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