TSTP Solution File: SWV814-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SWV814-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n012.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Sep 29 15:24:36 EDT 2022

% Result   : Unsatisfiable 0.58s 0.69s
% Output   : Proof 0.67s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   64
% Syntax   : Number of formulae    :  104 (  24 unt;  29 typ;   0 def)
%            Number of atoms       :  336 ( 132 equ)
%            Maximal formula atoms :   16 (   4 avg)
%            Number of connectives :  425 ( 183   ~; 205   |;   0   &)
%                                         (  37 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Maximal term depth    :    9 (   2 avg)
%            Number of FOOLs       :   19 (  19 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   20 (  11   >;   9   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :   28 (  28 usr;  18 con; 0-3 aty)
%            Number of variables   :  318 ( 288   !;   0   ?; 318   :)

% Comments : 
%------------------------------------------------------------------------------
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_Aa_type,type,
    v_Aa: $i ).

tff(hAPP_type,type,
    hAPP: ( $i * $i ) > $i ).

tff(v_Ka_type,type,
    v_Ka: $i ).

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

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

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

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

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

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

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

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(v_NA_type,type,
    v_NA: $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(v_S_type,type,
    v_S: $i ).

tff(v_X_type,type,
    v_X: $i ).

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

tff(c_NS__Shared__Mirabelle_Ons__shared_type,type,
    c_NS__Shared__Mirabelle_Ons__shared: $i ).

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

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

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

tff(1,plain,
    ^ [V_nat_H: $i,V_agent: $i] :
      refl(
        ( ( c_Message_Omsg_ONonce(V_nat_H) != c_Message_Omsg_OAgent(V_agent) )
      <=> ( c_Message_Omsg_ONonce(V_nat_H) != c_Message_Omsg_OAgent(V_agent) ) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [V_nat_H: $i,V_agent: $i] : ( c_Message_Omsg_ONonce(V_nat_H) != c_Message_Omsg_OAgent(V_agent) )
  <=> ! [V_nat_H: $i,V_agent: $i] : ( c_Message_Omsg_ONonce(V_nat_H) != c_Message_Omsg_OAgent(V_agent) ) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ( ! [V_nat_H: $i,V_agent: $i] : ( c_Message_Omsg_ONonce(V_nat_H) != c_Message_Omsg_OAgent(V_agent) )
  <=> ! [V_nat_H: $i,V_agent: $i] : ( c_Message_Omsg_ONonce(V_nat_H) != c_Message_Omsg_OAgent(V_agent) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,axiom,
    ! [V_nat_H: $i,V_agent: $i] : ( c_Message_Omsg_ONonce(V_nat_H) != c_Message_Omsg_OAgent(V_agent) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I11_J_0) ).

tff(5,plain,
    ! [V_nat_H: $i,V_agent: $i] : ( c_Message_Omsg_ONonce(V_nat_H) != c_Message_Omsg_OAgent(V_agent) ),
    inference(modus_ponens,[status(thm)],[4,3]) ).

tff(6,plain,
    ! [V_nat_H: $i,V_agent: $i] : ( c_Message_Omsg_ONonce(V_nat_H) != c_Message_Omsg_OAgent(V_agent) ),
    inference(skolemize,[status(sab)],[5]) ).

tff(7,plain,
    ! [V_nat_H: $i,V_agent: $i] : ( c_Message_Omsg_ONonce(V_nat_H) != c_Message_Omsg_OAgent(V_agent) ),
    inference(modus_ponens,[status(thm)],[6,2]) ).

tff(8,plain,
    ( ~ ! [V_nat_H: $i,V_agent: $i] : ( c_Message_Omsg_ONonce(V_nat_H) != c_Message_Omsg_OAgent(V_agent) )
    | ( c_Message_Omsg_ONonce(v_NB) != c_Message_Omsg_OAgent(v_Aa) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(9,plain,
    c_Message_Omsg_ONonce(v_NB) != c_Message_Omsg_OAgent(v_Aa),
    inference(unit_resolution,[status(thm)],[8,7]) ).

tff(10,plain,
    ^ [V_msg1_H: $i,V_msg2: $i,V_msg2_H: $i,V_msg1: $i] :
      refl(
        ( ( ( c_Message_Omsg_OMPair(V_msg1,V_msg2) != c_Message_Omsg_OMPair(V_msg1_H,V_msg2_H) )
          | ( V_msg2 = V_msg2_H ) )
      <=> ( ( c_Message_Omsg_OMPair(V_msg1,V_msg2) != c_Message_Omsg_OMPair(V_msg1_H,V_msg2_H) )
          | ( V_msg2 = V_msg2_H ) ) )),
    inference(bind,[status(th)],]) ).

tff(11,plain,
    ( ! [V_msg1_H: $i,V_msg2: $i,V_msg2_H: $i,V_msg1: $i] :
        ( ( c_Message_Omsg_OMPair(V_msg1,V_msg2) != c_Message_Omsg_OMPair(V_msg1_H,V_msg2_H) )
        | ( V_msg2 = V_msg2_H ) )
  <=> ! [V_msg1_H: $i,V_msg2: $i,V_msg2_H: $i,V_msg1: $i] :
        ( ( c_Message_Omsg_OMPair(V_msg1,V_msg2) != c_Message_Omsg_OMPair(V_msg1_H,V_msg2_H) )
        | ( V_msg2 = V_msg2_H ) ) ),
    inference(quant_intro,[status(thm)],[10]) ).

tff(12,plain,
    ( ! [V_msg1_H: $i,V_msg2: $i,V_msg2_H: $i,V_msg1: $i] :
        ( ( c_Message_Omsg_OMPair(V_msg1,V_msg2) != c_Message_Omsg_OMPair(V_msg1_H,V_msg2_H) )
        | ( V_msg2 = V_msg2_H ) )
  <=> ! [V_msg1_H: $i,V_msg2: $i,V_msg2_H: $i,V_msg1: $i] :
        ( ( c_Message_Omsg_OMPair(V_msg1,V_msg2) != c_Message_Omsg_OMPair(V_msg1_H,V_msg2_H) )
        | ( V_msg2 = V_msg2_H ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(13,axiom,
    ! [V_msg1_H: $i,V_msg2: $i,V_msg2_H: $i,V_msg1: $i] :
      ( ( c_Message_Omsg_OMPair(V_msg1,V_msg2) != c_Message_Omsg_OMPair(V_msg1_H,V_msg2_H) )
      | ( V_msg2 = V_msg2_H ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I6_J_1) ).

tff(14,plain,
    ! [V_msg1_H: $i,V_msg2: $i,V_msg2_H: $i,V_msg1: $i] :
      ( ( c_Message_Omsg_OMPair(V_msg1,V_msg2) != c_Message_Omsg_OMPair(V_msg1_H,V_msg2_H) )
      | ( V_msg2 = V_msg2_H ) ),
    inference(modus_ponens,[status(thm)],[13,12]) ).

tff(15,plain,
    ! [V_msg1_H: $i,V_msg2: $i,V_msg2_H: $i,V_msg1: $i] :
      ( ( c_Message_Omsg_OMPair(V_msg1,V_msg2) != c_Message_Omsg_OMPair(V_msg1_H,V_msg2_H) )
      | ( V_msg2 = V_msg2_H ) ),
    inference(skolemize,[status(sab)],[14]) ).

tff(16,plain,
    ! [V_msg1_H: $i,V_msg2: $i,V_msg2_H: $i,V_msg1: $i] :
      ( ( c_Message_Omsg_OMPair(V_msg1,V_msg2) != c_Message_Omsg_OMPair(V_msg1_H,V_msg2_H) )
      | ( V_msg2 = V_msg2_H ) ),
    inference(modus_ponens,[status(thm)],[15,11]) ).

tff(17,plain,
    ( ( ~ ! [V_msg1_H: $i,V_msg2: $i,V_msg2_H: $i,V_msg1: $i] :
            ( ( c_Message_Omsg_OMPair(V_msg1,V_msg2) != c_Message_Omsg_OMPair(V_msg1_H,V_msg2_H) )
            | ( V_msg2 = V_msg2_H ) )
      | ( c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)) != c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa)) )
      | ( c_Message_Omsg_ONonce(v_NB) = c_Message_Omsg_OAgent(v_Aa) ) )
  <=> ( ~ ! [V_msg1_H: $i,V_msg2: $i,V_msg2_H: $i,V_msg1: $i] :
            ( ( c_Message_Omsg_OMPair(V_msg1,V_msg2) != c_Message_Omsg_OMPair(V_msg1_H,V_msg2_H) )
            | ( V_msg2 = V_msg2_H ) )
      | ( c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)) != c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa)) )
      | ( c_Message_Omsg_ONonce(v_NB) = c_Message_Omsg_OAgent(v_Aa) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(18,plain,
    ( ~ ! [V_msg1_H: $i,V_msg2: $i,V_msg2_H: $i,V_msg1: $i] :
          ( ( c_Message_Omsg_OMPair(V_msg1,V_msg2) != c_Message_Omsg_OMPair(V_msg1_H,V_msg2_H) )
          | ( V_msg2 = V_msg2_H ) )
    | ( c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)) != c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa)) )
    | ( c_Message_Omsg_ONonce(v_NB) = c_Message_Omsg_OAgent(v_Aa) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(19,plain,
    ( ~ ! [V_msg1_H: $i,V_msg2: $i,V_msg2_H: $i,V_msg1: $i] :
          ( ( c_Message_Omsg_OMPair(V_msg1,V_msg2) != c_Message_Omsg_OMPair(V_msg1_H,V_msg2_H) )
          | ( V_msg2 = V_msg2_H ) )
    | ( c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)) != c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa)) )
    | ( c_Message_Omsg_ONonce(v_NB) = c_Message_Omsg_OAgent(v_Aa) ) ),
    inference(modus_ponens,[status(thm)],[18,17]) ).

tff(20,plain,
    c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)) != c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa)),
    inference(unit_resolution,[status(thm)],[19,16,9]) ).

tff(21,plain,
    ( c_in(c_Event_Oevent_OSays(v_S,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))))),c_List_Oset(v_evs3,tc_Event_Oevent),tc_Event_Oevent)
  <=> c_in(c_Event_Oevent_OSays(v_S,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))))))),c_List_Oset(v_evs3,tc_Event_Oevent),tc_Event_Oevent) ),
    inference(rewrite,[status(thm)],]) ).

tff(22,plain,
    ( c_in(c_Event_Oevent_OSays(v_S,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))))),c_List_Oset(v_evs3,tc_Event_Oevent),tc_Event_Oevent)
  <=> c_in(c_Event_Oevent_OSays(v_S,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))))),c_List_Oset(v_evs3,tc_Event_Oevent),tc_Event_Oevent) ),
    inference(rewrite,[status(thm)],]) ).

tff(23,axiom,
    c_in(c_Event_Oevent_OSays(v_S,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))))),c_List_Oset(v_evs3,tc_Event_Oevent),tc_Event_Oevent),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).

tff(24,plain,
    c_in(c_Event_Oevent_OSays(v_S,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))))),c_List_Oset(v_evs3,tc_Event_Oevent),tc_Event_Oevent),
    inference(modus_ponens,[status(thm)],[23,22]) ).

tff(25,plain,
    c_in(c_Event_Oevent_OSays(v_S,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))))))),c_List_Oset(v_evs3,tc_Event_Oevent),tc_Event_Oevent),
    inference(modus_ponens,[status(thm)],[24,21]) ).

tff(26,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_Oparts(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_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ) )),
    inference(bind,[status(th)],]) ).

tff(27,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_Oparts(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_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ) ),
    inference(quant_intro,[status(thm)],[26]) ).

tff(28,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_Oparts(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_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(29,plain,
    ^ [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
      rewrite(
        ( ( c_in(V_X,c_Message_Oparts(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(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_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ) )),
    inference(bind,[status(th)],]) ).

tff(30,plain,
    ( ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
        ( c_in(V_X,c_Message_Oparts(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) )
  <=> ! [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_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ) ),
    inference(quant_intro,[status(thm)],[29]) ).

tff(31,axiom,
    ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
      ( c_in(V_X,c_Message_Oparts(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) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Says__imp__parts__knows__Spy_0) ).

tff(32,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_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ),
    inference(modus_ponens,[status(thm)],[31,30]) ).

tff(33,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_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ),
    inference(modus_ponens,[status(thm)],[32,28]) ).

tff(34,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_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ),
    inference(skolemize,[status(sab)],[33]) ).

tff(35,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_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ),
    inference(modus_ponens,[status(thm)],[34,27]) ).

tff(36,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_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
      | ~ c_in(c_Event_Oevent_OSays(v_S,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))))))),c_List_Oset(v_evs3,tc_Event_Oevent),tc_Event_Oevent)
      | c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))))))),c_Message_Oparts(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_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
      | ~ c_in(c_Event_Oevent_OSays(v_S,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))))))),c_List_Oset(v_evs3,tc_Event_Oevent),tc_Event_Oevent)
      | c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(37,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_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
    | ~ c_in(c_Event_Oevent_OSays(v_S,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))))))),c_List_Oset(v_evs3,tc_Event_Oevent),tc_Event_Oevent)
    | c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ),
    inference(quant_inst,[status(thm)],]) ).

tff(38,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_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
    | ~ c_in(c_Event_Oevent_OSays(v_S,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))))))),c_List_Oset(v_evs3,tc_Event_Oevent),tc_Event_Oevent)
    | c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ),
    inference(modus_ponens,[status(thm)],[37,36]) ).

tff(39,plain,
    c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg),
    inference(unit_resolution,[status(thm)],[38,35,25]) ).

tff(40,plain,
    ( c_in(v_evs3,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
  <=> c_in(v_evs3,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)) ),
    inference(rewrite,[status(thm)],]) ).

tff(41,axiom,
    c_in(v_evs3,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

tff(42,plain,
    c_in(v_evs3,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)),
    inference(modus_ponens,[status(thm)],[41,40]) ).

tff(43,plain,
    ( ~ c_in(v_A,c_Event_Obad,tc_Message_Oagent)
  <=> ~ c_in(v_Aa,c_Event_Obad,tc_Message_Oagent) ),
    inference(rewrite,[status(thm)],]) ).

tff(44,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(45,axiom,
    ~ c_in(v_A,c_Event_Obad,tc_Message_Oagent),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

tff(46,plain,
    ~ c_in(v_A,c_Event_Obad,tc_Message_Oagent),
    inference(modus_ponens,[status(thm)],[45,44]) ).

tff(47,plain,
    ~ c_in(v_Aa,c_Event_Obad,tc_Message_Oagent),
    inference(modus_ponens,[status(thm)],[46,43]) ).

tff(48,plain,
    ^ [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
      refl(
        ( ( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
          | ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),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_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) )
      <=> ( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
          | ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),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_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) ) )),
    inference(bind,[status(th)],]) ).

tff(49,plain,
    ( ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
        ( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
        | ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),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_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) )
  <=> ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
        ( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
        | ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),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_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) ) ),
    inference(quant_intro,[status(thm)],[48]) ).

tff(50,plain,
    ( ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
        ( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
        | ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),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_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) )
  <=> ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
        ( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
        | ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),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_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(51,plain,
    ^ [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              rewrite(
                ( ( ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) )
                  | ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)) )
              <=> ( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
                  | ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) ) )),
              ( ( ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) )
                | ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
                | c_in(V_A,c_Event_Obad,tc_Message_Oagent) )
            <=> ( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
                | ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) )
                | c_in(V_A,c_Event_Obad,tc_Message_Oagent) ) )),
            rewrite(
              ( ( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
                | ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) )
                | c_in(V_A,c_Event_Obad,tc_Message_Oagent) )
            <=> ( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
                | c_in(V_A,c_Event_Obad,tc_Message_Oagent)
                | ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) ) )),
            ( ( ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) )
              | ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
              | c_in(V_A,c_Event_Obad,tc_Message_Oagent) )
          <=> ( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
              | c_in(V_A,c_Event_Obad,tc_Message_Oagent)
              | ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) ) )),
          ( ( ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) )
            | ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
            | c_in(V_A,c_Event_Obad,tc_Message_Oagent)
            | ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
        <=> ( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
            | c_in(V_A,c_Event_Obad,tc_Message_Oagent)
            | ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) )
            | ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ) )),
        rewrite(
          ( ( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
            | c_in(V_A,c_Event_Obad,tc_Message_Oagent)
            | ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) )
            | ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
        <=> ( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
            | ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),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_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) ) )),
        ( ( ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) )
          | ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
          | c_in(V_A,c_Event_Obad,tc_Message_Oagent)
          | ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
      <=> ( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
          | ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),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_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) ) )),
    inference(bind,[status(th)],]) ).

tff(52,plain,
    ( ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
        ( ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) )
        | ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
        | c_in(V_A,c_Event_Obad,tc_Message_Oagent)
        | ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
  <=> ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
        ( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
        | ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),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_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) ) ),
    inference(quant_intro,[status(thm)],[51]) ).

tff(53,axiom,
    ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
      ( ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) )
      | ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
      | c_in(V_A,c_Event_Obad,tc_Message_Oagent)
      | ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cert__A__form_1) ).

tff(54,plain,
    ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
      ( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
      | ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),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_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) ),
    inference(modus_ponens,[status(thm)],[53,52]) ).

tff(55,plain,
    ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
      ( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
      | ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),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_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) ),
    inference(modus_ponens,[status(thm)],[54,50]) ).

tff(56,plain,
    ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
      ( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
      | ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),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_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) ),
    inference(skolemize,[status(sab)],[55]) ).

tff(57,plain,
    ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
      ( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
      | ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),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_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) ),
    inference(modus_ponens,[status(thm)],[56,49]) ).

tff(58,plain,
    ( ( ~ ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
            ( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
            | ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),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_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) )
      | c_in(v_Aa,c_Event_Obad,tc_Message_Oagent)
      | ~ c_in(v_evs3,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
      | ( c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))) = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa))) )
      | ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) )
  <=> ( ~ ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
            ( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
            | ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),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_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) )
      | c_in(v_Aa,c_Event_Obad,tc_Message_Oagent)
      | ~ c_in(v_evs3,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
      | ( c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))) = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa))) )
      | ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(59,plain,
    ( ( ~ c_in(v_evs3,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
      | ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
      | c_in(v_Aa,c_Event_Obad,tc_Message_Oagent)
      | ( c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))) = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa))) ) )
  <=> ( c_in(v_Aa,c_Event_Obad,tc_Message_Oagent)
      | ~ c_in(v_evs3,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
      | ( c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))) = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa))) )
      | ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(60,plain,
    ( ( ~ ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
            ( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
            | ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),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_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) )
      | ~ c_in(v_evs3,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
      | ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
      | c_in(v_Aa,c_Event_Obad,tc_Message_Oagent)
      | ( c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))) = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa))) ) )
  <=> ( ~ ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
            ( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
            | ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),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_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) )
      | c_in(v_Aa,c_Event_Obad,tc_Message_Oagent)
      | ~ c_in(v_evs3,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
      | ( c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))) = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa))) )
      | ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ) ),
    inference(monotonicity,[status(thm)],[59]) ).

tff(61,plain,
    ( ( ~ ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
            ( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
            | ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),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_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) )
      | ~ c_in(v_evs3,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
      | ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
      | c_in(v_Aa,c_Event_Obad,tc_Message_Oagent)
      | ( c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))) = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa))) ) )
  <=> ( ~ ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
            ( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
            | ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),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_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) )
      | c_in(v_Aa,c_Event_Obad,tc_Message_Oagent)
      | ~ c_in(v_evs3,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
      | ( c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))) = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa))) )
      | ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ) ),
    inference(transitivity,[status(thm)],[60,58]) ).

tff(62,plain,
    ( ~ ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
          ( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
          | ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),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_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) )
    | ~ c_in(v_evs3,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
    | ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
    | c_in(v_Aa,c_Event_Obad,tc_Message_Oagent)
    | ( c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))) = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(63,plain,
    ( ~ ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
          ( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
          | ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),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_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) )
    | c_in(v_Aa,c_Event_Obad,tc_Message_Oagent)
    | ~ c_in(v_evs3,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
    | ( c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))) = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa))) )
    | ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ),
    inference(modus_ponens,[status(thm)],[62,61]) ).

tff(64,plain,
    c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))) = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa))),
    inference(unit_resolution,[status(thm)],[63,57,47,42,39]) ).

tff(65,plain,
    ^ [V_nat_H: $i,V_nat: $i,V_msg_H: $i,V_msg: $i] :
      refl(
        ( ( ( c_Message_Omsg_OCrypt(V_nat,V_msg) != c_Message_Omsg_OCrypt(V_nat_H,V_msg_H) )
          | ( V_msg = V_msg_H ) )
      <=> ( ( c_Message_Omsg_OCrypt(V_nat,V_msg) != c_Message_Omsg_OCrypt(V_nat_H,V_msg_H) )
          | ( V_msg = V_msg_H ) ) )),
    inference(bind,[status(th)],]) ).

tff(66,plain,
    ( ! [V_nat_H: $i,V_nat: $i,V_msg_H: $i,V_msg: $i] :
        ( ( c_Message_Omsg_OCrypt(V_nat,V_msg) != c_Message_Omsg_OCrypt(V_nat_H,V_msg_H) )
        | ( V_msg = V_msg_H ) )
  <=> ! [V_nat_H: $i,V_nat: $i,V_msg_H: $i,V_msg: $i] :
        ( ( c_Message_Omsg_OCrypt(V_nat,V_msg) != c_Message_Omsg_OCrypt(V_nat_H,V_msg_H) )
        | ( V_msg = V_msg_H ) ) ),
    inference(quant_intro,[status(thm)],[65]) ).

tff(67,plain,
    ( ! [V_nat_H: $i,V_nat: $i,V_msg_H: $i,V_msg: $i] :
        ( ( c_Message_Omsg_OCrypt(V_nat,V_msg) != c_Message_Omsg_OCrypt(V_nat_H,V_msg_H) )
        | ( V_msg = V_msg_H ) )
  <=> ! [V_nat_H: $i,V_nat: $i,V_msg_H: $i,V_msg: $i] :
        ( ( c_Message_Omsg_OCrypt(V_nat,V_msg) != c_Message_Omsg_OCrypt(V_nat_H,V_msg_H) )
        | ( V_msg = V_msg_H ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(68,axiom,
    ! [V_nat_H: $i,V_nat: $i,V_msg_H: $i,V_msg: $i] :
      ( ( c_Message_Omsg_OCrypt(V_nat,V_msg) != c_Message_Omsg_OCrypt(V_nat_H,V_msg_H) )
      | ( V_msg = V_msg_H ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I7_J_1) ).

tff(69,plain,
    ! [V_nat_H: $i,V_nat: $i,V_msg_H: $i,V_msg: $i] :
      ( ( c_Message_Omsg_OCrypt(V_nat,V_msg) != c_Message_Omsg_OCrypt(V_nat_H,V_msg_H) )
      | ( V_msg = V_msg_H ) ),
    inference(modus_ponens,[status(thm)],[68,67]) ).

tff(70,plain,
    ! [V_nat_H: $i,V_nat: $i,V_msg_H: $i,V_msg: $i] :
      ( ( c_Message_Omsg_OCrypt(V_nat,V_msg) != c_Message_Omsg_OCrypt(V_nat_H,V_msg_H) )
      | ( V_msg = V_msg_H ) ),
    inference(skolemize,[status(sab)],[69]) ).

tff(71,plain,
    ! [V_nat_H: $i,V_nat: $i,V_msg_H: $i,V_msg: $i] :
      ( ( c_Message_Omsg_OCrypt(V_nat,V_msg) != c_Message_Omsg_OCrypt(V_nat_H,V_msg_H) )
      | ( V_msg = V_msg_H ) ),
    inference(modus_ponens,[status(thm)],[70,66]) ).

tff(72,plain,
    ( ( ~ ! [V_nat_H: $i,V_nat: $i,V_msg_H: $i,V_msg: $i] :
            ( ( c_Message_Omsg_OCrypt(V_nat,V_msg) != c_Message_Omsg_OCrypt(V_nat_H,V_msg_H) )
            | ( V_msg = V_msg_H ) )
      | ( c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))) != c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa))) )
      | ( c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)) = c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa)) ) )
  <=> ( ~ ! [V_nat_H: $i,V_nat: $i,V_msg_H: $i,V_msg: $i] :
            ( ( c_Message_Omsg_OCrypt(V_nat,V_msg) != c_Message_Omsg_OCrypt(V_nat_H,V_msg_H) )
            | ( V_msg = V_msg_H ) )
      | ( c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))) != c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa))) )
      | ( c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)) = c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa)) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(73,plain,
    ( ~ ! [V_nat_H: $i,V_nat: $i,V_msg_H: $i,V_msg: $i] :
          ( ( c_Message_Omsg_OCrypt(V_nat,V_msg) != c_Message_Omsg_OCrypt(V_nat_H,V_msg_H) )
          | ( V_msg = V_msg_H ) )
    | ( c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))) != c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa))) )
    | ( c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)) = c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(74,plain,
    ( ~ ! [V_nat_H: $i,V_nat: $i,V_msg_H: $i,V_msg: $i] :
          ( ( c_Message_Omsg_OCrypt(V_nat,V_msg) != c_Message_Omsg_OCrypt(V_nat_H,V_msg_H) )
          | ( V_msg = V_msg_H ) )
    | ( c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))) != c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa))) )
    | ( c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)) = c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa)) ) ),
    inference(modus_ponens,[status(thm)],[73,72]) ).

tff(75,plain,
    $false,
    inference(unit_resolution,[status(thm)],[74,71,64,20]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : SWV814-1 : TPTP v8.1.0. Released v4.1.0.
% 0.12/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35  % Computer : n012.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Sun Sep  4 08:12:48 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.14/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35  Usage: tptp [options] [-file:]file
% 0.14/0.35    -h, -?       prints this message.
% 0.14/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.14/0.35    -m, -model   generate model.
% 0.14/0.35    -p, -proof   generate proof.
% 0.14/0.35    -c, -core    generate unsat core of named formulas.
% 0.14/0.35    -st, -statistics display statistics.
% 0.14/0.35    -t:timeout   set timeout (in second).
% 0.14/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.14/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35    -<param>:<value> configuration parameter and value.
% 0.14/0.35    -o:<output-file> file to place output in.
% 0.58/0.69  % SZS status Unsatisfiable
% 0.58/0.69  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------