%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV354-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:57:27 AM UTC 2026
% Result : Unsatisfiable 0.64s 0.32s
% Output : CNFRefutation 0.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 11
% Syntax : Number of formulae : 103 ( 71 unt; 0 typ; 0 def)
% Number of atoms : 641 ( 236 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 3518 ( 174 ~; 248 |; 0 &;3096 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 31 usr; 18 con; 0-3 aty)
% Number of variables : 650 ( 0 ^; 650 !; 0 ?; 650 :)
% Comments :
%------------------------------------------------------------------------------
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_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_Public_OshrK,type,
c_Public_OshrK: $i > $i ).
thf(tp_c_Yahalom_Oyahalom,type,
c_Yahalom_Oyahalom: $i ).
thf(tp_c_in,type,
c_in: $i > $i > $i > $o ).
thf(tp_c_insert,type,
c_insert: $i > $i > $i > $i ).
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_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_NA,type,
v_NA: $i ).
thf(tp_v_NAa,type,
v_NAa: $i ).
thf(tp_v_NB,type,
v_NB: $i ).
thf(tp_v_NBa,type,
v_NBa: $i ).
thf(tp_v_X,type,
v_X: $i ).
thf(tp_v_evso,type,
v_evso: $i ).
thf(tp_v_sko__2VY,type,
v_sko__2VY: $i > $i ).
thf(1,axiom,
! [V_evs: $i,V_A: $i,V_B: $i,V_x: $i,V_na: $i,V_nb: $i,V_X: $i] :
( ~ ( c_in @ V_evs @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ V_A @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ V_A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ V_B ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ V_x ) ) @ ( c_Message_Omsg_OMPair @ V_na @ V_nb ) ) ) ) @ V_X ) ) @ ( c_List_Oset @ V_evs @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Yahalom_OSays__Server__not__shrK_0) ).
thf(2,axiom,
! [V_evs: $i,V_S_H: $i,V_X_H: $i,V_B_H: $i,V_A_H: $i,V_NA_H: $i,V_nb: $i,V_C: $i,V_S: $i,V_X: $i,V_B: $i,V_A: $i,V_NA: $i] :
( ~ ( c_in @ V_evs @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OGets @ V_S_H @ ( c_Message_Omsg_OMPair @ V_X_H @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ V_B_H ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ V_A_H ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ V_NA_H ) @ V_nb ) ) ) ) ) @ ( c_List_Oset @ V_evs @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ V_C @ V_S @ ( c_Message_Omsg_OMPair @ V_X @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ V_B ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ V_A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ V_NA ) @ V_nb ) ) ) ) ) @ ( c_List_Oset @ V_evs @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ V_nb @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ V_evs ) ) @ tc_Message_Omsg )
| ( V_NA_H = V_NA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Yahalom_OSays__unique__NB_0) ).
thf(3,axiom,
! [V_evs: $i,V_A: $i,V_B: $i,V_k: $i,V_na: $i,V_nb: $i,V_X: $i] :
( ~ ( c_in @ V_evs @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ V_A @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ V_A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ V_B ) @ ( c_Message_Omsg_OMPair @ V_k @ ( c_Message_Omsg_OMPair @ V_na @ V_nb ) ) ) ) @ V_X ) ) @ ( c_List_Oset @ V_evs @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ ( c_Event_Oevent_OGets @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ V_B ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ V_B ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ V_A ) @ ( c_Message_Omsg_OMPair @ V_na @ V_nb ) ) ) ) ) @ ( c_List_Oset @ V_evs @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Yahalom_OSays__Server__imp__YM2_0) ).
thf(4,axiom,
! [V_evs: $i,V_A: $i,V_B: $i,V_KAB: $i,V_na: $i,V_NB_H: $i,V_X: $i,V_NB: $i] :
( ~ ( c_in @ V_evs @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ V_A @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ V_A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ V_B ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ V_KAB ) @ ( c_Message_Omsg_OMPair @ V_na @ ( c_Message_Omsg_ONonce @ V_NB_H ) ) ) ) ) @ V_X ) ) @ ( c_List_Oset @ V_evs @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Message_Omsg_ONonce @ V_NB ) @ ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OKey @ V_KAB ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ V_evs ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_ONonce @ V_NB ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ V_evs ) ) @ tc_Message_Omsg )
| ( V_NB = V_NB_H )
| ( V_KAB
= ( c_Public_OshrK @ ( v_sko__2VY @ V_KAB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Yahalom_Osingle__Nonce__secrecy_0) ).
thf(5,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(6,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[5]) ).
thf(7,negated_conjecture,
! [V_U: $i] :
( ( V_U
!= ( c_Message_Omsg_OKey @ v_K ) )
| ( v_NA != v_NAa )
| ( v_NB != v_NBa ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_9) ).
thf(8,negated_conjecture,
c_in @ ( c_Message_Omsg_ONonce @ v_NB ) @ ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OKey @ v_K ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evso ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_7) ).
thf(9,negated_conjecture,
~ ( c_in @ ( c_Message_Omsg_ONonce @ v_NB ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evso ) ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).
thf(10,negated_conjecture,
c_in @ ( c_Event_Oevent_OSays @ v_B @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_B ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_B ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NA ) @ ( c_Message_Omsg_ONonce @ v_NB ) ) ) ) ) ) @ ( c_List_Oset @ v_evso @ tc_Event_Oevent ) @ tc_Event_Oevent,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
thf(11,negated_conjecture,
c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ v_Aa @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_Aa ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_Ba ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ v_K ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NAa ) @ ( c_Message_Omsg_ONonce @ v_NBa ) ) ) ) ) @ v_X ) ) @ ( c_List_Oset @ v_evso @ tc_Event_Oevent ) @ tc_Event_Oevent,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(12,negated_conjecture,
c_in @ v_evso @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(13,plain,
$false = $false,
inference(unfold_def,[status(thm)],[6]) ).
thf(14,plain,
( ( ! [V_evs: $i,V_A: $i,V_B: $i,V_x: $i,V_na: $i,V_nb: $i,V_X: $i] :
( ~ ( c_in @ V_evs @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ V_A @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ V_A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ V_B ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ V_x ) ) @ ( c_Message_Omsg_OMPair @ V_na @ V_nb ) ) ) ) @ V_X ) ) @ ( c_List_Oset @ V_evs @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(15,plain,
( ( ! [V_evs: $i,V_S_H: $i,V_X_H: $i,V_B_H: $i,V_A_H: $i,V_NA_H: $i,V_nb: $i,V_C: $i,V_S: $i,V_X: $i,V_B: $i,V_A: $i,V_NA: $i] :
( ~ ( c_in @ V_evs @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OGets @ V_S_H @ ( c_Message_Omsg_OMPair @ V_X_H @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ V_B_H ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ V_A_H ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ V_NA_H ) @ V_nb ) ) ) ) ) @ ( c_List_Oset @ V_evs @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ V_C @ V_S @ ( c_Message_Omsg_OMPair @ V_X @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ V_B ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ V_A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ V_NA ) @ V_nb ) ) ) ) ) @ ( c_List_Oset @ V_evs @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ V_nb @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ V_evs ) ) @ tc_Message_Omsg )
| ( V_NA_H = V_NA ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(16,plain,
( ( ! [V_evs: $i,V_A: $i,V_B: $i,V_k: $i,V_na: $i,V_nb: $i,V_X: $i] :
( ~ ( c_in @ V_evs @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ V_A @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ V_A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ V_B ) @ ( c_Message_Omsg_OMPair @ V_k @ ( c_Message_Omsg_OMPair @ V_na @ V_nb ) ) ) ) @ V_X ) ) @ ( c_List_Oset @ V_evs @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ ( c_Event_Oevent_OGets @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ V_B ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ V_B ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ V_A ) @ ( c_Message_Omsg_OMPair @ V_na @ V_nb ) ) ) ) ) @ ( c_List_Oset @ V_evs @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(17,plain,
( ( ! [V_evs: $i,V_A: $i,V_B: $i,V_KAB: $i,V_na: $i,V_NB_H: $i,V_X: $i,V_NB: $i] :
( ~ ( c_in @ V_evs @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ V_A @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ V_A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ V_B ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ V_KAB ) @ ( c_Message_Omsg_OMPair @ V_na @ ( c_Message_Omsg_ONonce @ V_NB_H ) ) ) ) ) @ V_X ) ) @ ( c_List_Oset @ V_evs @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Message_Omsg_ONonce @ V_NB ) @ ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OKey @ V_KAB ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ V_evs ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_ONonce @ V_NB ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ V_evs ) ) @ tc_Message_Omsg )
| ( V_NB = V_NB_H )
| ( V_KAB
= ( c_Public_OshrK @ ( v_sko__2VY @ V_KAB ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(18,plain,
( ( ! [V_U: $i] :
( ( V_U
!= ( c_Message_Omsg_OKey @ v_K ) )
| ( v_NA != v_NAa )
| ( v_NB != v_NBa ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(19,plain,
( ( c_in @ ( c_Message_Omsg_ONonce @ v_NB ) @ ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OKey @ v_K ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evso ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(20,plain,
( ( ~ ( c_in @ ( c_Message_Omsg_ONonce @ v_NB ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evso ) ) @ tc_Message_Omsg ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(21,plain,
( ( c_in @ ( c_Event_Oevent_OSays @ v_B @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_B ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_B ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NA ) @ ( c_Message_Omsg_ONonce @ v_NB ) ) ) ) ) ) @ ( c_List_Oset @ v_evso @ tc_Event_Oevent ) @ tc_Event_Oevent )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(22,plain,
( ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ v_Aa @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_Aa ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_Ba ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ v_K ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NAa ) @ ( c_Message_Omsg_ONonce @ v_NBa ) ) ) ) ) @ v_X ) ) @ ( c_List_Oset @ v_evso @ tc_Event_Oevent ) @ tc_Event_Oevent )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(23,plain,
( ( c_in @ v_evso @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(24,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[13]) ).
thf(25,plain,
( ( c_in @ v_evso @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(26,plain,
( ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ v_Aa @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_Aa ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_Ba ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ v_K ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NAa ) @ ( c_Message_Omsg_ONonce @ v_NBa ) ) ) ) ) @ v_X ) ) @ ( c_List_Oset @ v_evso @ tc_Event_Oevent ) @ tc_Event_Oevent )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(27,plain,
( ( c_in @ ( c_Event_Oevent_OSays @ v_B @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_B ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_B ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NA ) @ ( c_Message_Omsg_ONonce @ v_NB ) ) ) ) ) ) @ ( c_List_Oset @ v_evso @ tc_Event_Oevent ) @ tc_Event_Oevent )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(28,plain,
( ( ~ ( c_in @ ( c_Message_Omsg_ONonce @ v_NB ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evso ) ) @ tc_Message_Omsg ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(29,plain,
( ( c_in @ ( c_Message_Omsg_ONonce @ v_NB ) @ ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OKey @ v_K ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evso ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(30,plain,
( ( ! [V_U: $i] :
( ( V_U
!= ( c_Message_Omsg_OKey @ v_K ) )
| ( v_NA != v_NAa )
| ( v_NB != v_NBa ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(31,plain,
( ( ! [V_evs: $i,V_A: $i,V_B: $i,V_KAB: $i,V_na: $i,V_NB_H: $i,V_X: $i,V_NB: $i] :
( ~ ( c_in @ V_evs @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ V_A @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ V_A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ V_B ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ V_KAB ) @ ( c_Message_Omsg_OMPair @ V_na @ ( c_Message_Omsg_ONonce @ V_NB_H ) ) ) ) ) @ V_X ) ) @ ( c_List_Oset @ V_evs @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Message_Omsg_ONonce @ V_NB ) @ ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OKey @ V_KAB ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ V_evs ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_ONonce @ V_NB ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ V_evs ) ) @ tc_Message_Omsg )
| ( V_NB = V_NB_H )
| ( V_KAB
= ( c_Public_OshrK @ ( v_sko__2VY @ V_KAB ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(32,plain,
( ( ! [V_evs: $i,V_A: $i,V_B: $i,V_k: $i,V_na: $i,V_nb: $i,V_X: $i] :
( ~ ( c_in @ V_evs @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ V_A @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ V_A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ V_B ) @ ( c_Message_Omsg_OMPair @ V_k @ ( c_Message_Omsg_OMPair @ V_na @ V_nb ) ) ) ) @ V_X ) ) @ ( c_List_Oset @ V_evs @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ ( c_Event_Oevent_OGets @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ V_B ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ V_B ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ V_A ) @ ( c_Message_Omsg_OMPair @ V_na @ V_nb ) ) ) ) ) @ ( c_List_Oset @ V_evs @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(33,plain,
( ( ! [V_evs: $i,V_S_H: $i,V_X_H: $i,V_B_H: $i,V_A_H: $i,V_NA_H: $i,V_nb: $i,V_C: $i,V_S: $i,V_X: $i,V_B: $i,V_A: $i,V_NA: $i] :
( ~ ( c_in @ V_evs @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OGets @ V_S_H @ ( c_Message_Omsg_OMPair @ V_X_H @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ V_B_H ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ V_A_H ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ V_NA_H ) @ V_nb ) ) ) ) ) @ ( c_List_Oset @ V_evs @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ V_C @ V_S @ ( c_Message_Omsg_OMPair @ V_X @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ V_B ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ V_A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ V_NA ) @ V_nb ) ) ) ) ) @ ( c_List_Oset @ V_evs @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ V_nb @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ V_evs ) ) @ tc_Message_Omsg )
| ( V_NA_H = V_NA ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(34,plain,
( ( ! [V_evs: $i,V_A: $i,V_B: $i,V_x: $i,V_na: $i,V_nb: $i,V_X: $i] :
( ~ ( c_in @ V_evs @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ V_A @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ V_A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ V_B ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ V_x ) ) @ ( c_Message_Omsg_OMPair @ V_na @ V_nb ) ) ) ) @ V_X ) ) @ ( c_List_Oset @ V_evs @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(35,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[24]) ).
thf(36,plain,
( ( ! [SX0: $i] :
( ( SX0
!= ( c_Message_Omsg_OKey @ v_K ) )
| ( v_NA != v_NAa )
| ( v_NB != v_NBa ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(37,plain,
( ( c_in @ ( c_Message_Omsg_ONonce @ v_NB ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evso ) ) @ tc_Message_Omsg )
= $false ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(38,plain,
! [SV1: $i] :
( ( ! [SY36: $i,SY37: $i,SY38: $i,SY39: $i,SY40: $i,SY41: $i,SY42: $i] :
( ~ ( c_in @ SV1 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SY36 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SY36 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY37 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ SY38 ) @ ( c_Message_Omsg_OMPair @ SY39 @ ( c_Message_Omsg_ONonce @ SY40 ) ) ) ) ) @ SY41 ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Message_Omsg_ONonce @ SY42 ) @ ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OKey @ SY38 ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV1 ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_ONonce @ SY42 ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV1 ) ) @ tc_Message_Omsg )
| ( SY42 = SY40 )
| ( SY38
= ( c_Public_OshrK @ ( v_sko__2VY @ SY38 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(39,plain,
! [SV2: $i] :
( ( ! [SY43: $i,SY44: $i,SY45: $i,SY46: $i,SY47: $i,SY48: $i] :
( ~ ( c_in @ SV2 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SY43 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SY43 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY44 ) @ ( c_Message_Omsg_OMPair @ SY45 @ ( c_Message_Omsg_OMPair @ SY46 @ SY47 ) ) ) ) @ SY48 ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ ( c_Event_Oevent_OGets @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY44 ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SY44 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY43 ) @ ( c_Message_Omsg_OMPair @ SY46 @ SY47 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(40,plain,
! [SV3: $i] :
( ( ! [SY49: $i,SY50: $i,SY51: $i,SY52: $i,SY53: $i,SY54: $i,SY55: $i,SY56: $i,SY57: $i,SY58: $i,SY59: $i,SY60: $i] :
( ~ ( c_in @ SV3 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OGets @ SY49 @ ( c_Message_Omsg_OMPair @ SY50 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SY51 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY52 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SY53 ) @ SY54 ) ) ) ) ) @ ( c_List_Oset @ SV3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ SY55 @ SY56 @ ( c_Message_Omsg_OMPair @ SY57 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SY58 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY59 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SY60 ) @ SY54 ) ) ) ) ) @ ( c_List_Oset @ SV3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ SY54 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV3 ) ) @ tc_Message_Omsg )
| ( SY53 = SY60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(41,plain,
! [SV4: $i] :
( ( ! [SY61: $i,SY62: $i,SY63: $i,SY64: $i,SY65: $i,SY66: $i] :
( ~ ( c_in @ SV4 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SY61 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SY61 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY62 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ SY63 ) ) @ ( c_Message_Omsg_OMPair @ SY64 @ SY65 ) ) ) ) @ SY66 ) ) @ ( c_List_Oset @ SV4 @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(42,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(43,plain,
! [SV5: $i] :
( ( ( SV5
!= ( c_Message_Omsg_OKey @ v_K ) )
| ( v_NA != v_NAa )
| ( v_NB != v_NBa ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(44,plain,
! [SV6: $i,SV1: $i] :
( ( ! [SY67: $i,SY68: $i,SY69: $i,SY70: $i,SY71: $i,SY72: $i] :
( ~ ( c_in @ SV1 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV6 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV6 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY67 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ SY68 ) @ ( c_Message_Omsg_OMPair @ SY69 @ ( c_Message_Omsg_ONonce @ SY70 ) ) ) ) ) @ SY71 ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Message_Omsg_ONonce @ SY72 ) @ ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OKey @ SY68 ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV1 ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_ONonce @ SY72 ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV1 ) ) @ tc_Message_Omsg )
| ( SY72 = SY70 )
| ( SY68
= ( c_Public_OshrK @ ( v_sko__2VY @ SY68 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(45,plain,
! [SV7: $i,SV2: $i] :
( ( ! [SY73: $i,SY74: $i,SY75: $i,SY76: $i,SY77: $i] :
( ~ ( c_in @ SV2 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV7 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV7 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY73 ) @ ( c_Message_Omsg_OMPair @ SY74 @ ( c_Message_Omsg_OMPair @ SY75 @ SY76 ) ) ) ) @ SY77 ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ ( c_Event_Oevent_OGets @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY73 ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SY73 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV7 ) @ ( c_Message_Omsg_OMPair @ SY75 @ SY76 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(46,plain,
! [SV8: $i,SV3: $i] :
( ( ! [SY78: $i,SY79: $i,SY80: $i,SY81: $i,SY82: $i,SY83: $i,SY84: $i,SY85: $i,SY86: $i,SY87: $i,SY88: $i] :
( ~ ( c_in @ SV3 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OGets @ SV8 @ ( c_Message_Omsg_OMPair @ SY78 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SY79 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY80 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SY81 ) @ SY82 ) ) ) ) ) @ ( c_List_Oset @ SV3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ SY83 @ SY84 @ ( c_Message_Omsg_OMPair @ SY85 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SY86 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY87 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SY88 ) @ SY82 ) ) ) ) ) @ ( c_List_Oset @ SV3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ SY82 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV3 ) ) @ tc_Message_Omsg )
| ( SY81 = SY88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(47,plain,
! [SV9: $i,SV4: $i] :
( ( ! [SY89: $i,SY90: $i,SY91: $i,SY92: $i,SY93: $i] :
( ~ ( c_in @ SV4 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV9 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV9 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY89 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ SY90 ) ) @ ( c_Message_Omsg_OMPair @ SY91 @ SY92 ) ) ) ) @ SY93 ) ) @ ( c_List_Oset @ SV4 @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(48,plain,
! [SV5: $i] :
( ( ( SV5
!= ( c_Message_Omsg_OKey @ v_K ) )
= $true )
| ( ( ( v_NA != v_NAa )
| ( v_NB != v_NBa ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(49,plain,
! [SV10: $i,SV6: $i,SV1: $i] :
( ( ! [SY94: $i,SY95: $i,SY96: $i,SY97: $i,SY98: $i] :
( ~ ( c_in @ SV1 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV6 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV6 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV10 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ SY94 ) @ ( c_Message_Omsg_OMPair @ SY95 @ ( c_Message_Omsg_ONonce @ SY96 ) ) ) ) ) @ SY97 ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Message_Omsg_ONonce @ SY98 ) @ ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OKey @ SY94 ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV1 ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_ONonce @ SY98 ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV1 ) ) @ tc_Message_Omsg )
| ( SY98 = SY96 )
| ( SY94
= ( c_Public_OshrK @ ( v_sko__2VY @ SY94 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(50,plain,
! [SV11: $i,SV7: $i,SV2: $i] :
( ( ! [SY99: $i,SY100: $i,SY101: $i,SY102: $i] :
( ~ ( c_in @ SV2 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV7 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV7 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV11 ) @ ( c_Message_Omsg_OMPair @ SY99 @ ( c_Message_Omsg_OMPair @ SY100 @ SY101 ) ) ) ) @ SY102 ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ ( c_Event_Oevent_OGets @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV11 ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV11 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV7 ) @ ( c_Message_Omsg_OMPair @ SY100 @ SY101 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(51,plain,
! [SV12: $i,SV8: $i,SV3: $i] :
( ( ! [SY103: $i,SY104: $i,SY105: $i,SY106: $i,SY107: $i,SY108: $i,SY109: $i,SY110: $i,SY111: $i,SY112: $i] :
( ~ ( c_in @ SV3 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OGets @ SV8 @ ( c_Message_Omsg_OMPair @ SV12 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SY103 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY104 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SY105 ) @ SY106 ) ) ) ) ) @ ( c_List_Oset @ SV3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ SY107 @ SY108 @ ( c_Message_Omsg_OMPair @ SY109 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SY110 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY111 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SY112 ) @ SY106 ) ) ) ) ) @ ( c_List_Oset @ SV3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ SY106 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV3 ) ) @ tc_Message_Omsg )
| ( SY105 = SY112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(52,plain,
! [SV13: $i,SV9: $i,SV4: $i] :
( ( ! [SY113: $i,SY114: $i,SY115: $i,SY116: $i] :
( ~ ( c_in @ SV4 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV9 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV9 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV13 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ SY113 ) ) @ ( c_Message_Omsg_OMPair @ SY114 @ SY115 ) ) ) ) @ SY116 ) ) @ ( c_List_Oset @ SV4 @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(53,plain,
! [SV5: $i] :
( ( ( SV5
= ( c_Message_Omsg_OKey @ v_K ) )
= $false )
| ( ( ( v_NA != v_NAa )
| ( v_NB != v_NBa ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(54,plain,
! [SV14: $i,SV10: $i,SV6: $i,SV1: $i] :
( ( ! [SY117: $i,SY118: $i,SY119: $i,SY120: $i] :
( ~ ( c_in @ SV1 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV6 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV6 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV10 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ SV14 ) @ ( c_Message_Omsg_OMPair @ SY117 @ ( c_Message_Omsg_ONonce @ SY118 ) ) ) ) ) @ SY119 ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Message_Omsg_ONonce @ SY120 ) @ ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OKey @ SV14 ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV1 ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_ONonce @ SY120 ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV1 ) ) @ tc_Message_Omsg )
| ( SY120 = SY118 )
| ( SV14
= ( c_Public_OshrK @ ( v_sko__2VY @ SV14 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(55,plain,
! [SV15: $i,SV11: $i,SV7: $i,SV2: $i] :
( ( ! [SY121: $i,SY122: $i,SY123: $i] :
( ~ ( c_in @ SV2 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV7 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV7 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV11 ) @ ( c_Message_Omsg_OMPair @ SV15 @ ( c_Message_Omsg_OMPair @ SY121 @ SY122 ) ) ) ) @ SY123 ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ ( c_Event_Oevent_OGets @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV11 ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV11 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV7 ) @ ( c_Message_Omsg_OMPair @ SY121 @ SY122 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(56,plain,
! [SV16: $i,SV12: $i,SV8: $i,SV3: $i] :
( ( ! [SY124: $i,SY125: $i,SY126: $i,SY127: $i,SY128: $i,SY129: $i,SY130: $i,SY131: $i,SY132: $i] :
( ~ ( c_in @ SV3 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OGets @ SV8 @ ( c_Message_Omsg_OMPair @ SV12 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV16 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY124 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SY125 ) @ SY126 ) ) ) ) ) @ ( c_List_Oset @ SV3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ SY127 @ SY128 @ ( c_Message_Omsg_OMPair @ SY129 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SY130 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY131 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SY132 ) @ SY126 ) ) ) ) ) @ ( c_List_Oset @ SV3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ SY126 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV3 ) ) @ tc_Message_Omsg )
| ( SY125 = SY132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(57,plain,
! [SV17: $i,SV13: $i,SV9: $i,SV4: $i] :
( ( ! [SY133: $i,SY134: $i,SY135: $i] :
( ~ ( c_in @ SV4 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV9 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV9 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV13 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ SV17 ) ) @ ( c_Message_Omsg_OMPair @ SY133 @ SY134 ) ) ) ) @ SY135 ) ) @ ( c_List_Oset @ SV4 @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(58,plain,
! [SV5: $i] :
( ( ( v_NA != v_NAa )
= $true )
| ( ( v_NB != v_NBa )
= $true )
| ( ( SV5
= ( c_Message_Omsg_OKey @ v_K ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[53]) ).
thf(59,plain,
! [SV18: $i,SV14: $i,SV10: $i,SV6: $i,SV1: $i] :
( ( ! [SY136: $i,SY137: $i,SY138: $i] :
( ~ ( c_in @ SV1 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV6 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV6 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV10 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ SV14 ) @ ( c_Message_Omsg_OMPair @ SV18 @ ( c_Message_Omsg_ONonce @ SY136 ) ) ) ) ) @ SY137 ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Message_Omsg_ONonce @ SY138 ) @ ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OKey @ SV14 ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV1 ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_ONonce @ SY138 ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV1 ) ) @ tc_Message_Omsg )
| ( SY138 = SY136 )
| ( SV14
= ( c_Public_OshrK @ ( v_sko__2VY @ SV14 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(60,plain,
! [SV19: $i,SV15: $i,SV11: $i,SV7: $i,SV2: $i] :
( ( ! [SY139: $i,SY140: $i] :
( ~ ( c_in @ SV2 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV7 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV7 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV11 ) @ ( c_Message_Omsg_OMPair @ SV15 @ ( c_Message_Omsg_OMPair @ SV19 @ SY139 ) ) ) ) @ SY140 ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ ( c_Event_Oevent_OGets @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV11 ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV11 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV7 ) @ ( c_Message_Omsg_OMPair @ SV19 @ SY139 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(61,plain,
! [SV20: $i,SV16: $i,SV12: $i,SV8: $i,SV3: $i] :
( ( ! [SY141: $i,SY142: $i,SY143: $i,SY144: $i,SY145: $i,SY146: $i,SY147: $i,SY148: $i] :
( ~ ( c_in @ SV3 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OGets @ SV8 @ ( c_Message_Omsg_OMPair @ SV12 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV16 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV20 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SY141 ) @ SY142 ) ) ) ) ) @ ( c_List_Oset @ SV3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ SY143 @ SY144 @ ( c_Message_Omsg_OMPair @ SY145 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SY146 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY147 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SY148 ) @ SY142 ) ) ) ) ) @ ( c_List_Oset @ SV3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ SY142 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV3 ) ) @ tc_Message_Omsg )
| ( SY141 = SY148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(62,plain,
! [SV21: $i,SV17: $i,SV13: $i,SV9: $i,SV4: $i] :
( ( ! [SY149: $i,SY150: $i] :
( ~ ( c_in @ SV4 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV9 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV9 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV13 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ SV17 ) ) @ ( c_Message_Omsg_OMPair @ SV21 @ SY149 ) ) ) ) @ SY150 ) ) @ ( c_List_Oset @ SV4 @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(63,plain,
! [SV5: $i] :
( ( ( v_NA = v_NAa )
= $false )
| ( ( v_NB != v_NBa )
= $true )
| ( ( SV5
= ( c_Message_Omsg_OKey @ v_K ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(64,plain,
! [SV22: $i,SV18: $i,SV14: $i,SV10: $i,SV6: $i,SV1: $i] :
( ( ! [SY151: $i,SY152: $i] :
( ~ ( c_in @ SV1 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV6 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV6 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV10 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ SV14 ) @ ( c_Message_Omsg_OMPair @ SV18 @ ( c_Message_Omsg_ONonce @ SV22 ) ) ) ) ) @ SY151 ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Message_Omsg_ONonce @ SY152 ) @ ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OKey @ SV14 ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV1 ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_ONonce @ SY152 ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV1 ) ) @ tc_Message_Omsg )
| ( SY152 = SV22 )
| ( SV14
= ( c_Public_OshrK @ ( v_sko__2VY @ SV14 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(65,plain,
! [SV23: $i,SV19: $i,SV15: $i,SV11: $i,SV7: $i,SV2: $i] :
( ( ! [SY153: $i] :
( ~ ( c_in @ SV2 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV7 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV7 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV11 ) @ ( c_Message_Omsg_OMPair @ SV15 @ ( c_Message_Omsg_OMPair @ SV19 @ SV23 ) ) ) ) @ SY153 ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ ( c_Event_Oevent_OGets @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV11 ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV11 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV7 ) @ ( c_Message_Omsg_OMPair @ SV19 @ SV23 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(66,plain,
! [SV24: $i,SV20: $i,SV16: $i,SV12: $i,SV8: $i,SV3: $i] :
( ( ! [SY154: $i,SY155: $i,SY156: $i,SY157: $i,SY158: $i,SY159: $i,SY160: $i] :
( ~ ( c_in @ SV3 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OGets @ SV8 @ ( c_Message_Omsg_OMPair @ SV12 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV16 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV20 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SV24 ) @ SY154 ) ) ) ) ) @ ( c_List_Oset @ SV3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ SY155 @ SY156 @ ( c_Message_Omsg_OMPair @ SY157 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SY158 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY159 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SY160 ) @ SY154 ) ) ) ) ) @ ( c_List_Oset @ SV3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ SY154 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV3 ) ) @ tc_Message_Omsg )
| ( SV24 = SY160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(67,plain,
! [SV25: $i,SV21: $i,SV17: $i,SV13: $i,SV9: $i,SV4: $i] :
( ( ! [SY161: $i] :
( ~ ( c_in @ SV4 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV9 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV9 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV13 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ SV17 ) ) @ ( c_Message_Omsg_OMPair @ SV21 @ SV25 ) ) ) ) @ SY161 ) ) @ ( c_List_Oset @ SV4 @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(68,plain,
! [SV5: $i] :
( ( ( v_NB = v_NBa )
= $false )
| ( ( v_NA = v_NAa )
= $false )
| ( ( SV5
= ( c_Message_Omsg_OKey @ v_K ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(69,plain,
! [SV26: $i,SV22: $i,SV18: $i,SV14: $i,SV10: $i,SV6: $i,SV1: $i] :
( ( ! [SY162: $i] :
( ~ ( c_in @ SV1 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV6 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV6 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV10 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ SV14 ) @ ( c_Message_Omsg_OMPair @ SV18 @ ( c_Message_Omsg_ONonce @ SV22 ) ) ) ) ) @ SV26 ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Message_Omsg_ONonce @ SY162 ) @ ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OKey @ SV14 ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV1 ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_ONonce @ SY162 ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV1 ) ) @ tc_Message_Omsg )
| ( SY162 = SV22 )
| ( SV14
= ( c_Public_OshrK @ ( v_sko__2VY @ SV14 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(70,plain,
! [SV27: $i,SV23: $i,SV19: $i,SV15: $i,SV11: $i,SV7: $i,SV2: $i] :
( ( ~ ( c_in @ SV2 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV7 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV7 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV11 ) @ ( c_Message_Omsg_OMPair @ SV15 @ ( c_Message_Omsg_OMPair @ SV19 @ SV23 ) ) ) ) @ SV27 ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ ( c_Event_Oevent_OGets @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV11 ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV11 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV7 ) @ ( c_Message_Omsg_OMPair @ SV19 @ SV23 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(71,plain,
! [SV28: $i,SV24: $i,SV20: $i,SV16: $i,SV12: $i,SV8: $i,SV3: $i] :
( ( ! [SY163: $i,SY164: $i,SY165: $i,SY166: $i,SY167: $i,SY168: $i] :
( ~ ( c_in @ SV3 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OGets @ SV8 @ ( c_Message_Omsg_OMPair @ SV12 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV16 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV20 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SV24 ) @ SV28 ) ) ) ) ) @ ( c_List_Oset @ SV3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ SY163 @ SY164 @ ( c_Message_Omsg_OMPair @ SY165 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SY166 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY167 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SY168 ) @ SV28 ) ) ) ) ) @ ( c_List_Oset @ SV3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ SV28 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV3 ) ) @ tc_Message_Omsg )
| ( SV24 = SY168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(72,plain,
! [SV29: $i,SV25: $i,SV21: $i,SV17: $i,SV13: $i,SV9: $i,SV4: $i] :
( ( ~ ( c_in @ SV4 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV9 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV9 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV13 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ SV17 ) ) @ ( c_Message_Omsg_OMPair @ SV21 @ SV25 ) ) ) ) @ SV29 ) ) @ ( c_List_Oset @ SV4 @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(73,plain,
! [SV30: $i,SV26: $i,SV22: $i,SV18: $i,SV14: $i,SV10: $i,SV6: $i,SV1: $i] :
( ( ~ ( c_in @ SV1 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV6 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV6 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV10 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ SV14 ) @ ( c_Message_Omsg_OMPair @ SV18 @ ( c_Message_Omsg_ONonce @ SV22 ) ) ) ) ) @ SV26 ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Message_Omsg_ONonce @ SV30 ) @ ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OKey @ SV14 ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV1 ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_ONonce @ SV30 ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV1 ) ) @ tc_Message_Omsg )
| ( SV30 = SV22 )
| ( SV14
= ( c_Public_OshrK @ ( v_sko__2VY @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(74,plain,
! [SV27: $i,SV23: $i,SV19: $i,SV15: $i,SV11: $i,SV7: $i,SV2: $i] :
( ( ( ~ ( c_in @ SV2 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV7 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV7 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV11 ) @ ( c_Message_Omsg_OMPair @ SV15 @ ( c_Message_Omsg_OMPair @ SV19 @ SV23 ) ) ) ) @ SV27 ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ ( c_Event_Oevent_OGets @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV11 ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV11 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV7 ) @ ( c_Message_Omsg_OMPair @ SV19 @ SV23 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(75,plain,
! [SV31: $i,SV28: $i,SV24: $i,SV20: $i,SV16: $i,SV12: $i,SV8: $i,SV3: $i] :
( ( ! [SY169: $i,SY170: $i,SY171: $i,SY172: $i,SY173: $i] :
( ~ ( c_in @ SV3 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OGets @ SV8 @ ( c_Message_Omsg_OMPair @ SV12 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV16 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV20 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SV24 ) @ SV28 ) ) ) ) ) @ ( c_List_Oset @ SV3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ SV31 @ SY169 @ ( c_Message_Omsg_OMPair @ SY170 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SY171 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY172 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SY173 ) @ SV28 ) ) ) ) ) @ ( c_List_Oset @ SV3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ SV28 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV3 ) ) @ tc_Message_Omsg )
| ( SV24 = SY173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(76,plain,
! [SV29: $i,SV25: $i,SV21: $i,SV17: $i,SV13: $i,SV9: $i,SV4: $i] :
( ( ( ~ ( c_in @ SV4 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV9 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV9 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV13 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ SV17 ) ) @ ( c_Message_Omsg_OMPair @ SV21 @ SV25 ) ) ) ) @ SV29 ) ) @ ( c_List_Oset @ SV4 @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(77,plain,
! [SV30: $i,SV26: $i,SV22: $i,SV18: $i,SV14: $i,SV10: $i,SV6: $i,SV1: $i] :
( ( ( ~ ( c_in @ SV1 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV6 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV6 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV10 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ SV14 ) @ ( c_Message_Omsg_OMPair @ SV18 @ ( c_Message_Omsg_ONonce @ SV22 ) ) ) ) ) @ SV26 ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Message_Omsg_ONonce @ SV30 ) @ ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OKey @ SV14 ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV1 ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_ONonce @ SV30 ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV1 ) ) @ tc_Message_Omsg )
| ( SV30 = SV22 )
| ( SV14
= ( c_Public_OshrK @ ( v_sko__2VY @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(78,plain,
! [SV27: $i,SV23: $i,SV19: $i,SV15: $i,SV11: $i,SV7: $i,SV2: $i] :
( ( ( c_in @ SV2 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $false )
| ( ( ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV7 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV7 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV11 ) @ ( c_Message_Omsg_OMPair @ SV15 @ ( c_Message_Omsg_OMPair @ SV19 @ SV23 ) ) ) ) @ SV27 ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ ( c_Event_Oevent_OGets @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV11 ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV11 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV7 ) @ ( c_Message_Omsg_OMPair @ SV19 @ SV23 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(79,plain,
! [SV32: $i,SV31: $i,SV28: $i,SV24: $i,SV20: $i,SV16: $i,SV12: $i,SV8: $i,SV3: $i] :
( ( ! [SY174: $i,SY175: $i,SY176: $i,SY177: $i] :
( ~ ( c_in @ SV3 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OGets @ SV8 @ ( c_Message_Omsg_OMPair @ SV12 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV16 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV20 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SV24 ) @ SV28 ) ) ) ) ) @ ( c_List_Oset @ SV3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ SV31 @ SV32 @ ( c_Message_Omsg_OMPair @ SY174 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SY175 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY176 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SY177 ) @ SV28 ) ) ) ) ) @ ( c_List_Oset @ SV3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ SV28 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV3 ) ) @ tc_Message_Omsg )
| ( SV24 = SY177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(80,plain,
! [SV29: $i,SV25: $i,SV21: $i,SV17: $i,SV13: $i,SV9: $i,SV4: $i] :
( ( ( c_in @ SV4 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $false )
| ( ( ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV9 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV9 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV13 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ SV17 ) ) @ ( c_Message_Omsg_OMPair @ SV21 @ SV25 ) ) ) ) @ SV29 ) ) @ ( c_List_Oset @ SV4 @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(81,plain,
! [SV30: $i,SV26: $i,SV22: $i,SV18: $i,SV14: $i,SV10: $i,SV6: $i,SV1: $i] :
( ( ( c_in @ SV1 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $false )
| ( ( ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV6 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV6 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV10 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ SV14 ) @ ( c_Message_Omsg_OMPair @ SV18 @ ( c_Message_Omsg_ONonce @ SV22 ) ) ) ) ) @ SV26 ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Message_Omsg_ONonce @ SV30 ) @ ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OKey @ SV14 ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV1 ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_ONonce @ SV30 ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV1 ) ) @ tc_Message_Omsg )
| ( SV30 = SV22 )
| ( SV14
= ( c_Public_OshrK @ ( v_sko__2VY @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(82,plain,
! [SV2: $i,SV27: $i,SV23: $i,SV19: $i,SV15: $i,SV11: $i,SV7: $i] :
( ( ( ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV7 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV7 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV11 ) @ ( c_Message_Omsg_OMPair @ SV15 @ ( c_Message_Omsg_OMPair @ SV19 @ SV23 ) ) ) ) @ SV27 ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
= $true )
| ( ( c_in @ ( c_Event_Oevent_OGets @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV11 ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV11 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV7 ) @ ( c_Message_Omsg_OMPair @ SV19 @ SV23 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
= $true )
| ( ( c_in @ SV2 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[78]) ).
thf(83,plain,
! [SV33: $i,SV32: $i,SV31: $i,SV28: $i,SV24: $i,SV20: $i,SV16: $i,SV12: $i,SV8: $i,SV3: $i] :
( ( ! [SY178: $i,SY179: $i,SY180: $i] :
( ~ ( c_in @ SV3 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OGets @ SV8 @ ( c_Message_Omsg_OMPair @ SV12 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV16 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV20 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SV24 ) @ SV28 ) ) ) ) ) @ ( c_List_Oset @ SV3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ SV31 @ SV32 @ ( c_Message_Omsg_OMPair @ SV33 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SY178 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY179 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SY180 ) @ SV28 ) ) ) ) ) @ ( c_List_Oset @ SV3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ SV28 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV3 ) ) @ tc_Message_Omsg )
| ( SV24 = SY180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(84,plain,
! [SV4: $i,SV29: $i,SV25: $i,SV21: $i,SV17: $i,SV13: $i,SV9: $i] :
( ( ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV9 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV9 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV13 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ SV17 ) ) @ ( c_Message_Omsg_OMPair @ SV21 @ SV25 ) ) ) ) @ SV29 ) ) @ ( c_List_Oset @ SV4 @ tc_Event_Oevent ) @ tc_Event_Oevent )
= $false )
| ( ( c_in @ SV4 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(85,plain,
! [SV30: $i,SV1: $i,SV26: $i,SV22: $i,SV18: $i,SV14: $i,SV10: $i,SV6: $i] :
( ( ( ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV6 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV6 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV10 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ SV14 ) @ ( c_Message_Omsg_OMPair @ SV18 @ ( c_Message_Omsg_ONonce @ SV22 ) ) ) ) ) @ SV26 ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
= $true )
| ( ( ~ ( c_in @ ( c_Message_Omsg_ONonce @ SV30 ) @ ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OKey @ SV14 ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV1 ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_ONonce @ SV30 ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV1 ) ) @ tc_Message_Omsg )
| ( SV30 = SV22 )
| ( SV14
= ( c_Public_OshrK @ ( v_sko__2VY @ SV14 ) ) ) )
= $true )
| ( ( c_in @ SV1 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[81]) ).
thf(86,plain,
! [SV2: $i,SV27: $i,SV23: $i,SV19: $i,SV15: $i,SV11: $i,SV7: $i] :
( ( ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV7 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV7 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV11 ) @ ( c_Message_Omsg_OMPair @ SV15 @ ( c_Message_Omsg_OMPair @ SV19 @ SV23 ) ) ) ) @ SV27 ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
= $false )
| ( ( c_in @ ( c_Event_Oevent_OGets @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV11 ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV11 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV7 ) @ ( c_Message_Omsg_OMPair @ SV19 @ SV23 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
= $true )
| ( ( c_in @ SV2 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(87,plain,
! [SV34: $i,SV33: $i,SV32: $i,SV31: $i,SV28: $i,SV24: $i,SV20: $i,SV16: $i,SV12: $i,SV8: $i,SV3: $i] :
( ( ! [SY181: $i,SY182: $i] :
( ~ ( c_in @ SV3 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OGets @ SV8 @ ( c_Message_Omsg_OMPair @ SV12 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV16 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV20 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SV24 ) @ SV28 ) ) ) ) ) @ ( c_List_Oset @ SV3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ SV31 @ SV32 @ ( c_Message_Omsg_OMPair @ SV33 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV34 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY181 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SY182 ) @ SV28 ) ) ) ) ) @ ( c_List_Oset @ SV3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ SV28 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV3 ) ) @ tc_Message_Omsg )
| ( SV24 = SY182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(88,plain,
! [SV30: $i,SV1: $i,SV26: $i,SV22: $i,SV18: $i,SV14: $i,SV10: $i,SV6: $i] :
( ( ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV6 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV6 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV10 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ SV14 ) @ ( c_Message_Omsg_OMPair @ SV18 @ ( c_Message_Omsg_ONonce @ SV22 ) ) ) ) ) @ SV26 ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent )
= $false )
| ( ( ~ ( c_in @ ( c_Message_Omsg_ONonce @ SV30 ) @ ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OKey @ SV14 ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV1 ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_ONonce @ SV30 ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV1 ) ) @ tc_Message_Omsg )
| ( SV30 = SV22 )
| ( SV14
= ( c_Public_OshrK @ ( v_sko__2VY @ SV14 ) ) ) )
= $true )
| ( ( c_in @ SV1 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(89,plain,
! [SV35: $i,SV34: $i,SV33: $i,SV32: $i,SV31: $i,SV28: $i,SV24: $i,SV20: $i,SV16: $i,SV12: $i,SV8: $i,SV3: $i] :
( ( ! [SY183: $i] :
( ~ ( c_in @ SV3 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OGets @ SV8 @ ( c_Message_Omsg_OMPair @ SV12 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV16 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV20 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SV24 ) @ SV28 ) ) ) ) ) @ ( c_List_Oset @ SV3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ SV31 @ SV32 @ ( c_Message_Omsg_OMPair @ SV33 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV34 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV35 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SY183 ) @ SV28 ) ) ) ) ) @ ( c_List_Oset @ SV3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ SV28 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV3 ) ) @ tc_Message_Omsg )
| ( SV24 = SY183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(90,plain,
! [SV26: $i,SV18: $i,SV10: $i,SV6: $i,SV22: $i,SV1: $i,SV14: $i,SV30: $i] :
( ( ( ~ ( c_in @ ( c_Message_Omsg_ONonce @ SV30 ) @ ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OKey @ SV14 ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV1 ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) )
= $true )
| ( ( ( c_in @ ( c_Message_Omsg_ONonce @ SV30 ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV1 ) ) @ tc_Message_Omsg )
| ( SV30 = SV22 )
| ( SV14
= ( c_Public_OshrK @ ( v_sko__2VY @ SV14 ) ) ) )
= $true )
| ( ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV6 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV6 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV10 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ SV14 ) @ ( c_Message_Omsg_OMPair @ SV18 @ ( c_Message_Omsg_ONonce @ SV22 ) ) ) ) ) @ SV26 ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent )
= $false )
| ( ( c_in @ SV1 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(91,plain,
! [SV36: $i,SV35: $i,SV34: $i,SV33: $i,SV32: $i,SV31: $i,SV28: $i,SV24: $i,SV20: $i,SV16: $i,SV12: $i,SV8: $i,SV3: $i] :
( ( ~ ( c_in @ SV3 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OGets @ SV8 @ ( c_Message_Omsg_OMPair @ SV12 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV16 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV20 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SV24 ) @ SV28 ) ) ) ) ) @ ( c_List_Oset @ SV3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ SV31 @ SV32 @ ( c_Message_Omsg_OMPair @ SV33 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV34 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV35 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SV36 ) @ SV28 ) ) ) ) ) @ ( c_List_Oset @ SV3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ SV28 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV3 ) ) @ tc_Message_Omsg )
| ( SV24 = SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(92,plain,
! [SV26: $i,SV18: $i,SV10: $i,SV6: $i,SV22: $i,SV1: $i,SV14: $i,SV30: $i] :
( ( ( c_in @ ( c_Message_Omsg_ONonce @ SV30 ) @ ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OKey @ SV14 ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV1 ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
= $false )
| ( ( ( c_in @ ( c_Message_Omsg_ONonce @ SV30 ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV1 ) ) @ tc_Message_Omsg )
| ( SV30 = SV22 )
| ( SV14
= ( c_Public_OshrK @ ( v_sko__2VY @ SV14 ) ) ) )
= $true )
| ( ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV6 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV6 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV10 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ SV14 ) @ ( c_Message_Omsg_OMPair @ SV18 @ ( c_Message_Omsg_ONonce @ SV22 ) ) ) ) ) @ SV26 ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent )
= $false )
| ( ( c_in @ SV1 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(93,plain,
! [SV36: $i,SV35: $i,SV34: $i,SV33: $i,SV32: $i,SV31: $i,SV28: $i,SV24: $i,SV20: $i,SV16: $i,SV12: $i,SV8: $i,SV3: $i] :
( ( ( ~ ( c_in @ SV3 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Event_Oevent_OGets @ SV8 @ ( c_Message_Omsg_OMPair @ SV12 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV16 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV20 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SV24 ) @ SV28 ) ) ) ) ) @ ( c_List_Oset @ SV3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ SV31 @ SV32 @ ( c_Message_Omsg_OMPair @ SV33 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV34 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV35 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SV36 ) @ SV28 ) ) ) ) ) @ ( c_List_Oset @ SV3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ SV28 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV3 ) ) @ tc_Message_Omsg )
| ( SV24 = SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(94,plain,
! [SV26: $i,SV18: $i,SV10: $i,SV6: $i,SV14: $i,SV22: $i,SV1: $i,SV30: $i] :
( ( ( c_in @ ( c_Message_Omsg_ONonce @ SV30 ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV1 ) ) @ tc_Message_Omsg )
= $true )
| ( ( ( SV30 = SV22 )
| ( SV14
= ( c_Public_OshrK @ ( v_sko__2VY @ SV14 ) ) ) )
= $true )
| ( ( c_in @ ( c_Message_Omsg_ONonce @ SV30 ) @ ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OKey @ SV14 ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV1 ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
= $false )
| ( ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV6 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV6 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV10 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ SV14 ) @ ( c_Message_Omsg_OMPair @ SV18 @ ( c_Message_Omsg_ONonce @ SV22 ) ) ) ) ) @ SV26 ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent )
= $false )
| ( ( c_in @ SV1 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(95,plain,
! [SV36: $i,SV35: $i,SV34: $i,SV33: $i,SV32: $i,SV31: $i,SV28: $i,SV24: $i,SV20: $i,SV16: $i,SV12: $i,SV8: $i,SV3: $i] :
( ( ( c_in @ SV3 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $false )
| ( ( ~ ( c_in @ ( c_Event_Oevent_OGets @ SV8 @ ( c_Message_Omsg_OMPair @ SV12 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV16 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV20 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SV24 ) @ SV28 ) ) ) ) ) @ ( c_List_Oset @ SV3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ SV31 @ SV32 @ ( c_Message_Omsg_OMPair @ SV33 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV34 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV35 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SV36 ) @ SV28 ) ) ) ) ) @ ( c_List_Oset @ SV3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ SV28 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV3 ) ) @ tc_Message_Omsg )
| ( SV24 = SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(96,plain,
! [SV26: $i,SV18: $i,SV10: $i,SV6: $i,SV1: $i,SV14: $i,SV22: $i,SV30: $i] :
( ( ( SV30 = SV22 )
= $true )
| ( ( SV14
= ( c_Public_OshrK @ ( v_sko__2VY @ SV14 ) ) )
= $true )
| ( ( c_in @ ( c_Message_Omsg_ONonce @ SV30 ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV1 ) ) @ tc_Message_Omsg )
= $true )
| ( ( c_in @ ( c_Message_Omsg_ONonce @ SV30 ) @ ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OKey @ SV14 ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV1 ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
= $false )
| ( ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV6 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV6 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV10 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ SV14 ) @ ( c_Message_Omsg_OMPair @ SV18 @ ( c_Message_Omsg_ONonce @ SV22 ) ) ) ) ) @ SV26 ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent )
= $false )
| ( ( c_in @ SV1 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(97,plain,
! [SV36: $i,SV35: $i,SV34: $i,SV33: $i,SV32: $i,SV31: $i,SV3: $i,SV28: $i,SV24: $i,SV20: $i,SV16: $i,SV12: $i,SV8: $i] :
( ( ( ~ ( c_in @ ( c_Event_Oevent_OGets @ SV8 @ ( c_Message_Omsg_OMPair @ SV12 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV16 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV20 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SV24 ) @ SV28 ) ) ) ) ) @ ( c_List_Oset @ SV3 @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
= $true )
| ( ( ~ ( c_in @ ( c_Event_Oevent_OSays @ SV31 @ SV32 @ ( c_Message_Omsg_OMPair @ SV33 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV34 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV35 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SV36 ) @ SV28 ) ) ) ) ) @ ( c_List_Oset @ SV3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ SV28 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV3 ) ) @ tc_Message_Omsg )
| ( SV24 = SV36 ) )
= $true )
| ( ( c_in @ SV3 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(98,plain,
! [SV36: $i,SV35: $i,SV34: $i,SV33: $i,SV32: $i,SV31: $i,SV3: $i,SV28: $i,SV24: $i,SV20: $i,SV16: $i,SV12: $i,SV8: $i] :
( ( ( c_in @ ( c_Event_Oevent_OGets @ SV8 @ ( c_Message_Omsg_OMPair @ SV12 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV16 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV20 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SV24 ) @ SV28 ) ) ) ) ) @ ( c_List_Oset @ SV3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
= $false )
| ( ( ~ ( c_in @ ( c_Event_Oevent_OSays @ SV31 @ SV32 @ ( c_Message_Omsg_OMPair @ SV33 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV34 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV35 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SV36 ) @ SV28 ) ) ) ) ) @ ( c_List_Oset @ SV3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ SV28 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV3 ) ) @ tc_Message_Omsg )
| ( SV24 = SV36 ) )
= $true )
| ( ( c_in @ SV3 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(99,plain,
! [SV20: $i,SV16: $i,SV12: $i,SV8: $i,SV24: $i,SV3: $i,SV28: $i,SV36: $i,SV35: $i,SV34: $i,SV33: $i,SV32: $i,SV31: $i] :
( ( ( ~ ( c_in @ ( c_Event_Oevent_OSays @ SV31 @ SV32 @ ( c_Message_Omsg_OMPair @ SV33 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV34 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV35 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SV36 ) @ SV28 ) ) ) ) ) @ ( c_List_Oset @ SV3 @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
= $true )
| ( ( ( c_in @ SV28 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV3 ) ) @ tc_Message_Omsg )
| ( SV24 = SV36 ) )
= $true )
| ( ( c_in @ ( c_Event_Oevent_OGets @ SV8 @ ( c_Message_Omsg_OMPair @ SV12 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV16 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV20 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SV24 ) @ SV28 ) ) ) ) ) @ ( c_List_Oset @ SV3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
= $false )
| ( ( c_in @ SV3 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(100,plain,
! [SV20: $i,SV16: $i,SV12: $i,SV8: $i,SV24: $i,SV3: $i,SV28: $i,SV36: $i,SV35: $i,SV34: $i,SV33: $i,SV32: $i,SV31: $i] :
( ( ( c_in @ ( c_Event_Oevent_OSays @ SV31 @ SV32 @ ( c_Message_Omsg_OMPair @ SV33 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV34 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV35 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SV36 ) @ SV28 ) ) ) ) ) @ ( c_List_Oset @ SV3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
= $false )
| ( ( ( c_in @ SV28 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV3 ) ) @ tc_Message_Omsg )
| ( SV24 = SV36 ) )
= $true )
| ( ( c_in @ ( c_Event_Oevent_OGets @ SV8 @ ( c_Message_Omsg_OMPair @ SV12 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV16 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV20 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SV24 ) @ SV28 ) ) ) ) ) @ ( c_List_Oset @ SV3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
= $false )
| ( ( c_in @ SV3 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(101,plain,
! [SV20: $i,SV16: $i,SV12: $i,SV8: $i,SV35: $i,SV34: $i,SV33: $i,SV32: $i,SV31: $i,SV36: $i,SV24: $i,SV3: $i,SV28: $i] :
( ( ( c_in @ SV28 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV3 ) ) @ tc_Message_Omsg )
= $true )
| ( ( SV24 = SV36 )
= $true )
| ( ( c_in @ ( c_Event_Oevent_OSays @ SV31 @ SV32 @ ( c_Message_Omsg_OMPair @ SV33 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV34 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV35 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SV36 ) @ SV28 ) ) ) ) ) @ ( c_List_Oset @ SV3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
= $false )
| ( ( c_in @ ( c_Event_Oevent_OGets @ SV8 @ ( c_Message_Omsg_OMPair @ SV12 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV16 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV20 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SV24 ) @ SV28 ) ) ) ) ) @ ( c_List_Oset @ SV3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
= $false )
| ( ( c_in @ SV3 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(102,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[25,101,96,86,84,68,42,37,29,27,26]) ).
thf(103,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV354-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.17 % Computer : n011.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Oct 6 16:27:01 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.64/0.32
% 0.64/0.32 No.of.Axioms: 10
% 0.64/0.32
% 0.64/0.32 Length.of.Defs: 0
% 0.64/0.32
% 0.64/0.32 Contains.Choice.Funs: false
% 0.64/0.32 ......
% 0.64/0.32
% 0.64/0.32 ********************************
% 0.64/0.32 * All subproblems solved! *
% 0.64/0.32 ********************************
% 0.64/0.32 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:10,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:102,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.64/0.32
% 0.64/0.32 %**** Beginning of derivation protocol ****
% 0.64/0.32 % SZS output start CNFRefutation
% See solution above
% 0.64/0.32
% 0.64/0.32 %**** End of derivation protocol ****
% 0.64/0.32 %**** no. of clauses in derivation: 103 ****
% 0.64/0.32 %**** clause counter: 102 ****
% 0.64/0.32
% 0.64/0.32 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:10,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:102,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------