TSTP Solution File: SWV296-2 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SWV296-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n027.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  : 600s
% DateTime : Wed Jul 20 20:11:40 EDT 2022

% Result   : Unsatisfiable 0.44s 0.83s
% Output   : CNFRefutation 0.67s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   59
% Syntax   : Number of formulae    :  232 (  98 unt;  34 typ;   0 def)
%            Number of atoms       : 1375 ( 673 equ;   0 cnn)
%            Maximal formula atoms :    7 (   6 avg)
%            Number of connectives : 4080 ( 296   ~; 471   |;   0   &;3313   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   27 (  27   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   37 (  34 usr;  20 con; 0-3 aty)
%            Number of variables   :  448 (   0   ^ 448   !;   0   ?; 448   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_c_Event_Obad,type,
    c_Event_Obad: $i ).

thf(tp_c_Event_Oevent_OGets,type,
    c_Event_Oevent_OGets: $i > $i > $i ).

thf(tp_c_Event_Oevent_OSays,type,
    c_Event_Oevent_OSays: $i > $i > $i > $i ).

thf(tp_c_Event_Oknows,type,
    c_Event_Oknows: $i > $i > $i ).

thf(tp_c_Event_Oused,type,
    c_Event_Oused: $i > $i ).

thf(tp_c_List_Oset,type,
    c_List_Oset: $i > $i > $i ).

thf(tp_c_Message_Oagent_OServer,type,
    c_Message_Oagent_OServer: $i ).

thf(tp_c_Message_Oagent_OSpy,type,
    c_Message_Oagent_OSpy: $i ).

thf(tp_c_Message_Oanalz,type,
    c_Message_Oanalz: $i > $i ).

thf(tp_c_Message_Omsg_OAgent,type,
    c_Message_Omsg_OAgent: $i > $i ).

thf(tp_c_Message_Omsg_OCrypt,type,
    c_Message_Omsg_OCrypt: $i > $i > $i ).

thf(tp_c_Message_Omsg_OKey,type,
    c_Message_Omsg_OKey: $i > $i ).

thf(tp_c_Message_Omsg_OMPair,type,
    c_Message_Omsg_OMPair: $i > $i > $i ).

thf(tp_c_Message_Omsg_ONonce,type,
    c_Message_Omsg_ONonce: $i > $i ).

thf(tp_c_Message_Oparts,type,
    c_Message_Oparts: $i > $i ).

thf(tp_c_OtwayRees_Ootway,type,
    c_OtwayRees_Ootway: $i ).

thf(tp_c_Public_OshrK,type,
    c_Public_OshrK: $i > $i ).

thf(tp_c_in,type,
    c_in: $i > $i > $i > $o ).

thf(tp_tc_Event_Oevent,type,
    tc_Event_Oevent: $i ).

thf(tp_tc_List_Olist,type,
    tc_List_Olist: $i > $i ).

thf(tp_tc_Message_Oagent,type,
    tc_Message_Oagent: $i ).

thf(tp_tc_Message_Omsg,type,
    tc_Message_Omsg: $i ).

thf(tp_v_A,type,
    v_A: $i ).

thf(tp_v_Aa,type,
    v_Aa: $i ).

thf(tp_v_B,type,
    v_B: $i ).

thf(tp_v_Ba,type,
    v_Ba: $i ).

thf(tp_v_K,type,
    v_K: $i ).

thf(tp_v_KAB,type,
    v_KAB: $i ).

thf(tp_v_NA,type,
    v_NA: $i ).

thf(tp_v_NAa,type,
    v_NAa: $i ).

thf(tp_v_NB,type,
    v_NB: $i ).

thf(tp_v_evs3,type,
    v_evs3: $i ).

thf(tp_v_sko__usf,type,
    v_sko__usf: $i > $i > $i > $i ).

thf(tp_v_x,type,
    v_x: $i ).

thf(1,axiom,
    ! [V_X: $i,V_Y: $i,V_H: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ V_X @ V_Y ) @ ( c_Event_Oused @ V_H ) @ tc_Message_Omsg )
      | ( c_in @ V_Y @ ( c_Event_Oused @ V_H ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OMPair__used_0) ).

thf(2,axiom,
    ! [V_evs: $i,V_A: $i,V_NA: $i,V_C: $i,V_B: $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) ).

thf(3,axiom,
    ! [V_evs: $i,V_A: $i,V_NA_H: $i,V_NA: $i,V_A_H: $i,V_B: $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_H @ ( c_Message_Omsg_OMPair @ V_NA @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ V_A_H ) @ ( c_Message_Omsg_OAgent @ V_A ) ) ) ) ) @ ( 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 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OtwayRees_Ono__nonce__OR1__OR2__dest_0) ).

thf(4,axiom,
    ! [V_evs: $i,V_B: $i,V_X: $i] :
      ( ~ ( c_in @ V_evs @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
      | ~ ( c_in @ ( c_Event_Oevent_OGets @ V_B @ V_X ) @ ( c_List_Oset @ V_evs @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ( c_in @ ( c_Event_Oevent_OSays @ ( v_sko__usf @ V_B @ V_X @ V_evs ) @ V_B @ V_X ) @ ( c_List_Oset @ V_evs @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OtwayRees_OGets__imp__Says__dest_0) ).

thf(5,axiom,
    ! [V_K: $i,V_X: $i,V_H: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ V_K @ V_X ) @ ( 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/theBenchmark.p',cls_Message_Oparts_OBody__dest_0) ).

thf(6,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/theBenchmark.p',cls_Message_Oanalz__into__parts__dest_0) ).

thf(7,axiom,
    ! [V_X: $i,V_Y: $i,V_H: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ V_X @ V_Y ) @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg )
      | ( c_in @ V_X @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__analz_1) ).

thf(8,axiom,
    ! [V_X: $i,V_Y: $i,V_H: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ V_X @ V_Y ) @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg )
      | ( c_in @ V_Y @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__analz_0) ).

thf(9,axiom,
    ! [V_c: $i,V_evs: $i] :
      ( ~ ( c_in @ V_c @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ V_evs ) ) @ tc_Message_Omsg )
      | ( c_in @ V_c @ ( c_Event_Oused @ V_evs ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oc_A_58_Aparts_A_Iknows_ASpy_Aevs1_J_A_61_61_62_Ac_A_58_Aused_Aevs1_0) ).

thf(10,axiom,
    ! [V_A: $i,V_B: $i,V_X: $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/theBenchmark.p',cls_Event_OSays__imp__analz__Spy__dest_0) ).

thf(11,conjecture,
    $false,
    file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(12,negated_conjecture,
    $false = $false,
    inference(negate_conjecture,[status(cth)],[11]) ).

thf(13,negated_conjecture,
    ( ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs3 ) ) @ tc_Message_Omsg )
    | ( v_NA
      = ( c_Message_Omsg_ONonce @ v_NB ) )
    | ( v_A = v_Aa ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_9) ).

thf(14,negated_conjecture,
    ( ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs3 ) ) @ tc_Message_Omsg )
    | ( v_A = v_Ba )
    | ( v_A = v_Aa ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_7) ).

thf(15,negated_conjecture,
    ! [V_BP: $i,V_U: $i] :
      ( ( V_BP
       != ( c_Message_Omsg_ONonce @ v_NB ) )
      | ( v_K != v_KAB )
      | ( v_A != v_Aa )
      | ( v_NA
       != ( c_Message_Omsg_ONonce @ v_NAa ) )
      | ( v_NA
        = ( c_Message_Omsg_ONonce @ v_NB ) )
      | ( V_U
       != ( c_Message_Omsg_ONonce @ v_NB ) )
      | ( v_B != v_Ba ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_69) ).

thf(16,negated_conjecture,
    ! [V_BO: $i,V_U: $i] :
      ( ( V_BO
       != ( c_Message_Omsg_ONonce @ v_NB ) )
      | ( v_K != v_KAB )
      | ( v_A != v_Aa )
      | ( v_NA
       != ( c_Message_Omsg_ONonce @ v_NAa ) )
      | ( v_A = v_Ba )
      | ( V_U
       != ( c_Message_Omsg_ONonce @ v_NB ) )
      | ( v_B != v_Ba ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_68) ).

thf(17,negated_conjecture,
    ! [V_BK: $i] :
      ( ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ v_B @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_B ) @ ( c_Message_Omsg_OMPair @ V_BK @ ( c_Message_Omsg_OKey @ v_K ) ) ) ) ) ) @ ( c_List_Oset @ v_evs3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ( v_K = v_KAB ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).

thf(18,negated_conjecture,
    ( ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs3 ) ) @ tc_Message_Omsg )
    | ( v_K = v_KAB ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).

thf(19,negated_conjecture,
    c_in @ ( c_Event_Oevent_OSays @ v_A @ v_B @ ( c_Message_Omsg_OMPair @ 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 @ 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_4) ).

thf(20,negated_conjecture,
    ( ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ v_B @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_B ) @ ( c_Message_Omsg_OMPair @ v_x @ ( c_Message_Omsg_OKey @ v_K ) ) ) ) ) ) @ ( c_List_Oset @ v_evs3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
    | ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs3 ) ) @ tc_Message_Omsg )
    | ~ ( c_in @ ( c_Event_Oevent_OSays @ v_A @ v_B @ ( c_Message_Omsg_OMPair @ 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 @ 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_37) ).

thf(21,negated_conjecture,
    c_in @ ( c_Event_Oevent_OGets @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NAa ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_Aa ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_Ba ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_Aa ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NAa ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_Aa ) @ ( c_Message_Omsg_OAgent @ v_Ba ) ) ) ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_Ba ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NAa ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NB ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_Aa ) @ ( 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_3) ).

thf(22,negated_conjecture,
    ~ ( c_in @ ( c_Message_Omsg_OKey @ v_KAB ) @ ( c_Event_Oused @ v_evs3 ) @ tc_Message_Omsg ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).

thf(23,negated_conjecture,
    ( ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs3 ) ) @ tc_Message_Omsg )
    | ( v_NA
      = ( c_Message_Omsg_ONonce @ v_NB ) )
    | ( v_NA
      = ( c_Message_Omsg_ONonce @ v_NAa ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_17) ).

thf(24,negated_conjecture,
    ( ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs3 ) ) @ tc_Message_Omsg )
    | ( v_A = v_Ba )
    | ( v_NA
      = ( c_Message_Omsg_ONonce @ v_NAa ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_15) ).

thf(25,negated_conjecture,
    c_in @ v_evs3 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(26,negated_conjecture,
    ~ ( c_in @ v_A @ c_Event_Obad @ tc_Message_Oagent ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(27,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[12]) ).

thf(28,plain,
    ( ( ! [V_X: $i,V_Y: $i,V_H: $i] :
          ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ V_X @ V_Y ) @ ( c_Event_Oused @ V_H ) @ tc_Message_Omsg )
          | ( c_in @ V_Y @ ( c_Event_Oused @ V_H ) @ tc_Message_Omsg ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(29,plain,
    ( ( ! [V_evs: $i,V_A: $i,V_NA: $i,V_C: $i,V_B: $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 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(30,plain,
    ( ( ! [V_evs: $i,V_A: $i,V_NA_H: $i,V_NA: $i,V_A_H: $i,V_B: $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_H @ ( c_Message_Omsg_OMPair @ V_NA @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ V_A_H ) @ ( c_Message_Omsg_OAgent @ V_A ) ) ) ) ) @ ( 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 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(31,plain,
    ( ( ! [V_evs: $i,V_B: $i,V_X: $i] :
          ( ~ ( c_in @ V_evs @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
          | ~ ( c_in @ ( c_Event_Oevent_OGets @ V_B @ V_X ) @ ( c_List_Oset @ V_evs @ tc_Event_Oevent ) @ tc_Event_Oevent )
          | ( c_in @ ( c_Event_Oevent_OSays @ ( v_sko__usf @ V_B @ V_X @ V_evs ) @ V_B @ V_X ) @ ( c_List_Oset @ V_evs @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(32,plain,
    ( ( ! [V_K: $i,V_X: $i,V_H: $i] :
          ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ V_K @ V_X ) @ ( c_Message_Oparts @ V_H ) @ tc_Message_Omsg )
          | ( c_in @ V_X @ ( c_Message_Oparts @ V_H ) @ tc_Message_Omsg ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(33,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 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(34,plain,
    ( ( ! [V_X: $i,V_Y: $i,V_H: $i] :
          ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ V_X @ V_Y ) @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg )
          | ( c_in @ V_X @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(35,plain,
    ( ( ! [V_X: $i,V_Y: $i,V_H: $i] :
          ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ V_X @ V_Y ) @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg )
          | ( c_in @ V_Y @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(36,plain,
    ( ( ! [V_c: $i,V_evs: $i] :
          ( ~ ( c_in @ V_c @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ V_evs ) ) @ tc_Message_Omsg )
          | ( c_in @ V_c @ ( c_Event_Oused @ V_evs ) @ tc_Message_Omsg ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(37,plain,
    ( ( ! [V_A: $i,V_B: $i,V_X: $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 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(38,plain,
    ( ( ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs3 ) ) @ tc_Message_Omsg )
      | ( v_NA
        = ( c_Message_Omsg_ONonce @ v_NB ) )
      | ( v_A = v_Aa ) )
    = $true ),
    inference(unfold_def,[status(thm)],[13]) ).

thf(39,plain,
    ( ( ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs3 ) ) @ tc_Message_Omsg )
      | ( v_A = v_Ba )
      | ( v_A = v_Aa ) )
    = $true ),
    inference(unfold_def,[status(thm)],[14]) ).

thf(40,plain,
    ( ( ! [V_BP: $i,V_U: $i] :
          ( ( V_BP
           != ( c_Message_Omsg_ONonce @ v_NB ) )
          | ( v_K != v_KAB )
          | ( v_A != v_Aa )
          | ( v_NA
           != ( c_Message_Omsg_ONonce @ v_NAa ) )
          | ( v_NA
            = ( c_Message_Omsg_ONonce @ v_NB ) )
          | ( V_U
           != ( c_Message_Omsg_ONonce @ v_NB ) )
          | ( v_B != v_Ba ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[15]) ).

thf(41,plain,
    ( ( ! [V_BO: $i,V_U: $i] :
          ( ( V_BO
           != ( c_Message_Omsg_ONonce @ v_NB ) )
          | ( v_K != v_KAB )
          | ( v_A != v_Aa )
          | ( v_NA
           != ( c_Message_Omsg_ONonce @ v_NAa ) )
          | ( v_A = v_Ba )
          | ( V_U
           != ( c_Message_Omsg_ONonce @ v_NB ) )
          | ( v_B != v_Ba ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[16]) ).

thf(42,plain,
    ( ( ! [V_BK: $i] :
          ( ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ v_B @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_B ) @ ( c_Message_Omsg_OMPair @ V_BK @ ( c_Message_Omsg_OKey @ v_K ) ) ) ) ) ) @ ( c_List_Oset @ v_evs3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
          | ( v_K = v_KAB ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[17]) ).

thf(43,plain,
    ( ( ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs3 ) ) @ tc_Message_Omsg )
      | ( v_K = v_KAB ) )
    = $true ),
    inference(unfold_def,[status(thm)],[18]) ).

thf(44,plain,
    ( ( c_in @ ( c_Event_Oevent_OSays @ v_A @ v_B @ ( c_Message_Omsg_OMPair @ 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 @ 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 )
    = $true ),
    inference(unfold_def,[status(thm)],[19]) ).

thf(45,plain,
    ( ( ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ v_B @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_B ) @ ( c_Message_Omsg_OMPair @ v_x @ ( c_Message_Omsg_OKey @ v_K ) ) ) ) ) ) @ ( c_List_Oset @ v_evs3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs3 ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Event_Oevent_OSays @ v_A @ v_B @ ( c_Message_Omsg_OMPair @ 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 @ 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 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[20]) ).

thf(46,plain,
    ( ( c_in @ ( c_Event_Oevent_OGets @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NAa ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_Aa ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_Ba ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_Aa ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NAa ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_Aa ) @ ( c_Message_Omsg_OAgent @ v_Ba ) ) ) ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_Ba ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NAa ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NB ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_Aa ) @ ( c_Message_Omsg_OAgent @ v_Ba ) ) ) ) ) ) ) ) ) ) @ ( c_List_Oset @ v_evs3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
    = $true ),
    inference(unfold_def,[status(thm)],[21]) ).

thf(47,plain,
    ( ( ~ ( c_in @ ( c_Message_Omsg_OKey @ v_KAB ) @ ( c_Event_Oused @ v_evs3 ) @ tc_Message_Omsg ) )
    = $true ),
    inference(unfold_def,[status(thm)],[22]) ).

thf(48,plain,
    ( ( ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs3 ) ) @ tc_Message_Omsg )
      | ( v_NA
        = ( c_Message_Omsg_ONonce @ v_NB ) )
      | ( v_NA
        = ( c_Message_Omsg_ONonce @ v_NAa ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[23]) ).

thf(49,plain,
    ( ( ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs3 ) ) @ tc_Message_Omsg )
      | ( v_A = v_Ba )
      | ( v_NA
        = ( c_Message_Omsg_ONonce @ v_NAa ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[24]) ).

thf(50,plain,
    ( ( c_in @ v_evs3 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
    = $true ),
    inference(unfold_def,[status(thm)],[25]) ).

thf(51,plain,
    ( ( ~ ( c_in @ v_A @ c_Event_Obad @ tc_Message_Oagent ) )
    = $true ),
    inference(unfold_def,[status(thm)],[26]) ).

thf(52,plain,
    ( ( ~ $false )
    = $true ),
    inference(polarity_switch,[status(thm)],[27]) ).

thf(53,plain,
    ( ( ! [V_evs: $i,V_A: $i,V_NA: $i] :
          ( ~ ( c_in @ V_evs @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
          | ! [V_C: $i] :
              ( ~ ( 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: $i] :
                  ( ~ ( 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 )
                  | ( V_B = V_C )
                  | ( c_in @ V_A @ c_Event_Obad @ tc_Message_Oagent ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[29]) ).

thf(54,plain,
    ( ( ! [V_evs: $i,V_A: $i,V_NA_H: $i,V_NA: $i] :
          ( ~ ( c_in @ V_evs @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
          | ! [V_A_H: $i] :
              ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ V_A ) @ ( c_Message_Omsg_OMPair @ V_NA_H @ ( c_Message_Omsg_OMPair @ V_NA @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ V_A_H ) @ ( c_Message_Omsg_OAgent @ V_A ) ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ V_evs ) ) @ tc_Message_Omsg )
          | ! [V_B: $i] :
              ~ ( 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 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[30]) ).

thf(55,plain,
    ( ( ! [V_evs: $i] :
          ( ~ ( c_in @ V_evs @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
          | ! [V_B: $i,V_X: $i] :
              ( ~ ( c_in @ ( c_Event_Oevent_OGets @ V_B @ V_X ) @ ( c_List_Oset @ V_evs @ tc_Event_Oevent ) @ tc_Event_Oevent )
              | ( c_in @ ( c_Event_Oevent_OSays @ ( v_sko__usf @ V_B @ V_X @ V_evs ) @ V_B @ V_X ) @ ( c_List_Oset @ V_evs @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[31]) ).

thf(56,plain,
    ( ( ! [V_BP: $i] :
          ( V_BP
         != ( c_Message_Omsg_ONonce @ v_NB ) )
      | ( v_K != v_KAB )
      | ( v_A != v_Aa )
      | ( v_NA
       != ( c_Message_Omsg_ONonce @ v_NAa ) )
      | ( v_NA
        = ( c_Message_Omsg_ONonce @ v_NB ) )
      | ! [V_U: $i] :
          ( V_U
         != ( c_Message_Omsg_ONonce @ v_NB ) )
      | ( v_B != v_Ba ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[40]) ).

thf(57,plain,
    ( ( ! [V_BO: $i] :
          ( V_BO
         != ( c_Message_Omsg_ONonce @ v_NB ) )
      | ( v_K != v_KAB )
      | ( v_A != v_Aa )
      | ( v_NA
       != ( c_Message_Omsg_ONonce @ v_NAa ) )
      | ( v_A = v_Ba )
      | ! [V_U: $i] :
          ( V_U
         != ( c_Message_Omsg_ONonce @ v_NB ) )
      | ( v_B != v_Ba ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[41]) ).

thf(58,plain,
    ( ( ! [V_BK: $i] :
          ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ v_B @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_B ) @ ( c_Message_Omsg_OMPair @ V_BK @ ( c_Message_Omsg_OKey @ v_K ) ) ) ) ) ) @ ( c_List_Oset @ v_evs3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ( v_K = v_KAB ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[42]) ).

thf(59,plain,
    ( ( ( v_K = v_KAB )
      | ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs3 ) ) @ tc_Message_Omsg ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[43]) ).

thf(60,plain,
    ( ( ~ ( c_in @ v_A @ c_Event_Obad @ tc_Message_Oagent ) )
    = $true ),
    inference(copy,[status(thm)],[51]) ).

thf(61,plain,
    ( ( c_in @ v_evs3 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
    = $true ),
    inference(copy,[status(thm)],[50]) ).

thf(62,plain,
    ( ( ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs3 ) ) @ tc_Message_Omsg )
      | ( v_A = v_Ba )
      | ( v_NA
        = ( c_Message_Omsg_ONonce @ v_NAa ) ) )
    = $true ),
    inference(copy,[status(thm)],[49]) ).

thf(63,plain,
    ( ( ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs3 ) ) @ tc_Message_Omsg )
      | ( v_NA
        = ( c_Message_Omsg_ONonce @ v_NB ) )
      | ( v_NA
        = ( c_Message_Omsg_ONonce @ v_NAa ) ) )
    = $true ),
    inference(copy,[status(thm)],[48]) ).

thf(64,plain,
    ( ( ~ ( c_in @ ( c_Message_Omsg_OKey @ v_KAB ) @ ( c_Event_Oused @ v_evs3 ) @ tc_Message_Omsg ) )
    = $true ),
    inference(copy,[status(thm)],[47]) ).

thf(65,plain,
    ( ( c_in @ ( c_Event_Oevent_OGets @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NAa ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_Aa ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_Ba ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_Aa ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NAa ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_Aa ) @ ( c_Message_Omsg_OAgent @ v_Ba ) ) ) ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_Ba ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NAa ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NB ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_Aa ) @ ( c_Message_Omsg_OAgent @ v_Ba ) ) ) ) ) ) ) ) ) ) @ ( c_List_Oset @ v_evs3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
    = $true ),
    inference(copy,[status(thm)],[46]) ).

thf(66,plain,
    ( ( ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ v_B @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_B ) @ ( c_Message_Omsg_OMPair @ v_x @ ( c_Message_Omsg_OKey @ v_K ) ) ) ) ) ) @ ( c_List_Oset @ v_evs3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs3 ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Event_Oevent_OSays @ v_A @ v_B @ ( c_Message_Omsg_OMPair @ 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 @ 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 ) )
    = $true ),
    inference(copy,[status(thm)],[45]) ).

thf(67,plain,
    ( ( c_in @ ( c_Event_Oevent_OSays @ v_A @ v_B @ ( c_Message_Omsg_OMPair @ 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 @ 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 )
    = $true ),
    inference(copy,[status(thm)],[44]) ).

thf(68,plain,
    ( ( ( v_K = v_KAB )
      | ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs3 ) ) @ tc_Message_Omsg ) )
    = $true ),
    inference(copy,[status(thm)],[59]) ).

thf(69,plain,
    ( ( ! [V_BK: $i] :
          ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ v_B @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_B ) @ ( c_Message_Omsg_OMPair @ V_BK @ ( c_Message_Omsg_OKey @ v_K ) ) ) ) ) ) @ ( c_List_Oset @ v_evs3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ( v_K = v_KAB ) )
    = $true ),
    inference(copy,[status(thm)],[58]) ).

thf(70,plain,
    ( ( ! [V_BO: $i] :
          ( V_BO
         != ( c_Message_Omsg_ONonce @ v_NB ) )
      | ( v_K != v_KAB )
      | ( v_A != v_Aa )
      | ( v_NA
       != ( c_Message_Omsg_ONonce @ v_NAa ) )
      | ( v_A = v_Ba )
      | ! [V_U: $i] :
          ( V_U
         != ( c_Message_Omsg_ONonce @ v_NB ) )
      | ( v_B != v_Ba ) )
    = $true ),
    inference(copy,[status(thm)],[57]) ).

thf(71,plain,
    ( ( ! [V_BP: $i] :
          ( V_BP
         != ( c_Message_Omsg_ONonce @ v_NB ) )
      | ( v_K != v_KAB )
      | ( v_A != v_Aa )
      | ( v_NA
       != ( c_Message_Omsg_ONonce @ v_NAa ) )
      | ( v_NA
        = ( c_Message_Omsg_ONonce @ v_NB ) )
      | ! [V_U: $i] :
          ( V_U
         != ( c_Message_Omsg_ONonce @ v_NB ) )
      | ( v_B != v_Ba ) )
    = $true ),
    inference(copy,[status(thm)],[56]) ).

thf(72,plain,
    ( ( ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs3 ) ) @ tc_Message_Omsg )
      | ( v_A = v_Ba )
      | ( v_A = v_Aa ) )
    = $true ),
    inference(copy,[status(thm)],[39]) ).

thf(73,plain,
    ( ( ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs3 ) ) @ tc_Message_Omsg )
      | ( v_NA
        = ( c_Message_Omsg_ONonce @ v_NB ) )
      | ( v_A = v_Aa ) )
    = $true ),
    inference(copy,[status(thm)],[38]) ).

thf(74,plain,
    ( ( ! [V_A: $i,V_B: $i,V_X: $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 ) ) )
    = $true ),
    inference(copy,[status(thm)],[37]) ).

thf(75,plain,
    ( ( ! [V_c: $i,V_evs: $i] :
          ( ~ ( c_in @ V_c @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ V_evs ) ) @ tc_Message_Omsg )
          | ( c_in @ V_c @ ( c_Event_Oused @ V_evs ) @ tc_Message_Omsg ) ) )
    = $true ),
    inference(copy,[status(thm)],[36]) ).

thf(76,plain,
    ( ( ! [V_X: $i,V_Y: $i,V_H: $i] :
          ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ V_X @ V_Y ) @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg )
          | ( c_in @ V_Y @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg ) ) )
    = $true ),
    inference(copy,[status(thm)],[35]) ).

thf(77,plain,
    ( ( ! [V_X: $i,V_Y: $i,V_H: $i] :
          ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ V_X @ V_Y ) @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg )
          | ( c_in @ V_X @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg ) ) )
    = $true ),
    inference(copy,[status(thm)],[34]) ).

thf(78,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 ) ) )
    = $true ),
    inference(copy,[status(thm)],[33]) ).

thf(79,plain,
    ( ( ! [V_K: $i,V_X: $i,V_H: $i] :
          ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ V_K @ V_X ) @ ( c_Message_Oparts @ V_H ) @ tc_Message_Omsg )
          | ( c_in @ V_X @ ( c_Message_Oparts @ V_H ) @ tc_Message_Omsg ) ) )
    = $true ),
    inference(copy,[status(thm)],[32]) ).

thf(80,plain,
    ( ( ! [V_evs: $i] :
          ( ~ ( c_in @ V_evs @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
          | ! [V_B: $i,V_X: $i] :
              ( ~ ( c_in @ ( c_Event_Oevent_OGets @ V_B @ V_X ) @ ( c_List_Oset @ V_evs @ tc_Event_Oevent ) @ tc_Event_Oevent )
              | ( c_in @ ( c_Event_Oevent_OSays @ ( v_sko__usf @ V_B @ V_X @ V_evs ) @ V_B @ V_X ) @ ( c_List_Oset @ V_evs @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[55]) ).

thf(81,plain,
    ( ( ! [V_evs: $i,V_A: $i,V_NA_H: $i,V_NA: $i] :
          ( ~ ( c_in @ V_evs @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
          | ! [V_A_H: $i] :
              ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ V_A ) @ ( c_Message_Omsg_OMPair @ V_NA_H @ ( c_Message_Omsg_OMPair @ V_NA @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ V_A_H ) @ ( c_Message_Omsg_OAgent @ V_A ) ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ V_evs ) ) @ tc_Message_Omsg )
          | ! [V_B: $i] :
              ~ ( 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 ) ) )
    = $true ),
    inference(copy,[status(thm)],[54]) ).

thf(82,plain,
    ( ( ! [V_evs: $i,V_A: $i,V_NA: $i] :
          ( ~ ( c_in @ V_evs @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
          | ! [V_C: $i] :
              ( ~ ( 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: $i] :
                  ( ~ ( 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 )
                  | ( V_B = V_C )
                  | ( c_in @ V_A @ c_Event_Obad @ tc_Message_Oagent ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[53]) ).

thf(83,plain,
    ( ( ! [V_X: $i,V_Y: $i,V_H: $i] :
          ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ V_X @ V_Y ) @ ( c_Event_Oused @ V_H ) @ tc_Message_Omsg )
          | ( c_in @ V_Y @ ( c_Event_Oused @ V_H ) @ tc_Message_Omsg ) ) )
    = $true ),
    inference(copy,[status(thm)],[28]) ).

thf(84,plain,
    ( ( ~ $false )
    = $true ),
    inference(copy,[status(thm)],[52]) ).

thf(85,plain,
    ( ( c_in @ v_A @ c_Event_Obad @ tc_Message_Oagent )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[60]) ).

thf(86,plain,
    ( ( ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs3 ) ) @ tc_Message_Omsg )
      = $true )
    | ( ( ( v_A = v_Ba )
        | ( v_NA
          = ( c_Message_Omsg_ONonce @ v_NAa ) ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[62]) ).

thf(87,plain,
    ( ( ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs3 ) ) @ tc_Message_Omsg )
      = $true )
    | ( ( ( v_NA
          = ( c_Message_Omsg_ONonce @ v_NB ) )
        | ( v_NA
          = ( c_Message_Omsg_ONonce @ v_NAa ) ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[63]) ).

thf(88,plain,
    ( ( c_in @ ( c_Message_Omsg_OKey @ v_KAB ) @ ( c_Event_Oused @ v_evs3 ) @ tc_Message_Omsg )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[64]) ).

thf(89,plain,
    ( ( ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ v_B @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_B ) @ ( c_Message_Omsg_OMPair @ v_x @ ( c_Message_Omsg_OKey @ v_K ) ) ) ) ) ) @ ( c_List_Oset @ v_evs3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
      = $true )
    | ( ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs3 ) ) @ tc_Message_Omsg )
        | ~ ( c_in @ ( c_Event_Oevent_OSays @ v_A @ v_B @ ( c_Message_Omsg_OMPair @ 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 @ 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 ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[66]) ).

thf(90,plain,
    ( ( ( v_K = v_KAB )
      = $true )
    | ( ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs3 ) ) @ tc_Message_Omsg )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[68]) ).

thf(91,plain,
    ( ( ( ! [V_BK: $i] :
            ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ v_B @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_B ) @ ( c_Message_Omsg_OMPair @ V_BK @ ( c_Message_Omsg_OKey @ v_K ) ) ) ) ) ) @ ( c_List_Oset @ v_evs3 @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      = $true )
    | ( ( v_K = v_KAB )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[69]) ).

thf(92,plain,
    ( ( ( ! [V_BO: $i] :
            ( V_BO
           != ( c_Message_Omsg_ONonce @ v_NB ) ) )
      = $true )
    | ( ( ( v_K != v_KAB )
        | ( v_A != v_Aa )
        | ( v_NA
         != ( c_Message_Omsg_ONonce @ v_NAa ) )
        | ( v_A = v_Ba )
        | ! [V_U: $i] :
            ( V_U
           != ( c_Message_Omsg_ONonce @ v_NB ) )
        | ( v_B != v_Ba ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[70]) ).

thf(93,plain,
    ( ( ( ! [V_BP: $i] :
            ( V_BP
           != ( c_Message_Omsg_ONonce @ v_NB ) ) )
      = $true )
    | ( ( ( v_K != v_KAB )
        | ( v_A != v_Aa )
        | ( v_NA
         != ( c_Message_Omsg_ONonce @ v_NAa ) )
        | ( v_NA
          = ( c_Message_Omsg_ONonce @ v_NB ) )
        | ! [V_U: $i] :
            ( V_U
           != ( c_Message_Omsg_ONonce @ v_NB ) )
        | ( v_B != v_Ba ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[71]) ).

thf(94,plain,
    ( ( ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs3 ) ) @ tc_Message_Omsg )
      = $true )
    | ( ( ( v_A = v_Ba )
        | ( v_A = v_Aa ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[72]) ).

thf(95,plain,
    ( ( ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs3 ) ) @ tc_Message_Omsg )
      = $true )
    | ( ( ( v_NA
          = ( c_Message_Omsg_ONonce @ v_NB ) )
        | ( v_A = v_Aa ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[73]) ).

thf(96,plain,
    ! [SV1: $i] :
      ( ( ! [SY39: $i,SY40: $i,SY41: $i] :
            ( ~ ( c_in @ ( c_Event_Oevent_OSays @ SV1 @ SY39 @ SY40 ) @ ( c_List_Oset @ SY41 @ tc_Event_Oevent ) @ tc_Event_Oevent )
            | ( c_in @ SY40 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SY41 ) ) @ tc_Message_Omsg ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[74]) ).

thf(97,plain,
    ! [SV2: $i] :
      ( ( ! [SY42: $i] :
            ( ~ ( c_in @ SV2 @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SY42 ) ) @ tc_Message_Omsg )
            | ( c_in @ SV2 @ ( c_Event_Oused @ SY42 ) @ tc_Message_Omsg ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[75]) ).

thf(98,plain,
    ! [SV3: $i] :
      ( ( ! [SY43: $i,SY44: $i] :
            ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV3 @ SY43 ) @ ( c_Message_Oanalz @ SY44 ) @ tc_Message_Omsg )
            | ( c_in @ SY43 @ ( c_Message_Oanalz @ SY44 ) @ tc_Message_Omsg ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[76]) ).

thf(99,plain,
    ! [SV4: $i] :
      ( ( ! [SY45: $i,SY46: $i] :
            ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV4 @ SY45 ) @ ( c_Message_Oanalz @ SY46 ) @ tc_Message_Omsg )
            | ( c_in @ SV4 @ ( c_Message_Oanalz @ SY46 ) @ tc_Message_Omsg ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[77]) ).

thf(100,plain,
    ! [SV5: $i] :
      ( ( ! [SY47: $i] :
            ( ~ ( c_in @ SV5 @ ( c_Message_Oanalz @ SY47 ) @ tc_Message_Omsg )
            | ( c_in @ SV5 @ ( c_Message_Oparts @ SY47 ) @ tc_Message_Omsg ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[78]) ).

thf(101,plain,
    ! [SV6: $i] :
      ( ( ! [SY48: $i,SY49: $i] :
            ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ SV6 @ SY48 ) @ ( c_Message_Oparts @ SY49 ) @ tc_Message_Omsg )
            | ( c_in @ SY48 @ ( c_Message_Oparts @ SY49 ) @ tc_Message_Omsg ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[79]) ).

thf(102,plain,
    ! [SV7: $i] :
      ( ( ~ ( c_in @ SV7 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
        | ! [SY50: $i,SY51: $i] :
            ( ~ ( c_in @ ( c_Event_Oevent_OGets @ SY50 @ SY51 ) @ ( c_List_Oset @ SV7 @ tc_Event_Oevent ) @ tc_Event_Oevent )
            | ( c_in @ ( c_Event_Oevent_OSays @ ( v_sko__usf @ SY50 @ SY51 @ SV7 ) @ SY50 @ SY51 ) @ ( c_List_Oset @ SV7 @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[80]) ).

thf(103,plain,
    ! [SV8: $i] :
      ( ( ! [SY52: $i,SY53: $i,SY54: $i] :
            ( ~ ( c_in @ SV8 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
            | ! [SY55: $i] :
                ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SY52 ) @ ( c_Message_Omsg_OMPair @ SY53 @ ( c_Message_Omsg_OMPair @ SY54 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY55 ) @ ( c_Message_Omsg_OAgent @ SY52 ) ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV8 ) ) @ tc_Message_Omsg )
            | ! [SY56: $i] :
                ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SY52 ) @ ( c_Message_Omsg_OMPair @ SY54 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY52 ) @ ( c_Message_Omsg_OAgent @ SY56 ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV8 ) ) @ tc_Message_Omsg )
            | ( c_in @ SY52 @ c_Event_Obad @ tc_Message_Oagent ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[81]) ).

thf(104,plain,
    ! [SV9: $i] :
      ( ( ! [SY57: $i,SY58: $i] :
            ( ~ ( c_in @ SV9 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
            | ! [SY59: $i] :
                ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SY57 ) @ ( c_Message_Omsg_OMPair @ SY58 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY57 ) @ ( c_Message_Omsg_OAgent @ SY59 ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV9 ) ) @ tc_Message_Omsg )
                | ! [SY60: $i] :
                    ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SY57 ) @ ( c_Message_Omsg_OMPair @ SY58 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY57 ) @ ( c_Message_Omsg_OAgent @ SY60 ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV9 ) ) @ tc_Message_Omsg )
                    | ( SY60 = SY59 )
                    | ( c_in @ SY57 @ c_Event_Obad @ tc_Message_Oagent ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[82]) ).

thf(105,plain,
    ! [SV10: $i] :
      ( ( ! [SY61: $i,SY62: $i] :
            ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV10 @ SY61 ) @ ( c_Event_Oused @ SY62 ) @ tc_Message_Omsg )
            | ( c_in @ SY61 @ ( c_Event_Oused @ SY62 ) @ tc_Message_Omsg ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[83]) ).

thf(106,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[84]) ).

thf(107,plain,
    ( ( ( v_A = v_Ba )
      = $true )
    | ( ( v_NA
        = ( c_Message_Omsg_ONonce @ v_NAa ) )
      = $true )
    | ( ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs3 ) ) @ tc_Message_Omsg )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[86]) ).

thf(108,plain,
    ( ( ( v_NA
        = ( c_Message_Omsg_ONonce @ v_NB ) )
      = $true )
    | ( ( v_NA
        = ( c_Message_Omsg_ONonce @ v_NAa ) )
      = $true )
    | ( ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs3 ) ) @ tc_Message_Omsg )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[87]) ).

thf(109,plain,
    ( ( ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs3 ) ) @ tc_Message_Omsg ) )
      = $true )
    | ( ( ~ ( c_in @ ( c_Event_Oevent_OSays @ v_A @ v_B @ ( c_Message_Omsg_OMPair @ 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 @ 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 ) )
      = $true )
    | ( ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ v_B @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_B ) @ ( c_Message_Omsg_OMPair @ v_x @ ( c_Message_Omsg_OKey @ v_K ) ) ) ) ) ) @ ( c_List_Oset @ v_evs3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[89]) ).

thf(110,plain,
    ! [SV11: $i] :
      ( ( ( ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ v_B @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_B ) @ ( c_Message_Omsg_OMPair @ SV11 @ ( c_Message_Omsg_OKey @ v_K ) ) ) ) ) ) @ ( c_List_Oset @ v_evs3 @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
        = $true )
      | ( ( v_K = v_KAB )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[91]) ).

thf(111,plain,
    ! [SV12: $i] :
      ( ( ( ( SV12
           != ( c_Message_Omsg_ONonce @ v_NB ) ) )
        = $true )
      | ( ( ( v_K != v_KAB )
          | ( v_A != v_Aa )
          | ( v_NA
           != ( c_Message_Omsg_ONonce @ v_NAa ) )
          | ( v_A = v_Ba )
          | ! [V_U: $i] :
              ( V_U
             != ( c_Message_Omsg_ONonce @ v_NB ) )
          | ( v_B != v_Ba ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[92]) ).

thf(112,plain,
    ! [SV13: $i] :
      ( ( ( ( SV13
           != ( c_Message_Omsg_ONonce @ v_NB ) ) )
        = $true )
      | ( ( ( v_K != v_KAB )
          | ( v_A != v_Aa )
          | ( v_NA
           != ( c_Message_Omsg_ONonce @ v_NAa ) )
          | ( v_NA
            = ( c_Message_Omsg_ONonce @ v_NB ) )
          | ! [V_U: $i] :
              ( V_U
             != ( c_Message_Omsg_ONonce @ v_NB ) )
          | ( v_B != v_Ba ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[93]) ).

thf(113,plain,
    ( ( ( v_A = v_Ba )
      = $true )
    | ( ( v_A = v_Aa )
      = $true )
    | ( ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs3 ) ) @ tc_Message_Omsg )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[94]) ).

thf(114,plain,
    ( ( ( v_NA
        = ( c_Message_Omsg_ONonce @ v_NB ) )
      = $true )
    | ( ( v_A = v_Aa )
      = $true )
    | ( ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs3 ) ) @ tc_Message_Omsg )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[95]) ).

thf(115,plain,
    ! [SV14: $i,SV1: $i] :
      ( ( ! [SY63: $i,SY64: $i] :
            ( ~ ( c_in @ ( c_Event_Oevent_OSays @ SV1 @ SV14 @ SY63 ) @ ( c_List_Oset @ SY64 @ tc_Event_Oevent ) @ tc_Event_Oevent )
            | ( c_in @ SY63 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SY64 ) ) @ tc_Message_Omsg ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[96]) ).

thf(116,plain,
    ! [SV15: $i,SV2: $i] :
      ( ( ~ ( c_in @ SV2 @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV15 ) ) @ tc_Message_Omsg )
        | ( c_in @ SV2 @ ( c_Event_Oused @ SV15 ) @ tc_Message_Omsg ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[97]) ).

thf(117,plain,
    ! [SV16: $i,SV3: $i] :
      ( ( ! [SY65: $i] :
            ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV3 @ SV16 ) @ ( c_Message_Oanalz @ SY65 ) @ tc_Message_Omsg )
            | ( c_in @ SV16 @ ( c_Message_Oanalz @ SY65 ) @ tc_Message_Omsg ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[98]) ).

thf(118,plain,
    ! [SV17: $i,SV4: $i] :
      ( ( ! [SY66: $i] :
            ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV4 @ SV17 ) @ ( c_Message_Oanalz @ SY66 ) @ tc_Message_Omsg )
            | ( c_in @ SV4 @ ( c_Message_Oanalz @ SY66 ) @ tc_Message_Omsg ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[99]) ).

thf(119,plain,
    ! [SV18: $i,SV5: $i] :
      ( ( ~ ( c_in @ SV5 @ ( c_Message_Oanalz @ SV18 ) @ tc_Message_Omsg )
        | ( c_in @ SV5 @ ( c_Message_Oparts @ SV18 ) @ tc_Message_Omsg ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[100]) ).

thf(120,plain,
    ! [SV19: $i,SV6: $i] :
      ( ( ! [SY67: $i] :
            ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ SV6 @ SV19 ) @ ( c_Message_Oparts @ SY67 ) @ tc_Message_Omsg )
            | ( c_in @ SV19 @ ( c_Message_Oparts @ SY67 ) @ tc_Message_Omsg ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[101]) ).

thf(121,plain,
    ! [SV7: $i] :
      ( ( ( ~ ( c_in @ SV7 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
        = $true )
      | ( ( ! [SY50: $i,SY51: $i] :
              ( ~ ( c_in @ ( c_Event_Oevent_OGets @ SY50 @ SY51 ) @ ( c_List_Oset @ SV7 @ tc_Event_Oevent ) @ tc_Event_Oevent )
              | ( c_in @ ( c_Event_Oevent_OSays @ ( v_sko__usf @ SY50 @ SY51 @ SV7 ) @ SY50 @ SY51 ) @ ( c_List_Oset @ SV7 @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[102]) ).

thf(122,plain,
    ! [SV20: $i,SV8: $i] :
      ( ( ! [SY68: $i,SY69: $i] :
            ( ~ ( c_in @ SV8 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
            | ! [SY70: $i] :
                ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV20 ) @ ( c_Message_Omsg_OMPair @ SY68 @ ( c_Message_Omsg_OMPair @ SY69 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY70 ) @ ( c_Message_Omsg_OAgent @ SV20 ) ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV8 ) ) @ tc_Message_Omsg )
            | ! [SY71: $i] :
                ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV20 ) @ ( c_Message_Omsg_OMPair @ SY69 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV20 ) @ ( c_Message_Omsg_OAgent @ SY71 ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV8 ) ) @ tc_Message_Omsg )
            | ( c_in @ SV20 @ c_Event_Obad @ tc_Message_Oagent ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[103]) ).

thf(123,plain,
    ! [SV21: $i,SV9: $i] :
      ( ( ! [SY72: $i] :
            ( ~ ( c_in @ SV9 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
            | ! [SY73: $i] :
                ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV21 ) @ ( c_Message_Omsg_OMPair @ SY72 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV21 ) @ ( c_Message_Omsg_OAgent @ SY73 ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV9 ) ) @ tc_Message_Omsg )
                | ! [SY74: $i] :
                    ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV21 ) @ ( c_Message_Omsg_OMPair @ SY72 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV21 ) @ ( c_Message_Omsg_OAgent @ SY74 ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV9 ) ) @ tc_Message_Omsg )
                    | ( SY74 = SY73 )
                    | ( c_in @ SV21 @ c_Event_Obad @ tc_Message_Oagent ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[104]) ).

thf(124,plain,
    ! [SV22: $i,SV10: $i] :
      ( ( ! [SY75: $i] :
            ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV10 @ SV22 ) @ ( c_Event_Oused @ SY75 ) @ tc_Message_Omsg )
            | ( c_in @ SV22 @ ( c_Event_Oused @ SY75 ) @ tc_Message_Omsg ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[105]) ).

thf(125,plain,
    ( ( ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs3 ) ) @ tc_Message_Omsg )
      = $false )
    | ( ( ~ ( c_in @ ( c_Event_Oevent_OSays @ v_A @ v_B @ ( c_Message_Omsg_OMPair @ 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 @ 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 ) )
      = $true )
    | ( ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ v_B @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_B ) @ ( c_Message_Omsg_OMPair @ v_x @ ( c_Message_Omsg_OKey @ v_K ) ) ) ) ) ) @ ( c_List_Oset @ v_evs3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[109]) ).

thf(126,plain,
    ! [SV11: $i] :
      ( ( ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ v_B @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_B ) @ ( c_Message_Omsg_OMPair @ SV11 @ ( c_Message_Omsg_OKey @ v_K ) ) ) ) ) ) @ ( c_List_Oset @ v_evs3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
        = $false )
      | ( ( v_K = v_KAB )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[110]) ).

thf(127,plain,
    ! [SV12: $i] :
      ( ( ( SV12
          = ( c_Message_Omsg_ONonce @ v_NB ) )
        = $false )
      | ( ( ( v_K != v_KAB )
          | ( v_A != v_Aa )
          | ( v_NA
           != ( c_Message_Omsg_ONonce @ v_NAa ) )
          | ( v_A = v_Ba )
          | ! [V_U: $i] :
              ( V_U
             != ( c_Message_Omsg_ONonce @ v_NB ) )
          | ( v_B != v_Ba ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[111]) ).

thf(128,plain,
    ! [SV13: $i] :
      ( ( ( SV13
          = ( c_Message_Omsg_ONonce @ v_NB ) )
        = $false )
      | ( ( ( v_K != v_KAB )
          | ( v_A != v_Aa )
          | ( v_NA
           != ( c_Message_Omsg_ONonce @ v_NAa ) )
          | ( v_NA
            = ( c_Message_Omsg_ONonce @ v_NB ) )
          | ! [V_U: $i] :
              ( V_U
             != ( c_Message_Omsg_ONonce @ v_NB ) )
          | ( v_B != v_Ba ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[112]) ).

thf(129,plain,
    ! [SV23: $i,SV14: $i,SV1: $i] :
      ( ( ! [SY76: $i] :
            ( ~ ( c_in @ ( c_Event_Oevent_OSays @ SV1 @ SV14 @ SV23 ) @ ( c_List_Oset @ SY76 @ tc_Event_Oevent ) @ tc_Event_Oevent )
            | ( c_in @ SV23 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SY76 ) ) @ tc_Message_Omsg ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[115]) ).

thf(130,plain,
    ! [SV15: $i,SV2: $i] :
      ( ( ( ~ ( c_in @ SV2 @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV15 ) ) @ tc_Message_Omsg ) )
        = $true )
      | ( ( c_in @ SV2 @ ( c_Event_Oused @ SV15 ) @ tc_Message_Omsg )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[116]) ).

thf(131,plain,
    ! [SV24: $i,SV16: $i,SV3: $i] :
      ( ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV3 @ SV16 ) @ ( c_Message_Oanalz @ SV24 ) @ tc_Message_Omsg )
        | ( c_in @ SV16 @ ( c_Message_Oanalz @ SV24 ) @ tc_Message_Omsg ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[117]) ).

thf(132,plain,
    ! [SV25: $i,SV17: $i,SV4: $i] :
      ( ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV4 @ SV17 ) @ ( c_Message_Oanalz @ SV25 ) @ tc_Message_Omsg )
        | ( c_in @ SV4 @ ( c_Message_Oanalz @ SV25 ) @ tc_Message_Omsg ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[118]) ).

thf(133,plain,
    ! [SV18: $i,SV5: $i] :
      ( ( ( ~ ( c_in @ SV5 @ ( c_Message_Oanalz @ SV18 ) @ tc_Message_Omsg ) )
        = $true )
      | ( ( c_in @ SV5 @ ( c_Message_Oparts @ SV18 ) @ tc_Message_Omsg )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[119]) ).

thf(134,plain,
    ! [SV26: $i,SV19: $i,SV6: $i] :
      ( ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ SV6 @ SV19 ) @ ( c_Message_Oparts @ SV26 ) @ tc_Message_Omsg )
        | ( c_in @ SV19 @ ( c_Message_Oparts @ SV26 ) @ tc_Message_Omsg ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[120]) ).

thf(135,plain,
    ! [SV7: $i] :
      ( ( ( c_in @ SV7 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
        = $false )
      | ( ( ! [SY50: $i,SY51: $i] :
              ( ~ ( c_in @ ( c_Event_Oevent_OGets @ SY50 @ SY51 ) @ ( c_List_Oset @ SV7 @ tc_Event_Oevent ) @ tc_Event_Oevent )
              | ( c_in @ ( c_Event_Oevent_OSays @ ( v_sko__usf @ SY50 @ SY51 @ SV7 ) @ SY50 @ SY51 ) @ ( c_List_Oset @ SV7 @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[121]) ).

thf(136,plain,
    ! [SV27: $i,SV20: $i,SV8: $i] :
      ( ( ! [SY77: $i] :
            ( ~ ( c_in @ SV8 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
            | ! [SY78: $i] :
                ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV20 ) @ ( c_Message_Omsg_OMPair @ SV27 @ ( c_Message_Omsg_OMPair @ SY77 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY78 ) @ ( c_Message_Omsg_OAgent @ SV20 ) ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV8 ) ) @ tc_Message_Omsg )
            | ! [SY71: $i] :
                ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV20 ) @ ( c_Message_Omsg_OMPair @ SY77 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV20 ) @ ( c_Message_Omsg_OAgent @ SY71 ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV8 ) ) @ tc_Message_Omsg )
            | ( c_in @ SV20 @ c_Event_Obad @ tc_Message_Oagent ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[122]) ).

thf(137,plain,
    ! [SV28: $i,SV21: $i,SV9: $i] :
      ( ( ~ ( c_in @ SV9 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
        | ! [SY80: $i] :
            ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV21 ) @ ( c_Message_Omsg_OMPair @ SV28 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV21 ) @ ( c_Message_Omsg_OAgent @ SY80 ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV9 ) ) @ tc_Message_Omsg )
            | ! [SY81: $i] :
                ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV21 ) @ ( c_Message_Omsg_OMPair @ SV28 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV21 ) @ ( c_Message_Omsg_OAgent @ SY81 ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV9 ) ) @ tc_Message_Omsg )
                | ( SY81 = SY80 )
                | ( c_in @ SV21 @ c_Event_Obad @ tc_Message_Oagent ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[123]) ).

thf(138,plain,
    ! [SV29: $i,SV22: $i,SV10: $i] :
      ( ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV10 @ SV22 ) @ ( c_Event_Oused @ SV29 ) @ tc_Message_Omsg )
        | ( c_in @ SV22 @ ( c_Event_Oused @ SV29 ) @ tc_Message_Omsg ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[124]) ).

thf(139,plain,
    ( ( ( c_in @ ( c_Event_Oevent_OSays @ v_A @ v_B @ ( c_Message_Omsg_OMPair @ 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 @ 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 )
      = $false )
    | ( ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs3 ) ) @ tc_Message_Omsg )
      = $false )
    | ( ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ v_B @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_B ) @ ( c_Message_Omsg_OMPair @ v_x @ ( c_Message_Omsg_OKey @ v_K ) ) ) ) ) ) @ ( c_List_Oset @ v_evs3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[125]) ).

thf(140,plain,
    ! [SV12: $i] :
      ( ( ( ( v_K != v_KAB ) )
        = $true )
      | ( ( ( v_A != v_Aa )
          | ( v_NA
           != ( c_Message_Omsg_ONonce @ v_NAa ) )
          | ( v_A = v_Ba )
          | ! [V_U: $i] :
              ( V_U
             != ( c_Message_Omsg_ONonce @ v_NB ) )
          | ( v_B != v_Ba ) )
        = $true )
      | ( ( SV12
          = ( c_Message_Omsg_ONonce @ v_NB ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[127]) ).

thf(141,plain,
    ! [SV13: $i] :
      ( ( ( ( v_K != v_KAB ) )
        = $true )
      | ( ( ( v_A != v_Aa )
          | ( v_NA
           != ( c_Message_Omsg_ONonce @ v_NAa ) )
          | ( v_NA
            = ( c_Message_Omsg_ONonce @ v_NB ) )
          | ! [V_U: $i] :
              ( V_U
             != ( c_Message_Omsg_ONonce @ v_NB ) )
          | ( v_B != v_Ba ) )
        = $true )
      | ( ( SV13
          = ( c_Message_Omsg_ONonce @ v_NB ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[128]) ).

thf(142,plain,
    ! [SV30: $i,SV23: $i,SV14: $i,SV1: $i] :
      ( ( ~ ( c_in @ ( c_Event_Oevent_OSays @ SV1 @ SV14 @ SV23 ) @ ( c_List_Oset @ SV30 @ tc_Event_Oevent ) @ tc_Event_Oevent )
        | ( c_in @ SV23 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV30 ) ) @ tc_Message_Omsg ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[129]) ).

thf(143,plain,
    ! [SV15: $i,SV2: $i] :
      ( ( ( c_in @ SV2 @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV15 ) ) @ tc_Message_Omsg )
        = $false )
      | ( ( c_in @ SV2 @ ( c_Event_Oused @ SV15 ) @ tc_Message_Omsg )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[130]) ).

thf(144,plain,
    ! [SV24: $i,SV16: $i,SV3: $i] :
      ( ( ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV3 @ SV16 ) @ ( c_Message_Oanalz @ SV24 ) @ tc_Message_Omsg ) )
        = $true )
      | ( ( c_in @ SV16 @ ( c_Message_Oanalz @ SV24 ) @ tc_Message_Omsg )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[131]) ).

thf(145,plain,
    ! [SV25: $i,SV17: $i,SV4: $i] :
      ( ( ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV4 @ SV17 ) @ ( c_Message_Oanalz @ SV25 ) @ tc_Message_Omsg ) )
        = $true )
      | ( ( c_in @ SV4 @ ( c_Message_Oanalz @ SV25 ) @ tc_Message_Omsg )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[132]) ).

thf(146,plain,
    ! [SV18: $i,SV5: $i] :
      ( ( ( c_in @ SV5 @ ( c_Message_Oanalz @ SV18 ) @ tc_Message_Omsg )
        = $false )
      | ( ( c_in @ SV5 @ ( c_Message_Oparts @ SV18 ) @ tc_Message_Omsg )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[133]) ).

thf(147,plain,
    ! [SV26: $i,SV19: $i,SV6: $i] :
      ( ( ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ SV6 @ SV19 ) @ ( c_Message_Oparts @ SV26 ) @ tc_Message_Omsg ) )
        = $true )
      | ( ( c_in @ SV19 @ ( c_Message_Oparts @ SV26 ) @ tc_Message_Omsg )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[134]) ).

thf(148,plain,
    ! [SV7: $i,SV31: $i] :
      ( ( ( ! [SY82: $i] :
              ( ~ ( c_in @ ( c_Event_Oevent_OGets @ SV31 @ SY82 ) @ ( c_List_Oset @ SV7 @ tc_Event_Oevent ) @ tc_Event_Oevent )
              | ( c_in @ ( c_Event_Oevent_OSays @ ( v_sko__usf @ SV31 @ SY82 @ SV7 ) @ SV31 @ SY82 ) @ ( c_List_Oset @ SV7 @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) )
        = $true )
      | ( ( c_in @ SV7 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[135]) ).

thf(149,plain,
    ! [SV32: $i,SV27: $i,SV20: $i,SV8: $i] :
      ( ( ~ ( c_in @ SV8 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
        | ! [SY83: $i] :
            ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV20 ) @ ( c_Message_Omsg_OMPair @ SV27 @ ( c_Message_Omsg_OMPair @ SV32 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY83 ) @ ( c_Message_Omsg_OAgent @ SV20 ) ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV8 ) ) @ tc_Message_Omsg )
        | ! [SY84: $i] :
            ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV20 ) @ ( c_Message_Omsg_OMPair @ SV32 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV20 ) @ ( c_Message_Omsg_OAgent @ SY84 ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV8 ) ) @ tc_Message_Omsg )
        | ( c_in @ SV20 @ c_Event_Obad @ tc_Message_Oagent ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[136]) ).

thf(150,plain,
    ! [SV28: $i,SV21: $i,SV9: $i] :
      ( ( ( ~ ( c_in @ SV9 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
        = $true )
      | ( ( ! [SY80: $i] :
              ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV21 ) @ ( c_Message_Omsg_OMPair @ SV28 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV21 ) @ ( c_Message_Omsg_OAgent @ SY80 ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV9 ) ) @ tc_Message_Omsg )
              | ! [SY81: $i] :
                  ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV21 ) @ ( c_Message_Omsg_OMPair @ SV28 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV21 ) @ ( c_Message_Omsg_OAgent @ SY81 ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV9 ) ) @ tc_Message_Omsg )
                  | ( SY81 = SY80 )
                  | ( c_in @ SV21 @ c_Event_Obad @ tc_Message_Oagent ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[137]) ).

thf(151,plain,
    ! [SV29: $i,SV22: $i,SV10: $i] :
      ( ( ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV10 @ SV22 ) @ ( c_Event_Oused @ SV29 ) @ tc_Message_Omsg ) )
        = $true )
      | ( ( c_in @ SV22 @ ( c_Event_Oused @ SV29 ) @ tc_Message_Omsg )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[138]) ).

thf(152,plain,
    ! [SV12: $i] :
      ( ( ( v_K = v_KAB )
        = $false )
      | ( ( ( v_A != v_Aa )
          | ( v_NA
           != ( c_Message_Omsg_ONonce @ v_NAa ) )
          | ( v_A = v_Ba )
          | ! [V_U: $i] :
              ( V_U
             != ( c_Message_Omsg_ONonce @ v_NB ) )
          | ( v_B != v_Ba ) )
        = $true )
      | ( ( SV12
          = ( c_Message_Omsg_ONonce @ v_NB ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[140]) ).

thf(153,plain,
    ! [SV13: $i] :
      ( ( ( v_K = v_KAB )
        = $false )
      | ( ( ( v_A != v_Aa )
          | ( v_NA
           != ( c_Message_Omsg_ONonce @ v_NAa ) )
          | ( v_NA
            = ( c_Message_Omsg_ONonce @ v_NB ) )
          | ! [V_U: $i] :
              ( V_U
             != ( c_Message_Omsg_ONonce @ v_NB ) )
          | ( v_B != v_Ba ) )
        = $true )
      | ( ( SV13
          = ( c_Message_Omsg_ONonce @ v_NB ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[141]) ).

thf(154,plain,
    ! [SV30: $i,SV23: $i,SV14: $i,SV1: $i] :
      ( ( ( ~ ( c_in @ ( c_Event_Oevent_OSays @ SV1 @ SV14 @ SV23 ) @ ( c_List_Oset @ SV30 @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
        = $true )
      | ( ( c_in @ SV23 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV30 ) ) @ tc_Message_Omsg )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[142]) ).

thf(155,plain,
    ! [SV24: $i,SV16: $i,SV3: $i] :
      ( ( ( c_in @ ( c_Message_Omsg_OMPair @ SV3 @ SV16 ) @ ( c_Message_Oanalz @ SV24 ) @ tc_Message_Omsg )
        = $false )
      | ( ( c_in @ SV16 @ ( c_Message_Oanalz @ SV24 ) @ tc_Message_Omsg )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[144]) ).

thf(156,plain,
    ! [SV25: $i,SV17: $i,SV4: $i] :
      ( ( ( c_in @ ( c_Message_Omsg_OMPair @ SV4 @ SV17 ) @ ( c_Message_Oanalz @ SV25 ) @ tc_Message_Omsg )
        = $false )
      | ( ( c_in @ SV4 @ ( c_Message_Oanalz @ SV25 ) @ tc_Message_Omsg )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[145]) ).

thf(157,plain,
    ! [SV26: $i,SV19: $i,SV6: $i] :
      ( ( ( c_in @ ( c_Message_Omsg_OCrypt @ SV6 @ SV19 ) @ ( c_Message_Oparts @ SV26 ) @ tc_Message_Omsg )
        = $false )
      | ( ( c_in @ SV19 @ ( c_Message_Oparts @ SV26 ) @ tc_Message_Omsg )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[147]) ).

thf(158,plain,
    ! [SV7: $i,SV33: $i,SV31: $i] :
      ( ( ( ~ ( c_in @ ( c_Event_Oevent_OGets @ SV31 @ SV33 ) @ ( c_List_Oset @ SV7 @ tc_Event_Oevent ) @ tc_Event_Oevent )
          | ( c_in @ ( c_Event_Oevent_OSays @ ( v_sko__usf @ SV31 @ SV33 @ SV7 ) @ SV31 @ SV33 ) @ ( c_List_Oset @ SV7 @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
        = $true )
      | ( ( c_in @ SV7 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[148]) ).

thf(159,plain,
    ! [SV32: $i,SV27: $i,SV20: $i,SV8: $i] :
      ( ( ( ~ ( c_in @ SV8 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
        = $true )
      | ( ( ! [SY83: $i] :
              ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV20 ) @ ( c_Message_Omsg_OMPair @ SV27 @ ( c_Message_Omsg_OMPair @ SV32 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY83 ) @ ( c_Message_Omsg_OAgent @ SV20 ) ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV8 ) ) @ tc_Message_Omsg )
          | ! [SY84: $i] :
              ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV20 ) @ ( c_Message_Omsg_OMPair @ SV32 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV20 ) @ ( c_Message_Omsg_OAgent @ SY84 ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV8 ) ) @ tc_Message_Omsg )
          | ( c_in @ SV20 @ c_Event_Obad @ tc_Message_Oagent ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[149]) ).

thf(160,plain,
    ! [SV28: $i,SV21: $i,SV9: $i] :
      ( ( ( c_in @ SV9 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
        = $false )
      | ( ( ! [SY80: $i] :
              ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV21 ) @ ( c_Message_Omsg_OMPair @ SV28 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV21 ) @ ( c_Message_Omsg_OAgent @ SY80 ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV9 ) ) @ tc_Message_Omsg )
              | ! [SY81: $i] :
                  ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV21 ) @ ( c_Message_Omsg_OMPair @ SV28 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV21 ) @ ( c_Message_Omsg_OAgent @ SY81 ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV9 ) ) @ tc_Message_Omsg )
                  | ( SY81 = SY80 )
                  | ( c_in @ SV21 @ c_Event_Obad @ tc_Message_Oagent ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[150]) ).

thf(161,plain,
    ! [SV29: $i,SV22: $i,SV10: $i] :
      ( ( ( c_in @ ( c_Message_Omsg_OMPair @ SV10 @ SV22 ) @ ( c_Event_Oused @ SV29 ) @ tc_Message_Omsg )
        = $false )
      | ( ( c_in @ SV22 @ ( c_Event_Oused @ SV29 ) @ tc_Message_Omsg )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[151]) ).

thf(162,plain,
    ! [SV12: $i] :
      ( ( ( ( v_A != v_Aa ) )
        = $true )
      | ( ( ( v_NA
           != ( c_Message_Omsg_ONonce @ v_NAa ) )
          | ( v_A = v_Ba )
          | ! [V_U: $i] :
              ( V_U
             != ( c_Message_Omsg_ONonce @ v_NB ) )
          | ( v_B != v_Ba ) )
        = $true )
      | ( ( v_K = v_KAB )
        = $false )
      | ( ( SV12
          = ( c_Message_Omsg_ONonce @ v_NB ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[152]) ).

thf(163,plain,
    ! [SV13: $i] :
      ( ( ( ( v_A != v_Aa ) )
        = $true )
      | ( ( ( v_NA
           != ( c_Message_Omsg_ONonce @ v_NAa ) )
          | ( v_NA
            = ( c_Message_Omsg_ONonce @ v_NB ) )
          | ! [V_U: $i] :
              ( V_U
             != ( c_Message_Omsg_ONonce @ v_NB ) )
          | ( v_B != v_Ba ) )
        = $true )
      | ( ( v_K = v_KAB )
        = $false )
      | ( ( SV13
          = ( c_Message_Omsg_ONonce @ v_NB ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[153]) ).

thf(164,plain,
    ! [SV30: $i,SV23: $i,SV14: $i,SV1: $i] :
      ( ( ( c_in @ ( c_Event_Oevent_OSays @ SV1 @ SV14 @ SV23 ) @ ( c_List_Oset @ SV30 @ tc_Event_Oevent ) @ tc_Event_Oevent )
        = $false )
      | ( ( c_in @ SV23 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV30 ) ) @ tc_Message_Omsg )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[154]) ).

thf(165,plain,
    ! [SV7: $i,SV33: $i,SV31: $i] :
      ( ( ( ~ ( c_in @ ( c_Event_Oevent_OGets @ SV31 @ SV33 ) @ ( c_List_Oset @ SV7 @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
        = $true )
      | ( ( c_in @ ( c_Event_Oevent_OSays @ ( v_sko__usf @ SV31 @ SV33 @ SV7 ) @ SV31 @ SV33 ) @ ( c_List_Oset @ SV7 @ tc_Event_Oevent ) @ tc_Event_Oevent )
        = $true )
      | ( ( c_in @ SV7 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[158]) ).

thf(166,plain,
    ! [SV32: $i,SV27: $i,SV20: $i,SV8: $i] :
      ( ( ( c_in @ SV8 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
        = $false )
      | ( ( ! [SY83: $i] :
              ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV20 ) @ ( c_Message_Omsg_OMPair @ SV27 @ ( c_Message_Omsg_OMPair @ SV32 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY83 ) @ ( c_Message_Omsg_OAgent @ SV20 ) ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV8 ) ) @ tc_Message_Omsg )
          | ! [SY84: $i] :
              ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV20 ) @ ( c_Message_Omsg_OMPair @ SV32 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV20 ) @ ( c_Message_Omsg_OAgent @ SY84 ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV8 ) ) @ tc_Message_Omsg )
          | ( c_in @ SV20 @ c_Event_Obad @ tc_Message_Oagent ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[159]) ).

thf(167,plain,
    ! [SV9: $i,SV34: $i,SV28: $i,SV21: $i] :
      ( ( ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV21 ) @ ( c_Message_Omsg_OMPair @ SV28 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV21 ) @ ( c_Message_Omsg_OAgent @ SV34 ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV9 ) ) @ tc_Message_Omsg )
          | ! [SY85: $i] :
              ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV21 ) @ ( c_Message_Omsg_OMPair @ SV28 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV21 ) @ ( c_Message_Omsg_OAgent @ SY85 ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV9 ) ) @ tc_Message_Omsg )
              | ( SY85 = SV34 )
              | ( c_in @ SV21 @ c_Event_Obad @ tc_Message_Oagent ) ) )
        = $true )
      | ( ( c_in @ SV9 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[160]) ).

thf(168,plain,
    ! [SV12: $i] :
      ( ( ( v_A = v_Aa )
        = $false )
      | ( ( ( v_NA
           != ( c_Message_Omsg_ONonce @ v_NAa ) )
          | ( v_A = v_Ba )
          | ! [V_U: $i] :
              ( V_U
             != ( c_Message_Omsg_ONonce @ v_NB ) )
          | ( v_B != v_Ba ) )
        = $true )
      | ( ( v_K = v_KAB )
        = $false )
      | ( ( SV12
          = ( c_Message_Omsg_ONonce @ v_NB ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[162]) ).

thf(169,plain,
    ! [SV13: $i] :
      ( ( ( v_A = v_Aa )
        = $false )
      | ( ( ( v_NA
           != ( c_Message_Omsg_ONonce @ v_NAa ) )
          | ( v_NA
            = ( c_Message_Omsg_ONonce @ v_NB ) )
          | ! [V_U: $i] :
              ( V_U
             != ( c_Message_Omsg_ONonce @ v_NB ) )
          | ( v_B != v_Ba ) )
        = $true )
      | ( ( v_K = v_KAB )
        = $false )
      | ( ( SV13
          = ( c_Message_Omsg_ONonce @ v_NB ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[163]) ).

thf(170,plain,
    ! [SV7: $i,SV33: $i,SV31: $i] :
      ( ( ( c_in @ ( c_Event_Oevent_OGets @ SV31 @ SV33 ) @ ( c_List_Oset @ SV7 @ tc_Event_Oevent ) @ tc_Event_Oevent )
        = $false )
      | ( ( c_in @ ( c_Event_Oevent_OSays @ ( v_sko__usf @ SV31 @ SV33 @ SV7 ) @ SV31 @ SV33 ) @ ( c_List_Oset @ SV7 @ tc_Event_Oevent ) @ tc_Event_Oevent )
        = $true )
      | ( ( c_in @ SV7 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[165]) ).

thf(171,plain,
    ! [SV8: $i,SV32: $i,SV27: $i,SV20: $i] :
      ( ( ( ! [SY83: $i] :
              ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV20 ) @ ( c_Message_Omsg_OMPair @ SV27 @ ( c_Message_Omsg_OMPair @ SV32 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY83 ) @ ( c_Message_Omsg_OAgent @ SV20 ) ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV8 ) ) @ tc_Message_Omsg ) )
        = $true )
      | ( ( ! [SY84: $i] :
              ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV20 ) @ ( c_Message_Omsg_OMPair @ SV32 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV20 ) @ ( c_Message_Omsg_OAgent @ SY84 ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV8 ) ) @ tc_Message_Omsg )
          | ( c_in @ SV20 @ c_Event_Obad @ tc_Message_Oagent ) )
        = $true )
      | ( ( c_in @ SV8 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[166]) ).

thf(172,plain,
    ! [SV9: $i,SV34: $i,SV28: $i,SV21: $i] :
      ( ( ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV21 ) @ ( c_Message_Omsg_OMPair @ SV28 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV21 ) @ ( c_Message_Omsg_OAgent @ SV34 ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV9 ) ) @ tc_Message_Omsg ) )
        = $true )
      | ( ( ! [SY85: $i] :
              ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV21 ) @ ( c_Message_Omsg_OMPair @ SV28 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV21 ) @ ( c_Message_Omsg_OAgent @ SY85 ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV9 ) ) @ tc_Message_Omsg )
              | ( SY85 = SV34 )
              | ( c_in @ SV21 @ c_Event_Obad @ tc_Message_Oagent ) ) )
        = $true )
      | ( ( c_in @ SV9 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[167]) ).

thf(173,plain,
    ! [SV12: $i] :
      ( ( ( ( v_NA
           != ( c_Message_Omsg_ONonce @ v_NAa ) ) )
        = $true )
      | ( ( ( v_A = v_Ba )
          | ! [V_U: $i] :
              ( V_U
             != ( c_Message_Omsg_ONonce @ v_NB ) )
          | ( v_B != v_Ba ) )
        = $true )
      | ( ( v_A = v_Aa )
        = $false )
      | ( ( v_K = v_KAB )
        = $false )
      | ( ( SV12
          = ( c_Message_Omsg_ONonce @ v_NB ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[168]) ).

thf(174,plain,
    ! [SV13: $i] :
      ( ( ( ( v_NA
           != ( c_Message_Omsg_ONonce @ v_NAa ) ) )
        = $true )
      | ( ( ( v_NA
            = ( c_Message_Omsg_ONonce @ v_NB ) )
          | ! [V_U: $i] :
              ( V_U
             != ( c_Message_Omsg_ONonce @ v_NB ) )
          | ( v_B != v_Ba ) )
        = $true )
      | ( ( v_A = v_Aa )
        = $false )
      | ( ( v_K = v_KAB )
        = $false )
      | ( ( SV13
          = ( c_Message_Omsg_ONonce @ v_NB ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[169]) ).

thf(175,plain,
    ! [SV8: $i,SV35: $i,SV32: $i,SV27: $i,SV20: $i] :
      ( ( ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV20 ) @ ( c_Message_Omsg_OMPair @ SV27 @ ( c_Message_Omsg_OMPair @ SV32 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV35 ) @ ( c_Message_Omsg_OAgent @ SV20 ) ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV8 ) ) @ tc_Message_Omsg ) )
        = $true )
      | ( ( ! [SY84: $i] :
              ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV20 ) @ ( c_Message_Omsg_OMPair @ SV32 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV20 ) @ ( c_Message_Omsg_OAgent @ SY84 ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV8 ) ) @ tc_Message_Omsg )
          | ( c_in @ SV20 @ c_Event_Obad @ tc_Message_Oagent ) )
        = $true )
      | ( ( c_in @ SV8 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[171]) ).

thf(176,plain,
    ! [SV9: $i,SV34: $i,SV28: $i,SV21: $i] :
      ( ( ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV21 ) @ ( c_Message_Omsg_OMPair @ SV28 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV21 ) @ ( c_Message_Omsg_OAgent @ SV34 ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV9 ) ) @ tc_Message_Omsg )
        = $false )
      | ( ( ! [SY85: $i] :
              ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV21 ) @ ( c_Message_Omsg_OMPair @ SV28 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV21 ) @ ( c_Message_Omsg_OAgent @ SY85 ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV9 ) ) @ tc_Message_Omsg )
              | ( SY85 = SV34 )
              | ( c_in @ SV21 @ c_Event_Obad @ tc_Message_Oagent ) ) )
        = $true )
      | ( ( c_in @ SV9 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[172]) ).

thf(177,plain,
    ! [SV12: $i] :
      ( ( ( v_NA
          = ( c_Message_Omsg_ONonce @ v_NAa ) )
        = $false )
      | ( ( ( v_A = v_Ba )
          | ! [V_U: $i] :
              ( V_U
             != ( c_Message_Omsg_ONonce @ v_NB ) )
          | ( v_B != v_Ba ) )
        = $true )
      | ( ( v_A = v_Aa )
        = $false )
      | ( ( v_K = v_KAB )
        = $false )
      | ( ( SV12
          = ( c_Message_Omsg_ONonce @ v_NB ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[173]) ).

thf(178,plain,
    ! [SV13: $i] :
      ( ( ( v_NA
          = ( c_Message_Omsg_ONonce @ v_NAa ) )
        = $false )
      | ( ( ( v_NA
            = ( c_Message_Omsg_ONonce @ v_NB ) )
          | ! [V_U: $i] :
              ( V_U
             != ( c_Message_Omsg_ONonce @ v_NB ) )
          | ( v_B != v_Ba ) )
        = $true )
      | ( ( v_A = v_Aa )
        = $false )
      | ( ( v_K = v_KAB )
        = $false )
      | ( ( SV13
          = ( c_Message_Omsg_ONonce @ v_NB ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[174]) ).

thf(179,plain,
    ! [SV8: $i,SV35: $i,SV32: $i,SV27: $i,SV20: $i] :
      ( ( ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV20 ) @ ( c_Message_Omsg_OMPair @ SV27 @ ( c_Message_Omsg_OMPair @ SV32 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV35 ) @ ( c_Message_Omsg_OAgent @ SV20 ) ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV8 ) ) @ tc_Message_Omsg )
        = $false )
      | ( ( ! [SY84: $i] :
              ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV20 ) @ ( c_Message_Omsg_OMPair @ SV32 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV20 ) @ ( c_Message_Omsg_OAgent @ SY84 ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV8 ) ) @ tc_Message_Omsg )
          | ( c_in @ SV20 @ c_Event_Obad @ tc_Message_Oagent ) )
        = $true )
      | ( ( c_in @ SV8 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[175]) ).

thf(180,plain,
    ! [SV34: $i,SV9: $i,SV36: $i,SV28: $i,SV21: $i] :
      ( ( ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV21 ) @ ( c_Message_Omsg_OMPair @ SV28 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV21 ) @ ( c_Message_Omsg_OAgent @ SV36 ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV9 ) ) @ tc_Message_Omsg )
          | ( SV36 = SV34 )
          | ( c_in @ SV21 @ c_Event_Obad @ tc_Message_Oagent ) )
        = $true )
      | ( ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV21 ) @ ( c_Message_Omsg_OMPair @ SV28 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV21 ) @ ( c_Message_Omsg_OAgent @ SV34 ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV9 ) ) @ tc_Message_Omsg )
        = $false )
      | ( ( c_in @ SV9 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[176]) ).

thf(181,plain,
    ! [SV12: $i] :
      ( ( ( v_A = v_Ba )
        = $true )
      | ( ( ! [V_U: $i] :
              ( V_U
             != ( c_Message_Omsg_ONonce @ v_NB ) )
          | ( v_B != v_Ba ) )
        = $true )
      | ( ( v_NA
          = ( c_Message_Omsg_ONonce @ v_NAa ) )
        = $false )
      | ( ( v_A = v_Aa )
        = $false )
      | ( ( v_K = v_KAB )
        = $false )
      | ( ( SV12
          = ( c_Message_Omsg_ONonce @ v_NB ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[177]) ).

thf(182,plain,
    ! [SV13: $i] :
      ( ( ( v_NA
          = ( c_Message_Omsg_ONonce @ v_NB ) )
        = $true )
      | ( ( ! [V_U: $i] :
              ( V_U
             != ( c_Message_Omsg_ONonce @ v_NB ) )
          | ( v_B != v_Ba ) )
        = $true )
      | ( ( v_NA
          = ( c_Message_Omsg_ONonce @ v_NAa ) )
        = $false )
      | ( ( v_A = v_Aa )
        = $false )
      | ( ( v_K = v_KAB )
        = $false )
      | ( ( SV13
          = ( c_Message_Omsg_ONonce @ v_NB ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[178]) ).

thf(183,plain,
    ! [SV35: $i,SV27: $i,SV8: $i,SV32: $i,SV20: $i] :
      ( ( ( ! [SY84: $i] :
              ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV20 ) @ ( c_Message_Omsg_OMPair @ SV32 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV20 ) @ ( c_Message_Omsg_OAgent @ SY84 ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV8 ) ) @ tc_Message_Omsg ) )
        = $true )
      | ( ( c_in @ SV20 @ c_Event_Obad @ tc_Message_Oagent )
        = $true )
      | ( ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV20 ) @ ( c_Message_Omsg_OMPair @ SV27 @ ( c_Message_Omsg_OMPair @ SV32 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV35 ) @ ( c_Message_Omsg_OAgent @ SV20 ) ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV8 ) ) @ tc_Message_Omsg )
        = $false )
      | ( ( c_in @ SV8 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[179]) ).

thf(184,plain,
    ! [SV34: $i,SV9: $i,SV36: $i,SV28: $i,SV21: $i] :
      ( ( ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV21 ) @ ( c_Message_Omsg_OMPair @ SV28 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV21 ) @ ( c_Message_Omsg_OAgent @ SV36 ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV9 ) ) @ tc_Message_Omsg ) )
        = $true )
      | ( ( ( SV36 = SV34 )
          | ( c_in @ SV21 @ c_Event_Obad @ tc_Message_Oagent ) )
        = $true )
      | ( ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV21 ) @ ( c_Message_Omsg_OMPair @ SV28 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV21 ) @ ( c_Message_Omsg_OAgent @ SV34 ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV9 ) ) @ tc_Message_Omsg )
        = $false )
      | ( ( c_in @ SV9 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[180]) ).

thf(185,plain,
    ! [SV12: $i] :
      ( ( ( ! [V_U: $i] :
              ( V_U
             != ( c_Message_Omsg_ONonce @ v_NB ) ) )
        = $true )
      | ( ( ( v_B != v_Ba ) )
        = $true )
      | ( ( v_A = v_Ba )
        = $true )
      | ( ( v_NA
          = ( c_Message_Omsg_ONonce @ v_NAa ) )
        = $false )
      | ( ( v_A = v_Aa )
        = $false )
      | ( ( v_K = v_KAB )
        = $false )
      | ( ( SV12
          = ( c_Message_Omsg_ONonce @ v_NB ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[181]) ).

thf(186,plain,
    ! [SV13: $i] :
      ( ( ( ! [V_U: $i] :
              ( V_U
             != ( c_Message_Omsg_ONonce @ v_NB ) ) )
        = $true )
      | ( ( ( v_B != v_Ba ) )
        = $true )
      | ( ( v_NA
          = ( c_Message_Omsg_ONonce @ v_NB ) )
        = $true )
      | ( ( v_NA
          = ( c_Message_Omsg_ONonce @ v_NAa ) )
        = $false )
      | ( ( v_A = v_Aa )
        = $false )
      | ( ( v_K = v_KAB )
        = $false )
      | ( ( SV13
          = ( c_Message_Omsg_ONonce @ v_NB ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[182]) ).

thf(187,plain,
    ! [SV35: $i,SV27: $i,SV8: $i,SV37: $i,SV32: $i,SV20: $i] :
      ( ( ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV20 ) @ ( c_Message_Omsg_OMPair @ SV32 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV20 ) @ ( c_Message_Omsg_OAgent @ SV37 ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV8 ) ) @ tc_Message_Omsg ) )
        = $true )
      | ( ( c_in @ SV20 @ c_Event_Obad @ tc_Message_Oagent )
        = $true )
      | ( ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV20 ) @ ( c_Message_Omsg_OMPair @ SV27 @ ( c_Message_Omsg_OMPair @ SV32 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV35 ) @ ( c_Message_Omsg_OAgent @ SV20 ) ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV8 ) ) @ tc_Message_Omsg )
        = $false )
      | ( ( c_in @ SV8 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[183]) ).

thf(188,plain,
    ! [SV34: $i,SV9: $i,SV36: $i,SV28: $i,SV21: $i] :
      ( ( ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV21 ) @ ( c_Message_Omsg_OMPair @ SV28 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV21 ) @ ( c_Message_Omsg_OAgent @ SV36 ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV9 ) ) @ tc_Message_Omsg )
        = $false )
      | ( ( ( SV36 = SV34 )
          | ( c_in @ SV21 @ c_Event_Obad @ tc_Message_Oagent ) )
        = $true )
      | ( ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV21 ) @ ( c_Message_Omsg_OMPair @ SV28 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV21 ) @ ( c_Message_Omsg_OAgent @ SV34 ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV9 ) ) @ tc_Message_Omsg )
        = $false )
      | ( ( c_in @ SV9 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[184]) ).

thf(189,plain,
    ! [SV12: $i,SV38: $i] :
      ( ( ( ( SV38
           != ( c_Message_Omsg_ONonce @ v_NB ) ) )
        = $true )
      | ( ( ( v_B != v_Ba ) )
        = $true )
      | ( ( v_A = v_Ba )
        = $true )
      | ( ( v_NA
          = ( c_Message_Omsg_ONonce @ v_NAa ) )
        = $false )
      | ( ( v_A = v_Aa )
        = $false )
      | ( ( v_K = v_KAB )
        = $false )
      | ( ( SV12
          = ( c_Message_Omsg_ONonce @ v_NB ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[185]) ).

thf(190,plain,
    ! [SV13: $i,SV39: $i] :
      ( ( ( ( SV39
           != ( c_Message_Omsg_ONonce @ v_NB ) ) )
        = $true )
      | ( ( ( v_B != v_Ba ) )
        = $true )
      | ( ( v_NA
          = ( c_Message_Omsg_ONonce @ v_NB ) )
        = $true )
      | ( ( v_NA
          = ( c_Message_Omsg_ONonce @ v_NAa ) )
        = $false )
      | ( ( v_A = v_Aa )
        = $false )
      | ( ( v_K = v_KAB )
        = $false )
      | ( ( SV13
          = ( c_Message_Omsg_ONonce @ v_NB ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[186]) ).

thf(191,plain,
    ! [SV35: $i,SV27: $i,SV8: $i,SV37: $i,SV32: $i,SV20: $i] :
      ( ( ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV20 ) @ ( c_Message_Omsg_OMPair @ SV32 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV20 ) @ ( c_Message_Omsg_OAgent @ SV37 ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV8 ) ) @ tc_Message_Omsg )
        = $false )
      | ( ( c_in @ SV20 @ c_Event_Obad @ tc_Message_Oagent )
        = $true )
      | ( ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV20 ) @ ( c_Message_Omsg_OMPair @ SV27 @ ( c_Message_Omsg_OMPair @ SV32 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV35 ) @ ( c_Message_Omsg_OAgent @ SV20 ) ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV8 ) ) @ tc_Message_Omsg )
        = $false )
      | ( ( c_in @ SV8 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[187]) ).

thf(192,plain,
    ! [SV9: $i,SV28: $i,SV21: $i,SV34: $i,SV36: $i] :
      ( ( ( SV36 = SV34 )
        = $true )
      | ( ( c_in @ SV21 @ c_Event_Obad @ tc_Message_Oagent )
        = $true )
      | ( ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV21 ) @ ( c_Message_Omsg_OMPair @ SV28 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV21 ) @ ( c_Message_Omsg_OAgent @ SV36 ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV9 ) ) @ tc_Message_Omsg )
        = $false )
      | ( ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV21 ) @ ( c_Message_Omsg_OMPair @ SV28 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV21 ) @ ( c_Message_Omsg_OAgent @ SV34 ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV9 ) ) @ tc_Message_Omsg )
        = $false )
      | ( ( c_in @ SV9 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[188]) ).

thf(193,plain,
    ! [SV12: $i,SV38: $i] :
      ( ( ( SV38
          = ( c_Message_Omsg_ONonce @ v_NB ) )
        = $false )
      | ( ( ( v_B != v_Ba ) )
        = $true )
      | ( ( v_A = v_Ba )
        = $true )
      | ( ( v_NA
          = ( c_Message_Omsg_ONonce @ v_NAa ) )
        = $false )
      | ( ( v_A = v_Aa )
        = $false )
      | ( ( v_K = v_KAB )
        = $false )
      | ( ( SV12
          = ( c_Message_Omsg_ONonce @ v_NB ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[189]) ).

thf(194,plain,
    ! [SV13: $i,SV39: $i] :
      ( ( ( SV39
          = ( c_Message_Omsg_ONonce @ v_NB ) )
        = $false )
      | ( ( ( v_B != v_Ba ) )
        = $true )
      | ( ( v_NA
          = ( c_Message_Omsg_ONonce @ v_NB ) )
        = $true )
      | ( ( v_NA
          = ( c_Message_Omsg_ONonce @ v_NAa ) )
        = $false )
      | ( ( v_A = v_Aa )
        = $false )
      | ( ( v_K = v_KAB )
        = $false )
      | ( ( SV13
          = ( c_Message_Omsg_ONonce @ v_NB ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[190]) ).

thf(195,plain,
    ! [SV12: $i,SV38: $i] :
      ( ( ( v_B = v_Ba )
        = $false )
      | ( ( SV38
          = ( c_Message_Omsg_ONonce @ v_NB ) )
        = $false )
      | ( ( v_A = v_Ba )
        = $true )
      | ( ( v_NA
          = ( c_Message_Omsg_ONonce @ v_NAa ) )
        = $false )
      | ( ( v_A = v_Aa )
        = $false )
      | ( ( v_K = v_KAB )
        = $false )
      | ( ( SV12
          = ( c_Message_Omsg_ONonce @ v_NB ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[193]) ).

thf(196,plain,
    ! [SV13: $i,SV39: $i] :
      ( ( ( v_B = v_Ba )
        = $false )
      | ( ( SV39
          = ( c_Message_Omsg_ONonce @ v_NB ) )
        = $false )
      | ( ( v_NA
          = ( c_Message_Omsg_ONonce @ v_NB ) )
        = $true )
      | ( ( v_NA
          = ( c_Message_Omsg_ONonce @ v_NAa ) )
        = $false )
      | ( ( v_A = v_Aa )
        = $false )
      | ( ( v_K = v_KAB )
        = $false )
      | ( ( SV13
          = ( c_Message_Omsg_ONonce @ v_NB ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[194]) ).

thf(197,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[61,196,195,192,191,170,164,161,157,156,155,146,143,139,126,114,113,108,107,106,90,88,85,67,65]) ).

thf(198,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[197]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SWV296-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.14  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.35  % Computer : n027.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Tue Jun 14 15:59:03 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.20/0.40  
% 0.20/0.40   No.of.Axioms: 24
% 0.20/0.40  
% 0.20/0.40   Length.of.Defs: 0
% 0.20/0.40  
% 0.20/0.40   Contains.Choice.Funs: false
% 0.20/0.45  (rf:0,axioms:24,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:26,loop_count:0,foatp_calls:0,translation:fof_full)...........
% 0.44/0.83  
% 0.44/0.83  ********************************
% 0.44/0.83  *   All subproblems solved!    *
% 0.44/0.83  ********************************
% 0.44/0.83  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:24,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:197,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.67/0.87  
% 0.67/0.87  %**** Beginning of derivation protocol ****
% 0.67/0.87  % SZS output start CNFRefutation
% See solution above
% 0.67/0.87  
% 0.67/0.87  %**** End of derivation protocol ****
% 0.67/0.87  %**** no. of clauses in derivation: 198 ****
% 0.67/0.87  %**** clause counter: 197 ****
% 0.67/0.87  
% 0.67/0.87  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:24,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:197,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------