).

tff(17,plain,
    ( ! [V_c: $i,V_H: $i] :
        ( ~ c_in(V_c,c_Message_Oanalz(V_H),tc_Message_Omsg)
        | c_in(V_c,c_Message_Oparts(V_H),tc_Message_Omsg) )
  <=> ! [V_c: $i,V_H: $i] :
        ( ~ c_in(V_c,c_Message_Oanalz(V_H),tc_Message_Omsg)
        | c_in(V_c,c_Message_Oparts(V_H),tc_Message_Omsg) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(18,axiom,
    ! [V_c: $i,V_H: $i] :
      ( ~ c_in(V_c,c_Message_Oanalz(V_H),tc_Message_Omsg)
      | c_in(V_c,c_Message_Oparts(V_H),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV006-1.ax',cls_Message_Oanalz__into__parts__dest_0) ).

tff(19,plain,
    ! [V_c: $i,V_H: $i] :
      ( ~ c_in(V_c,c_Message_Oanalz(V_H),tc_Message_Omsg)
      | c_in(V_c,c_Message_Oparts(V_H),tc_Message_Omsg) ),
    inference(modus_ponens,[status(thm)],[18,17]) ).

tff(20,plain,
    ! [V_c: $i,V_H: $i] :
      ( ~ c_in(V_c,c_Message_Oanalz(V_H),tc_Message_Omsg)
      | c_in(V_c,c_Message_Oparts(V_H),tc_Message_Omsg) ),
    inference(skolemize,[status(sab)],[19]) ).

tff(21,plain,
    ! [V_c: $i,V_H: $i] :
      ( ~ c_in(V_c,c_Message_Oanalz(V_H),tc_Message_Omsg)
      | c_in(V_c,c_Message_Oparts(V_H),tc_Message_Omsg) ),
    inference(modus_ponens,[status(thm)],[20,16]) ).

tff(22,plain,
    ( ( ~ ! [V_c: $i,V_H: $i] :
            ( ~ c_in(V_c,c_Message_Oanalz(V_H),tc_Message_Omsg)
            | c_in(V_c,c_Message_Oparts(V_H),tc_Message_Omsg) )
      | ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba))))))))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba))))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) )
  <=> ( ~ ! [V_c: $i,V_H: $i] :
            ( ~ c_in(V_c,c_Message_Oanalz(V_H),tc_Message_Omsg)
            | c_in(V_c,c_Message_Oparts(V_H),tc_Message_Omsg) )
      | ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba))))))))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba))))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(23,plain,
    ( ~ ! [V_c: $i,V_H: $i] :
          ( ~ c_in(V_c,c_Message_Oanalz(V_H),tc_Message_Omsg)
          | c_in(V_c,c_Message_Oparts(V_H),tc_Message_Omsg) )
    | ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba))))))))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba))))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(24,plain,
    ( ~ ! [V_c: $i,V_H: $i] :
          ( ~ c_in(V_c,c_Message_Oanalz(V_H),tc_Message_Omsg)
          | c_in(V_c,c_Message_Oparts(V_H),tc_Message_Omsg) )
    | ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba))))))))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba))))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ),
    inference(modus_ponens,[status(thm)],[23,22]) ).

tff(25,plain,
    c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba))))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg),
    inference(unit_resolution,[status(thm)],[24,21,14]) ).

tff(26,plain,
    ^ [V_Y: $i,V_H: $i,V_X: $i] :
      refl(( ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
          | c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) )
      <=> ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
          | c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) ) )),
    inference(bind,[status(th)],[]) ).

tff(27,plain,
    ( ! [V_Y: $i,V_H: $i,V_X: $i] :
        ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
        | c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) )
  <=> ! [V_Y: $i,V_H: $i,V_X: $i] :
        ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
        | c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) ) ),
    inference(quant_intro,[status(thm)],[26]) ).

tff(28,plain,
    ( ! [V_Y: $i,V_H: $i,V_X: $i] :
        ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
        | c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) )
  <=> ! [V_Y: $i,V_H: $i,V_X: $i] :
        ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
        | c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(29,axiom,
    ! [V_Y: $i,V_H: $i,V_X: $i] :
      ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
      | c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV006-0.ax',cls_Message_OMPair__parts_0) ).

tff(30,plain,
    ! [V_Y: $i,V_H: $i,V_X: $i] :
      ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
      | c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) ),
    inference(modus_ponens,[status(thm)],[29,28]) ).

tff(31,plain,
    ! [V_Y: $i,V_H: $i,V_X: $i] :
      ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
      | c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) ),
    inference(skolemize,[status(sab)],[30]) ).

tff(32,plain,
    ! [V_Y: $i,V_H: $i,V_X: $i] :
      ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
      | c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) ),
    inference(modus_ponens,[status(thm)],[31,27]) ).

tff(33,plain,
    ( ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
            ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
            | c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) )
      | ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba))))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) )
  <=> ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
            ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
            | c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) )
      | ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba))))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(34,plain,
    ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
          ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
          | c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) )
    | ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba))))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(35,plain,
    ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
          ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
          | c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) )
    | ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba))))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ),
    inference(modus_ponens,[status(thm)],[34,33]) ).

tff(36,plain,
    ( ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba))))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ),
    inference(unit_resolution,[status(thm)],[35,32]) ).

tff(37,plain,
    c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg),
    inference(unit_resolution,[status(thm)],[36,25]) ).

tff(38,plain,
    ( ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
            ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
            | c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) )
      | ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) )
  <=> ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
            ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
            | c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) )
      | ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(39,plain,
    ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
          ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
          | c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) )
    | ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(40,plain,
    ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
          ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
          | c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) )
    | ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ),
    inference(modus_ponens,[status(thm)],[39,38]) ).

tff(41,plain,
    ( ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ),
    inference(unit_resolution,[status(thm)],[40,32]) ).

tff(42,plain,
    c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg),
    inference(unit_resolution,[status(thm)],[41,37]) ).

tff(43,plain,
    ( ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
            ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
            | c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) )
      | ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) )
  <=> ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
            ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
            | c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) )
      | ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(44,plain,
    ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
          ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
          | c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) )
    | ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(45,plain,
    ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
          ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
          | c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) )
    | ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ),
    inference(modus_ponens,[status(thm)],[44,43]) ).

tff(46,plain,
    ( ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ),
    inference(unit_resolution,[status(thm)],[45,32]) ).

tff(47,plain,
    c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg),
    inference(unit_resolution,[status(thm)],[46,42]) ).

tff(48,plain,
    ^ [V_Y: $i,V_H: $i,V_X: $i] :
      refl(( ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
          | c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
      <=> ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
          | c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ) )),
    inference(bind,[status(th)],[]) ).

tff(49,plain,
    ( ! [V_Y: $i,V_H: $i,V_X: $i] :
        ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
        | c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
  <=> ! [V_Y: $i,V_H: $i,V_X: $i] :
        ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
        | c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ) ),
    inference(quant_intro,[status(thm)],[48]) ).

tff(50,plain,
    ( ! [V_Y: $i,V_H: $i,V_X: $i] :
        ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
        | c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
  <=> ! [V_Y: $i,V_H: $i,V_X: $i] :
        ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
        | c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(51,axiom,
    ! [V_Y: $i,V_H: $i,V_X: $i] :
      ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
      | c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV006-0.ax',cls_Message_OMPair__parts_1) ).

tff(52,plain,
    ! [V_Y: $i,V_H: $i,V_X: $i] :
      ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
      | c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ),
    inference(modus_ponens,[status(thm)],[51,50]) ).

tff(53,plain,
    ! [V_Y: $i,V_H: $i,V_X: $i] :
      ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
      | c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ),
    inference(skolemize,[status(sab)],[52]) ).

tff(54,plain,
    ! [V_Y: $i,V_H: $i,V_X: $i] :
      ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
      | c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ),
    inference(modus_ponens,[status(thm)],[53,49]) ).

tff(55,plain,
    ( ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
            ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
            | c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
      | ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) )
  <=> ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
            ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
            | c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
      | ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(56,plain,
    ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
          ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
          | c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
    | ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(57,plain,
    ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
          ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
          | c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
    | ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ),
    inference(modus_ponens,[status(thm)],[56,55]) ).

tff(58,plain,
    ( ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ),
    inference(unit_resolution,[status(thm)],[57,54]) ).

tff(59,plain,
    c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg),
    inference(unit_resolution,[status(thm)],[58,47]) ).

tff(60,plain,
    ( c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B)))))))),c_List_Oset(v_evs3,tc_Event_Oevent),tc_Event_Oevent)
  <=> c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B)))))))),c_List_Oset(v_evs3,tc_Event_Oevent),tc_Event_Oevent) ),
    inference(rewrite,[status(thm)],[]) ).

tff(61,axiom,
    c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B)))))))),c_List_Oset(v_evs3,tc_Event_Oevent),tc_Event_Oevent),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).

tff(62,plain,
    c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B)))))))),c_List_Oset(v_evs3,tc_Event_Oevent),tc_Event_Oevent),
    inference(modus_ponens,[status(thm)],[61,60]) ).

tff(63,plain,
    ( ( ~ ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
            ( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
            | c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
      | ~ c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B)))))))),c_List_Oset(v_evs3,tc_Event_Oevent),tc_Event_Oevent)
      | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B))))))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) )
  <=> ( ~ ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
            ( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
            | c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
      | ~ c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B)))))))),c_List_Oset(v_evs3,tc_Event_Oevent),tc_Event_Oevent)
      | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B))))))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(64,plain,
    ( ~ ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
          ( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
          | c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
    | ~ c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B)))))))),c_List_Oset(v_evs3,tc_Event_Oevent),tc_Event_Oevent)
    | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B))))))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(65,plain,
    ( ~ ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
          ( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
          | c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
    | ~ c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B)))))))),c_List_Oset(v_evs3,tc_Event_Oevent),tc_Event_Oevent)
    | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B))))))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ),
    inference(modus_ponens,[status(thm)],[64,63]) ).

tff(66,plain,
    c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B))))))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg),
    inference(unit_resolution,[status(thm)],[65,10,62]) ).

tff(67,plain,
    ( ( ~ ! [V_c: $i,V_H: $i] :
            ( ~ c_in(V_c,c_Message_Oanalz(V_H),tc_Message_Omsg)
            | c_in(V_c,c_Message_Oparts(V_H),tc_Message_Omsg) )
      | ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B))))))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) )
  <=> ( ~ ! [V_c: $i,V_H: $i] :
            ( ~ c_in(V_c,c_Message_Oanalz(V_H),tc_Message_Omsg)
            | c_in(V_c,c_Message_Oparts(V_H),tc_Message_Omsg) )
      | ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B))))))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(68,plain,
    ( ~ ! [V_c: $i,V_H: $i] :
          ( ~ c_in(V_c,c_Message_Oanalz(V_H),tc_Message_Omsg)
          | c_in(V_c,c_Message_Oparts(V_H),tc_Message_Omsg) )
    | ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B))))))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(69,plain,
    ( ~ ! [V_c: $i,V_H: $i] :
          ( ~ c_in(V_c,c_Message_Oanalz(V_H),tc_Message_Omsg)
          | c_in(V_c,c_Message_Oparts(V_H),tc_Message_Omsg) )
    | ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B))))))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ),
    inference(modus_ponens,[status(thm)],[68,67]) ).

tff(70,plain,
    c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg),
    inference(unit_resolution,[status(thm)],[69,21,66]) ).

tff(71,plain,
    ( ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
            ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
            | c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) )
      | ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B)))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) )
  <=> ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
            ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
            | c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) )
      | ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B)))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(72,plain,
    ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
          ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
          | c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) )
    | ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B)))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(73,plain,
    ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
          ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
          | c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) )
    | ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B)))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ),
    inference(modus_ponens,[status(thm)],[72,71]) ).

tff(74,plain,
    ( ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B)))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ),
    inference(unit_resolution,[status(thm)],[73,32]) ).

tff(75,plain,
    c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B)))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg),
    inference(unit_resolution,[status(thm)],[74,70]) ).

tff(76,plain,
    ( ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
            ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
            | c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) )
      | ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B)))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) )
  <=> ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
            ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
            | c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) )
      | ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B)))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(77,plain,
    ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
          ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
          | c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) )
    | ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B)))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(78,plain,
    ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
          ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
          | c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) )
    | ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B)))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ),
    inference(modus_ponens,[status(thm)],[77,76]) ).

tff(79,plain,
    ( ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B)))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ),
    inference(unit_resolution,[status(thm)],[78,32]) ).

tff(80,plain,
    c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg),
    inference(unit_resolution,[status(thm)],[79,75]) ).

tff(81,plain,
    ( ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
            ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
            | c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) )
      | ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) )
  <=> ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
            ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
            | c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) )
      | ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(82,plain,
    ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
          ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
          | c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) )
    | ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(83,plain,
    ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
          ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
          | c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) )
    | ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ),
    inference(modus_ponens,[status(thm)],[82,81]) ).

tff(84,plain,
    ( ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ),
    inference(unit_resolution,[status(thm)],[83,32]) ).

tff(85,plain,
    c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg),
    inference(unit_resolution,[status(thm)],[84,80]) ).

tff(86,plain,
    ( ( v_B != v_Ba )
  <=> ( v_B != v_Ba ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(87,plain,
    ( ! [V_U: $i] : ( v_B != v_Ba )
  <=> ( v_B != v_Ba ) ),
    inference(elim_unused_vars,[status(thm)],[]) ).

tff(88,plain,
    ( ! [V_U: $i] :
        ( ( v_B != v_Ba )
        | ( V_U != c_Message_Omsg_ONonce(v_NB) ) )
  <=> ! [V_U: $i] : ( v_B != v_Ba ) ),
    inference(destructive_equality_resolution,[status(thm)],[]) ).

tff(89,plain,
    ( ! [V_U: $i] :
        ( ( v_B != v_Ba )
        | ( V_U != c_Message_Omsg_ONonce(v_NB) ) )
  <=> ( v_B != v_Ba ) ),
    inference(transitivity,[status(thm)],[88,87]) ).

tff(90,plain,
    ^ [V_U: $i] :
      rewrite(( ( ( V_U != c_Message_Omsg_ONonce(v_NB) )
          | ( v_B != v_Ba ) )
      <=> ( ( v_B != v_Ba )
          | ( V_U != c_Message_Omsg_ONonce(v_NB) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(91,plain,
    ( ! [V_U: $i] :
        ( ( V_U != c_Message_Omsg_ONonce(v_NB) )
        | ( v_B != v_Ba ) )
  <=> ! [V_U: $i] :
        ( ( v_B != v_Ba )
        | ( V_U != c_Message_Omsg_ONonce(v_NB) ) ) ),
    inference(quant_intro,[status(thm)],[90]) ).

tff(92,plain,
    ( ! [V_U: $i] :
        ( ( V_U != c_Message_Omsg_ONonce(v_NB) )
        | ( v_B != v_Ba ) )
  <=> ( v_B != v_Ba ) ),
    inference(transitivity,[status(thm)],[91,89]) ).

tff(93,axiom,
    ! [V_U: $i] :
      ( ( V_U != c_Message_Omsg_ONonce(v_NB) )
      | ( v_B != v_Ba ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_7) ).

tff(94,plain,
    v_B != v_Ba,
    inference(modus_ponens,[status(thm)],[93,92]) ).

tff(95,plain,
    v_B != v_Ba,
    inference(modus_ponens,[status(thm)],[94,86]) ).

tff(96,plain,
    ( c_in(v_evs3,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent))
  <=> c_in(v_evs3,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ),
    inference(rewrite,[status(thm)],[]) ).

tff(97,axiom,
    c_in(v_evs3,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

tff(98,plain,
    c_in(v_evs3,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)),
    inference(modus_ponens,[status(thm)],[97,96]) ).

tff(99,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(100,axiom,
    ~ c_in(v_A,c_Event_Obad,tc_Message_Oagent),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

tff(101,plain,
    ~ c_in(v_A,c_Event_Obad,tc_Message_Oagent),
    inference(modus_ponens,[status(thm)],[100,99]) ).

tff(102,plain,
    ^ [V_NA: $i,V_B: $i,V_A: $i,V_C: $i,V_evs: $i] :
      refl(( ( ( V_B = V_C )
          | ~ 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_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_B)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
          | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_C)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
      <=> ( ( V_B = V_C )
          | ~ 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_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_B)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
          | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_C)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ) )),
    inference(bind,[status(th)],[]) ).

tff(103,plain,
    ( ! [V_NA: $i,V_B: $i,V_A: $i,V_C: $i,V_evs: $i] :
        ( ( V_B = V_C )
        | ~ 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_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_B)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_C)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
  <=> ! [V_NA: $i,V_B: $i,V_A: $i,V_C: $i,V_evs: $i] :
        ( ( V_B = V_C )
        | ~ 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_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_B)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_C)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ) ),
    inference(quant_intro,[status(thm)],[102]) ).

tff(104,plain,
    ( ! [V_NA: $i,V_B: $i,V_A: $i,V_C: $i,V_evs: $i] :
        ( ( V_B = V_C )
        | ~ 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_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_B)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_C)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
  <=> ! [V_NA: $i,V_B: $i,V_A: $i,V_C: $i,V_evs: $i] :
        ( ( V_B = V_C )
        | ~ 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_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_B)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_C)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(105,plain,
    ^ [V_NA: $i,V_B: $i,V_A: $i,V_C: $i,V_evs: $i] :
      trans(monotonicity(trans(monotonicity(rewrite(( ( ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent))
                  | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_C)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
                  | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_B)))),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(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_B)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
                  | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_C)))),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(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_C)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
                | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_B)))),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_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent))
                | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_B)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
                | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_C)))),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) ) )),
            rewrite(( ( ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent))
                | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_B)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
                | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_C)))),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_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_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_B)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
                | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_C)))),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(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_C)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
              | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_B)))),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_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_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_B)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
              | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_C)))),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(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_C)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
            | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_B)))),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_B = V_C ) )
        <=> ( ~ 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_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_B)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
            | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_C)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
            | ( V_B = V_C ) ) )),
        rewrite(( ( ~ 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_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_B)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
            | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_C)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
            | ( V_B = V_C ) )
        <=> ( ( V_B = V_C )
            | ~ 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_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_B)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
            | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_C)))),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(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_C)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
          | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_B)))),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_B = V_C ) )
      <=> ( ( V_B = V_C )
          | ~ 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_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_B)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
          | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_C)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ) )),
    inference(bind,[status(th)],[]) ).

tff(106,plain,
    ( ! [V_NA: $i,V_B: $i,V_A: $i,V_C: $i,V_evs: $i] :
        ( ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent))
        | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_C)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_B)))),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_B = V_C ) )
  <=> ! [V_NA: $i,V_B: $i,V_A: $i,V_C: $i,V_evs: $i] :
        ( ( V_B = V_C )
        | ~ 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_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_B)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_C)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ) ),
    inference(quant_intro,[status(thm)],[105]) ).

tff(107,axiom,
    ! [V_NA: $i,V_B: $i,V_A: $i,V_C: $i,V_evs: $i] :
      ( ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent))
      | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_C)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_B)))),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_B = V_C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OtwayRees_Ounique__NA__dest_0) ).

tff(108,plain,
    ! [V_NA: $i,V_B: $i,V_A: $i,V_C: $i,V_evs: $i] :
      ( ( V_B = V_C )
      | ~ 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_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_B)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_C)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ),
    inference(modus_ponens,[status(thm)],[107,106]) ).

tff(109,plain,
    ! [V_NA: $i,V_B: $i,V_A: $i,V_C: $i,V_evs: $i] :
      ( ( V_B = V_C )
      | ~ 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_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_B)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_C)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ),
    inference(modus_ponens,[status(thm)],[108,104]) ).

tff(110,plain,
    ! [V_NA: $i,V_B: $i,V_A: $i,V_C: $i,V_evs: $i] :
      ( ( V_B = V_C )
      | ~ 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_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_B)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_C)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ),
    inference(skolemize,[status(sab)],[109]) ).

tff(111,plain,
    ! [V_NA: $i,V_B: $i,V_A: $i,V_C: $i,V_evs: $i] :
      ( ( V_B = V_C )
      | ~ 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_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_B)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_C)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ),
    inference(modus_ponens,[status(thm)],[110,103]) ).

tff(112,plain,
    ( ( ~ ! [V_NA: $i,V_B: $i,V_A: $i,V_C: $i,V_evs: $i] :
            ( ( V_B = V_C )
            | ~ 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_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_B)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
            | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_C)))),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_B = v_Ba )
      | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
      | ~ c_in(v_evs3,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) )
  <=> ( ~ ! [V_NA: $i,V_B: $i,V_A: $i,V_C: $i,V_evs: $i] :
            ( ( V_B = V_C )
            | ~ 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_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_B)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
            | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_C)))),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_B = v_Ba )
      | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
      | ~ c_in(v_evs3,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(113,plain,
    ( ( ( v_B = v_Ba )
      | ~ c_in(v_evs3,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent))
      | c_in(v_A,c_Event_Obad,tc_Message_Oagent)
      | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) )
  <=> ( c_in(v_A,c_Event_Obad,tc_Message_Oagent)
      | ( v_B = v_Ba )
      | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
      | ~ c_in(v_evs3,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(114,plain,
    ( ( ~ ! [V_NA: $i,V_B: $i,V_A: $i,V_C: $i,V_evs: $i] :
            ( ( V_B = V_C )
            | ~ 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_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_B)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
            | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_C)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
      | ( v_B = v_Ba )
      | ~ c_in(v_evs3,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent))
      | c_in(v_A,c_Event_Obad,tc_Message_Oagent)
      | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) )
  <=> ( ~ ! [V_NA: $i,V_B: $i,V_A: $i,V_C: $i,V_evs: $i] :
            ( ( V_B = V_C )
            | ~ 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_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_B)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
            | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_C)))),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_B = v_Ba )
      | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
      | ~ c_in(v_evs3,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ) ),
    inference(monotonicity,[status(thm)],[113]) ).

tff(115,plain,
    ( ( ~ ! [V_NA: $i,V_B: $i,V_A: $i,V_C: $i,V_evs: $i] :
            ( ( V_B = V_C )
            | ~ 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_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_B)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
            | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_C)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
      | ( v_B = v_Ba )
      | ~ c_in(v_evs3,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent))
      | c_in(v_A,c_Event_Obad,tc_Message_Oagent)
      | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) )
  <=> ( ~ ! [V_NA: $i,V_B: $i,V_A: $i,V_C: $i,V_evs: $i] :
            ( ( V_B = V_C )
            | ~ 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_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_B)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
            | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_C)))),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_B = v_Ba )
      | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
      | ~ c_in(v_evs3,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ) ),
    inference(transitivity,[status(thm)],[114,112]) ).

tff(116,plain,
    ( ~ ! [V_NA: $i,V_B: $i,V_A: $i,V_C: $i,V_evs: $i] :
          ( ( V_B = V_C )
          | ~ 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_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_B)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
          | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_C)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
    | ( v_B = v_Ba )
    | ~ c_in(v_evs3,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent))
    | c_in(v_A,c_Event_Obad,tc_Message_Oagent)
    | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(117,plain,
    ( ~ ! [V_NA: $i,V_B: $i,V_A: $i,V_C: $i,V_evs: $i] :
          ( ( V_B = V_C )
          | ~ 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_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_B)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
          | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OAgent(V_C)))),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_B = v_Ba )
    | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_Ba)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
    | ~ c_in(v_evs3,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ),
    inference(modus_ponens,[status(thm)],[116,115]) ).

tff(118,plain,
    $false,
    inference(unit_resolution,[status(thm)],[117,111,101,98,95,85,59]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SWV298-1 : TPTP v9.0.0. Released v3.2.0.
% 0.07/0.12  % Command    : run_E %s %d THM
% 0.11/0.33  % Computer : n014.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit   : 300
% 0.11/0.33  % WCLimit    : 300
% 0.11/0.33  % DateTime   : Fri Jun 20 09:38:54 EDT 2025
% 0.11/0.33  % CPUTime    : 
% 0.60/0.76  % SZS status Unsatisfiable
% 0.60/0.76  % SZS output start Proof
% See solution above
% 0.65/0.83  % E exiting
%------------------------------------------------------------------------------