%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV353-2 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 0.07s 0.16s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 8
% Syntax : Number of formulae : 66 ( 49 unt; 0 typ; 0 def)
% Number of atoms : 358 ( 121 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 2076 ( 99 ~; 128 |; 0 &;1849 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 28 usr; 17 con; 0-3 aty)
% Number of variables : 405 ( 0 ^; 405 !; 0 ?; 405 :)
% 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_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_X,type,
v_X: $i ).
thf(tp_v_evso,type,
v_evso: $i ).
thf(1,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/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OSays__unique__NB_0) ).
thf(2,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/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OSays__Server__imp__YM2_0) ).
thf(3,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(4,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[3]) ).
thf(5,negated_conjecture,
! [V_U: $i] :
( ( V_U
!= ( c_Message_Omsg_OKey @ v_K ) )
| ( v_NA != v_NAa ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_8) ).
thf(6,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/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).
thf(7,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/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
thf(8,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_NB ) ) ) ) ) @ v_X ) ) @ ( c_List_Oset @ v_evso @ tc_Event_Oevent ) @ tc_Event_Oevent,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(9,negated_conjecture,
c_in @ v_evso @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(10,plain,
$false = $false,
inference(unfold_def,[status(thm)],[4]) ).
thf(11,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)],[1]) ).
thf(12,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)],[2]) ).
thf(13,plain,
( ( ! [V_U: $i] :
( ( V_U
!= ( c_Message_Omsg_OKey @ v_K ) )
| ( v_NA != v_NAa ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(14,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)],[6]) ).
thf(15,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)],[7]) ).
thf(16,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_NB ) ) ) ) ) @ v_X ) ) @ ( c_List_Oset @ v_evso @ tc_Event_Oevent ) @ tc_Event_Oevent )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(17,plain,
( ( c_in @ v_evso @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(18,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[10]) ).
thf(19,plain,
( ( c_in @ v_evso @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(20,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_NB ) ) ) ) ) @ v_X ) ) @ ( c_List_Oset @ v_evso @ tc_Event_Oevent ) @ tc_Event_Oevent )
= $true ),
inference(copy,[status(thm)],[16]) ).
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(copy,[status(thm)],[15]) ).
thf(22,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)],[14]) ).
thf(23,plain,
( ( ! [V_U: $i] :
( ( V_U
!= ( c_Message_Omsg_OKey @ v_K ) )
| ( v_NA != v_NAa ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(24,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)],[12]) ).
thf(25,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)],[11]) ).
thf(26,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[18]) ).
thf(27,plain,
( ( ! [SX0: $i] :
( ( SX0
!= ( c_Message_Omsg_OKey @ v_K ) )
| ( v_NA != v_NAa ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
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 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(29,plain,
! [SV1: $i] :
( ( ! [SY21: $i,SY22: $i,SY23: $i,SY24: $i,SY25: $i,SY26: $i] :
( ~ ( c_in @ SV1 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SY21 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SY21 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY22 ) @ ( c_Message_Omsg_OMPair @ SY23 @ ( c_Message_Omsg_OMPair @ SY24 @ SY25 ) ) ) ) @ SY26 ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ ( c_Event_Oevent_OGets @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY22 ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SY22 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY21 ) @ ( c_Message_Omsg_OMPair @ SY24 @ SY25 ) ) ) ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(30,plain,
! [SV2: $i] :
( ( ! [SY27: $i,SY28: $i,SY29: $i,SY30: $i,SY31: $i,SY32: $i,SY33: $i,SY34: $i,SY35: $i,SY36: $i,SY37: $i,SY38: $i] :
( ~ ( c_in @ SV2 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OGets @ SY27 @ ( c_Message_Omsg_OMPair @ SY28 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SY29 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY30 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SY31 ) @ SY32 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ SY33 @ SY34 @ ( c_Message_Omsg_OMPair @ SY35 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SY36 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY37 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SY38 ) @ SY32 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ SY32 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV2 ) ) @ tc_Message_Omsg )
| ( SY31 = SY38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(31,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(32,plain,
! [SV3: $i] :
( ( ( SV3
!= ( c_Message_Omsg_OKey @ v_K ) )
| ( v_NA != v_NAa ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(33,plain,
! [SV4: $i,SV1: $i] :
( ( ! [SY39: $i,SY40: $i,SY41: $i,SY42: $i,SY43: $i] :
( ~ ( c_in @ SV1 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV4 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV4 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY39 ) @ ( c_Message_Omsg_OMPair @ SY40 @ ( c_Message_Omsg_OMPair @ SY41 @ SY42 ) ) ) ) @ SY43 ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ ( c_Event_Oevent_OGets @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY39 ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SY39 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV4 ) @ ( c_Message_Omsg_OMPair @ SY41 @ SY42 ) ) ) ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(34,plain,
! [SV5: $i,SV2: $i] :
( ( ! [SY44: $i,SY45: $i,SY46: $i,SY47: $i,SY48: $i,SY49: $i,SY50: $i,SY51: $i,SY52: $i,SY53: $i,SY54: $i] :
( ~ ( c_in @ SV2 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OGets @ SV5 @ ( c_Message_Omsg_OMPair @ SY44 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SY45 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY46 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SY47 ) @ SY48 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ SY49 @ SY50 @ ( c_Message_Omsg_OMPair @ SY51 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SY52 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY53 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SY54 ) @ SY48 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ SY48 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV2 ) ) @ tc_Message_Omsg )
| ( SY47 = SY54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(35,plain,
! [SV3: $i] :
( ( ( SV3
!= ( c_Message_Omsg_OKey @ v_K ) )
= $true )
| ( ( v_NA != v_NAa )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(36,plain,
! [SV6: $i,SV4: $i,SV1: $i] :
( ( ! [SY55: $i,SY56: $i,SY57: $i,SY58: $i] :
( ~ ( c_in @ SV1 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV4 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV4 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV6 ) @ ( c_Message_Omsg_OMPair @ SY55 @ ( c_Message_Omsg_OMPair @ SY56 @ SY57 ) ) ) ) @ SY58 ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ ( c_Event_Oevent_OGets @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV6 ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV6 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV4 ) @ ( c_Message_Omsg_OMPair @ SY56 @ SY57 ) ) ) ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(37,plain,
! [SV7: $i,SV5: $i,SV2: $i] :
( ( ! [SY59: $i,SY60: $i,SY61: $i,SY62: $i,SY63: $i,SY64: $i,SY65: $i,SY66: $i,SY67: $i,SY68: $i] :
( ~ ( c_in @ SV2 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OGets @ SV5 @ ( c_Message_Omsg_OMPair @ SV7 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SY59 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY60 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SY61 ) @ SY62 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ SY63 @ SY64 @ ( c_Message_Omsg_OMPair @ SY65 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SY66 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY67 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SY68 ) @ SY62 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ SY62 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV2 ) ) @ tc_Message_Omsg )
| ( SY61 = SY68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(38,plain,
! [SV3: $i] :
( ( ( SV3
= ( c_Message_Omsg_OKey @ v_K ) )
= $false )
| ( ( v_NA != v_NAa )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(39,plain,
! [SV8: $i,SV6: $i,SV4: $i,SV1: $i] :
( ( ! [SY69: $i,SY70: $i,SY71: $i] :
( ~ ( c_in @ SV1 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV4 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV4 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV6 ) @ ( c_Message_Omsg_OMPair @ SV8 @ ( c_Message_Omsg_OMPair @ SY69 @ SY70 ) ) ) ) @ SY71 ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ ( c_Event_Oevent_OGets @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV6 ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV6 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV4 ) @ ( c_Message_Omsg_OMPair @ SY69 @ SY70 ) ) ) ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(40,plain,
! [SV9: $i,SV7: $i,SV5: $i,SV2: $i] :
( ( ! [SY72: $i,SY73: $i,SY74: $i,SY75: $i,SY76: $i,SY77: $i,SY78: $i,SY79: $i,SY80: $i] :
( ~ ( c_in @ SV2 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OGets @ SV5 @ ( c_Message_Omsg_OMPair @ SV7 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV9 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY72 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SY73 ) @ SY74 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ SY75 @ SY76 @ ( c_Message_Omsg_OMPair @ SY77 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SY78 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY79 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SY80 ) @ SY74 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ SY74 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV2 ) ) @ tc_Message_Omsg )
| ( SY73 = SY80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(41,plain,
! [SV3: $i] :
( ( ( v_NA = v_NAa )
= $false )
| ( ( SV3
= ( c_Message_Omsg_OKey @ v_K ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(42,plain,
! [SV10: $i,SV8: $i,SV6: $i,SV4: $i,SV1: $i] :
( ( ! [SY81: $i,SY82: $i] :
( ~ ( c_in @ SV1 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV4 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV4 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV6 ) @ ( c_Message_Omsg_OMPair @ SV8 @ ( c_Message_Omsg_OMPair @ SV10 @ SY81 ) ) ) ) @ SY82 ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ ( c_Event_Oevent_OGets @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV6 ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV6 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV4 ) @ ( c_Message_Omsg_OMPair @ SV10 @ SY81 ) ) ) ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(43,plain,
! [SV11: $i,SV9: $i,SV7: $i,SV5: $i,SV2: $i] :
( ( ! [SY83: $i,SY84: $i,SY85: $i,SY86: $i,SY87: $i,SY88: $i,SY89: $i,SY90: $i] :
( ~ ( c_in @ SV2 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OGets @ SV5 @ ( c_Message_Omsg_OMPair @ SV7 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV9 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV11 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SY83 ) @ SY84 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ SY85 @ SY86 @ ( c_Message_Omsg_OMPair @ SY87 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SY88 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY89 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SY90 ) @ SY84 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ SY84 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV2 ) ) @ tc_Message_Omsg )
| ( SY83 = SY90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(44,plain,
! [SV12: $i,SV10: $i,SV8: $i,SV6: $i,SV4: $i,SV1: $i] :
( ( ! [SY91: $i] :
( ~ ( c_in @ SV1 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV4 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV4 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV6 ) @ ( c_Message_Omsg_OMPair @ SV8 @ ( c_Message_Omsg_OMPair @ SV10 @ SV12 ) ) ) ) @ SY91 ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ ( c_Event_Oevent_OGets @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV6 ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV6 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV4 ) @ ( c_Message_Omsg_OMPair @ SV10 @ SV12 ) ) ) ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(45,plain,
! [SV13: $i,SV11: $i,SV9: $i,SV7: $i,SV5: $i,SV2: $i] :
( ( ! [SY92: $i,SY93: $i,SY94: $i,SY95: $i,SY96: $i,SY97: $i,SY98: $i] :
( ~ ( c_in @ SV2 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OGets @ SV5 @ ( c_Message_Omsg_OMPair @ SV7 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV9 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV11 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SV13 ) @ SY92 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ SY93 @ SY94 @ ( c_Message_Omsg_OMPair @ SY95 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SY96 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY97 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SY98 ) @ SY92 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ SY92 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV2 ) ) @ tc_Message_Omsg )
| ( SV13 = SY98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(46,plain,
! [SV14: $i,SV12: $i,SV10: $i,SV8: $i,SV6: $i,SV4: $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 @ SV4 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV4 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV6 ) @ ( c_Message_Omsg_OMPair @ SV8 @ ( c_Message_Omsg_OMPair @ SV10 @ SV12 ) ) ) ) @ SV14 ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ ( c_Event_Oevent_OGets @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV6 ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV6 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV4 ) @ ( c_Message_Omsg_OMPair @ SV10 @ SV12 ) ) ) ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(47,plain,
! [SV15: $i,SV13: $i,SV11: $i,SV9: $i,SV7: $i,SV5: $i,SV2: $i] :
( ( ! [SY99: $i,SY100: $i,SY101: $i,SY102: $i,SY103: $i,SY104: $i] :
( ~ ( c_in @ SV2 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OGets @ SV5 @ ( c_Message_Omsg_OMPair @ SV7 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV9 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV11 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SV13 ) @ SV15 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ SY99 @ SY100 @ ( c_Message_Omsg_OMPair @ SY101 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SY102 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY103 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SY104 ) @ SV15 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ SV15 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV2 ) ) @ tc_Message_Omsg )
| ( SV13 = SY104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(48,plain,
! [SV14: $i,SV12: $i,SV10: $i,SV8: $i,SV6: $i,SV4: $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 @ SV4 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV4 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV6 ) @ ( c_Message_Omsg_OMPair @ SV8 @ ( c_Message_Omsg_OMPair @ SV10 @ SV12 ) ) ) ) @ SV14 ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ ( c_Event_Oevent_OGets @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV6 ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV6 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV4 ) @ ( c_Message_Omsg_OMPair @ SV10 @ SV12 ) ) ) ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(49,plain,
! [SV16: $i,SV15: $i,SV13: $i,SV11: $i,SV9: $i,SV7: $i,SV5: $i,SV2: $i] :
( ( ! [SY105: $i,SY106: $i,SY107: $i,SY108: $i,SY109: $i] :
( ~ ( c_in @ SV2 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OGets @ SV5 @ ( c_Message_Omsg_OMPair @ SV7 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV9 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV11 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SV13 ) @ SV15 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ SV16 @ SY105 @ ( c_Message_Omsg_OMPair @ SY106 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SY107 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY108 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SY109 ) @ SV15 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ SV15 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV2 ) ) @ tc_Message_Omsg )
| ( SV13 = SY109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(50,plain,
! [SV14: $i,SV12: $i,SV10: $i,SV8: $i,SV6: $i,SV4: $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 @ SV4 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV4 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV6 ) @ ( c_Message_Omsg_OMPair @ SV8 @ ( c_Message_Omsg_OMPair @ SV10 @ SV12 ) ) ) ) @ SV14 ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ ( c_Event_Oevent_OGets @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV6 ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV6 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV4 ) @ ( c_Message_Omsg_OMPair @ SV10 @ SV12 ) ) ) ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(51,plain,
! [SV17: $i,SV16: $i,SV15: $i,SV13: $i,SV11: $i,SV9: $i,SV7: $i,SV5: $i,SV2: $i] :
( ( ! [SY110: $i,SY111: $i,SY112: $i,SY113: $i] :
( ~ ( c_in @ SV2 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OGets @ SV5 @ ( c_Message_Omsg_OMPair @ SV7 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV9 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV11 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SV13 ) @ SV15 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ SV16 @ SV17 @ ( c_Message_Omsg_OMPair @ SY110 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SY111 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY112 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SY113 ) @ SV15 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ SV15 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV2 ) ) @ tc_Message_Omsg )
| ( SV13 = SY113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(52,plain,
! [SV1: $i,SV14: $i,SV12: $i,SV10: $i,SV8: $i,SV6: $i,SV4: $i] :
( ( ( ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV4 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV4 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV6 ) @ ( c_Message_Omsg_OMPair @ SV8 @ ( c_Message_Omsg_OMPair @ SV10 @ SV12 ) ) ) ) @ SV14 ) ) @ ( c_List_Oset @ SV1 @ 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 @ SV6 ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV6 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV4 ) @ ( c_Message_Omsg_OMPair @ SV10 @ SV12 ) ) ) ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent )
= $true )
| ( ( c_in @ SV1 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(53,plain,
! [SV18: $i,SV17: $i,SV16: $i,SV15: $i,SV13: $i,SV11: $i,SV9: $i,SV7: $i,SV5: $i,SV2: $i] :
( ( ! [SY114: $i,SY115: $i,SY116: $i] :
( ~ ( c_in @ SV2 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OGets @ SV5 @ ( c_Message_Omsg_OMPair @ SV7 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV9 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV11 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SV13 ) @ SV15 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ SV16 @ SV17 @ ( c_Message_Omsg_OMPair @ SV18 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SY114 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY115 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SY116 ) @ SV15 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ SV15 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV2 ) ) @ tc_Message_Omsg )
| ( SV13 = SY116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(54,plain,
! [SV1: $i,SV14: $i,SV12: $i,SV10: $i,SV8: $i,SV6: $i,SV4: $i] :
( ( ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV4 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV4 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV6 ) @ ( c_Message_Omsg_OMPair @ SV8 @ ( c_Message_Omsg_OMPair @ SV10 @ SV12 ) ) ) ) @ SV14 ) ) @ ( c_List_Oset @ SV1 @ 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 @ SV6 ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV6 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV4 ) @ ( c_Message_Omsg_OMPair @ SV10 @ SV12 ) ) ) ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent )
= $true )
| ( ( c_in @ SV1 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(55,plain,
! [SV19: $i,SV18: $i,SV17: $i,SV16: $i,SV15: $i,SV13: $i,SV11: $i,SV9: $i,SV7: $i,SV5: $i,SV2: $i] :
( ( ! [SY117: $i,SY118: $i] :
( ~ ( c_in @ SV2 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OGets @ SV5 @ ( c_Message_Omsg_OMPair @ SV7 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV9 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV11 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SV13 ) @ SV15 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ SV16 @ SV17 @ ( c_Message_Omsg_OMPair @ SV18 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV19 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SY117 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SY118 ) @ SV15 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ SV15 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV2 ) ) @ tc_Message_Omsg )
| ( SV13 = SY118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(56,plain,
! [SV20: $i,SV19: $i,SV18: $i,SV17: $i,SV16: $i,SV15: $i,SV13: $i,SV11: $i,SV9: $i,SV7: $i,SV5: $i,SV2: $i] :
( ( ! [SY119: $i] :
( ~ ( c_in @ SV2 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OGets @ SV5 @ ( c_Message_Omsg_OMPair @ SV7 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV9 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV11 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SV13 ) @ SV15 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ SV16 @ SV17 @ ( c_Message_Omsg_OMPair @ SV18 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV19 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV20 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SY119 ) @ SV15 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ SV15 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV2 ) ) @ tc_Message_Omsg )
| ( SV13 = SY119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(57,plain,
! [SV21: $i,SV20: $i,SV19: $i,SV18: $i,SV17: $i,SV16: $i,SV15: $i,SV13: $i,SV11: $i,SV9: $i,SV7: $i,SV5: $i,SV2: $i] :
( ( ~ ( c_in @ SV2 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OGets @ SV5 @ ( c_Message_Omsg_OMPair @ SV7 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV9 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV11 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SV13 ) @ SV15 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ SV16 @ SV17 @ ( c_Message_Omsg_OMPair @ SV18 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV19 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV20 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SV21 ) @ SV15 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ SV15 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV2 ) ) @ tc_Message_Omsg )
| ( SV13 = SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(58,plain,
! [SV21: $i,SV20: $i,SV19: $i,SV18: $i,SV17: $i,SV16: $i,SV15: $i,SV13: $i,SV11: $i,SV9: $i,SV7: $i,SV5: $i,SV2: $i] :
( ( ( ~ ( c_in @ SV2 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Event_Oevent_OGets @ SV5 @ ( c_Message_Omsg_OMPair @ SV7 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV9 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV11 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SV13 ) @ SV15 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ SV16 @ SV17 @ ( c_Message_Omsg_OMPair @ SV18 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV19 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV20 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SV21 ) @ SV15 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ SV15 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV2 ) ) @ tc_Message_Omsg )
| ( SV13 = SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(59,plain,
! [SV21: $i,SV20: $i,SV19: $i,SV18: $i,SV17: $i,SV16: $i,SV15: $i,SV13: $i,SV11: $i,SV9: $i,SV7: $i,SV5: $i,SV2: $i] :
( ( ( c_in @ SV2 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $false )
| ( ( ~ ( c_in @ ( c_Event_Oevent_OGets @ SV5 @ ( c_Message_Omsg_OMPair @ SV7 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV9 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV11 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SV13 ) @ SV15 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ SV16 @ SV17 @ ( c_Message_Omsg_OMPair @ SV18 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV19 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV20 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SV21 ) @ SV15 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ SV15 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV2 ) ) @ tc_Message_Omsg )
| ( SV13 = SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(60,plain,
! [SV21: $i,SV20: $i,SV19: $i,SV18: $i,SV17: $i,SV16: $i,SV2: $i,SV15: $i,SV13: $i,SV11: $i,SV9: $i,SV7: $i,SV5: $i] :
( ( ( ~ ( c_in @ ( c_Event_Oevent_OGets @ SV5 @ ( c_Message_Omsg_OMPair @ SV7 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV9 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV11 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SV13 ) @ SV15 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
= $true )
| ( ( ~ ( c_in @ ( c_Event_Oevent_OSays @ SV16 @ SV17 @ ( c_Message_Omsg_OMPair @ SV18 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV19 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV20 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SV21 ) @ SV15 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ SV15 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV2 ) ) @ tc_Message_Omsg )
| ( SV13 = SV21 ) )
= $true )
| ( ( c_in @ SV2 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(61,plain,
! [SV21: $i,SV20: $i,SV19: $i,SV18: $i,SV17: $i,SV16: $i,SV2: $i,SV15: $i,SV13: $i,SV11: $i,SV9: $i,SV7: $i,SV5: $i] :
( ( ( c_in @ ( c_Event_Oevent_OGets @ SV5 @ ( c_Message_Omsg_OMPair @ SV7 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV9 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV11 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SV13 ) @ SV15 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
= $false )
| ( ( ~ ( c_in @ ( c_Event_Oevent_OSays @ SV16 @ SV17 @ ( c_Message_Omsg_OMPair @ SV18 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV19 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV20 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SV21 ) @ SV15 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ SV15 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV2 ) ) @ tc_Message_Omsg )
| ( SV13 = SV21 ) )
= $true )
| ( ( c_in @ SV2 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(62,plain,
! [SV11: $i,SV9: $i,SV7: $i,SV5: $i,SV13: $i,SV2: $i,SV15: $i,SV21: $i,SV20: $i,SV19: $i,SV18: $i,SV17: $i,SV16: $i] :
( ( ( ~ ( c_in @ ( c_Event_Oevent_OSays @ SV16 @ SV17 @ ( c_Message_Omsg_OMPair @ SV18 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV19 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV20 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SV21 ) @ SV15 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
= $true )
| ( ( ( c_in @ SV15 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV2 ) ) @ tc_Message_Omsg )
| ( SV13 = SV21 ) )
= $true )
| ( ( c_in @ ( c_Event_Oevent_OGets @ SV5 @ ( c_Message_Omsg_OMPair @ SV7 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV9 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV11 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SV13 ) @ SV15 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
= $false )
| ( ( c_in @ SV2 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(63,plain,
! [SV11: $i,SV9: $i,SV7: $i,SV5: $i,SV13: $i,SV2: $i,SV15: $i,SV21: $i,SV20: $i,SV19: $i,SV18: $i,SV17: $i,SV16: $i] :
( ( ( c_in @ ( c_Event_Oevent_OSays @ SV16 @ SV17 @ ( c_Message_Omsg_OMPair @ SV18 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV19 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV20 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SV21 ) @ SV15 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
= $false )
| ( ( ( c_in @ SV15 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV2 ) ) @ tc_Message_Omsg )
| ( SV13 = SV21 ) )
= $true )
| ( ( c_in @ ( c_Event_Oevent_OGets @ SV5 @ ( c_Message_Omsg_OMPair @ SV7 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV9 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV11 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SV13 ) @ SV15 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
= $false )
| ( ( c_in @ SV2 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(64,plain,
! [SV11: $i,SV9: $i,SV7: $i,SV5: $i,SV20: $i,SV19: $i,SV18: $i,SV17: $i,SV16: $i,SV21: $i,SV13: $i,SV2: $i,SV15: $i] :
( ( ( c_in @ SV15 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV2 ) ) @ tc_Message_Omsg )
= $true )
| ( ( SV13 = SV21 )
= $true )
| ( ( c_in @ ( c_Event_Oevent_OSays @ SV16 @ SV17 @ ( c_Message_Omsg_OMPair @ SV18 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV19 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV20 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SV21 ) @ SV15 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
= $false )
| ( ( c_in @ ( c_Event_Oevent_OGets @ SV5 @ ( c_Message_Omsg_OMPair @ SV7 @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV9 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ SV11 ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ SV13 ) @ SV15 ) ) ) ) ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
= $false )
| ( ( c_in @ SV2 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(65,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[19,64,54,41,31,28,21,20]) ).
thf(66,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWV353-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Oct 6 16:26:26 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.16
% 0.07/0.16 No.of.Axioms: 7
% 0.07/0.16
% 0.07/0.16 Length.of.Defs: 0
% 0.07/0.16
% 0.07/0.16 Contains.Choice.Funs: false
% 0.07/0.16 ...
% 0.07/0.16
% 0.07/0.16 ********************************
% 0.07/0.16 * All subproblems solved! *
% 0.07/0.16 ********************************
% 0.07/0.16 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:7,ps:3,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:65,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.16
% 0.07/0.16 %**** Beginning of derivation protocol ****
% 0.07/0.16 % SZS output start CNFRefutation
% See solution above
% 0.07/0.16
% 0.07/0.16 %**** End of derivation protocol ****
% 0.07/0.16 %**** no. of clauses in derivation: 66 ****
% 0.07/0.16 %**** clause counter: 65 ****
% 0.07/0.16
% 0.07/0.16 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:7,ps:3,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:65,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------