%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV767-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:36:03 AM UTC 2025
% Result : Unsatisfiable 103.75s 103.92s
% Output : Proof 103.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 84
% Syntax : Number of formulae : 204 ( 59 unt; 0 typ; 0 def)
% Number of atoms : 799 ( 136 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 922 ( 364 ~; 464 |; 0 &)
% ( 94 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of FOOLs : 37 ( 37 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 30 ( 30 usr; 15 con; 0-3 aty)
% Number of variables : 675 ( 607 !; 0 ?; 675 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
tff(tc_Message_Omsg_type,type,
tc_Message_Omsg: $i ).
tff(c_Message_Osynth_type,type,
c_Message_Osynth: $i > $i ).
tff(c_Message_Oanalz_type,type,
c_Message_Oanalz: $i > $i ).
tff(c_Event_Oknows_type,type,
c_Event_Oknows: ( $i * $i ) > $i ).
tff(v_evsf_type,type,
v_evsf: $i ).
tff(c_Message_Oagent_OSpy_type,type,
c_Message_Oagent_OSpy: $i ).
tff(c_Message_Omsg_OCrypt_type,type,
c_Message_Omsg_OCrypt: ( $i * $i ) > $i ).
tff(c_Message_Omsg_OMPair_type,type,
c_Message_Omsg_OMPair: ( $i * $i ) > $i ).
tff(c_Message_Omsg_ONonce_type,type,
c_Message_Omsg_ONonce: $i > $i ).
tff(v_NB_type,type,
v_NB: $i ).
tff(v_K_type,type,
v_K: $i ).
tff(c_Lattices_Oupper__semilattice__class_Osup_type,type,
c_Lattices_Oupper__semilattice__class_Osup: ( $i * $i * $i ) > $i ).
tff(tc_fun_type,type,
tc_fun: ( $i * $i ) > $i ).
tff(tc_bool_type,type,
tc_bool: $i ).
tff(c_Message_Oparts_type,type,
c_Message_Oparts: $i > $i ).
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(c_Set_Oinsert_type,type,
c_Set_Oinsert: ( $i * $i * $i ) > $i ).
tff(c_List_Olist_OCons_type,type,
c_List_Olist_OCons: ( $i * $i * $i ) > $i ).
tff(tc_Event_Oevent_type,type,
tc_Event_Oevent: $i ).
tff(c_Event_Oevent_OSays_type,type,
c_Event_Oevent_OSays: ( $i * $i * $i ) > $i ).
tff(v_X_type,type,
v_X: $i ).
tff(v_Ba_type,type,
v_Ba: $i ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(c_Message_Omsg_OKey_type,type,
c_Message_Omsg_OKey: $i ).
tff(c_List_Oset_type,type,
c_List_Oset: ( $i * $i ) > $i ).
tff(c_Message_Omsg_OAgent_type,type,
c_Message_Omsg_OAgent: $i > $i ).
tff(v_A_type,type,
v_A: $i ).
tff(v_B_type,type,
v_B: $i ).
tff(c_Public_OshrK_type,type,
c_Public_OshrK: $i ).
tff(v_NA_type,type,
v_NA: $i ).
tff(c_Message_Oagent_OServer_type,type,
c_Message_Oagent_OServer: $i ).
tff(1,plain,
^ [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
refl(( ( c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(V_A,V_B,V_X),V_evs,tc_Event_Oevent)) = c_Set_Oinsert(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) )
<=> ( c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(V_A,V_B,V_X),V_evs,tc_Event_Oevent)) = c_Set_Oinsert(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] : ( c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(V_A,V_B,V_X),V_evs,tc_Event_Oevent)) = c_Set_Oinsert(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) )
<=> ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] : ( c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(V_A,V_B,V_X),V_evs,tc_Event_Oevent)) = c_Set_Oinsert(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] : ( c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(V_A,V_B,V_X),V_evs,tc_Event_Oevent)) = c_Set_Oinsert(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) )
<=> ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] : ( c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(V_A,V_B,V_X),V_evs,tc_Event_Oevent)) = c_Set_Oinsert(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] : ( c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(V_A,V_B,V_X),V_evs,tc_Event_Oevent)) = c_Set_Oinsert(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__Spy__Says_0) ).
tff(5,plain,
! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] : ( c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(V_A,V_B,V_X),V_evs,tc_Event_Oevent)) = c_Set_Oinsert(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] : ( c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(V_A,V_B,V_X),V_evs,tc_Event_Oevent)) = c_Set_Oinsert(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] : ( c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(V_A,V_B,V_X),V_evs,tc_Event_Oevent)) = c_Set_Oinsert(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] : ( c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(V_A,V_B,V_X),V_evs,tc_Event_Oevent)) = c_Set_Oinsert(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) )
| ( c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent)) = c_Set_Oinsert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent)) = c_Set_Oinsert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
c_Set_Oinsert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent)),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
c_Message_Oparts(c_Set_Oinsert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg)) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent))),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent))) = c_Message_Oparts(c_Set_Oinsert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg)),
inference(symmetry,[status(thm)],[11]) ).
tff(13,plain,
( c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent))),tc_Message_Omsg)
<=> c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent))),tc_Message_Omsg) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent))),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
tff(15,plain,
c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent))),tc_Message_Omsg),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
^ [V_a: $i,T_a: $i,V_A: $i] :
refl(( ( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
<=> ( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ) )),
inference(bind,[status(th)],[]) ).
tff(17,plain,
( ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
<=> ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
( ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
<=> ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
^ [V_a: $i,T_a: $i,V_A: $i] :
rewrite(( ( ( c_Set_Oinsert(V_a,V_A,T_a) = V_A )
| ~ c_in(V_a,V_A,T_a) )
<=> ( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ) )),
inference(bind,[status(th)],[]) ).
tff(20,plain,
( ! [V_a: $i,T_a: $i,V_A: $i] :
( ( c_Set_Oinsert(V_a,V_A,T_a) = V_A )
| ~ c_in(V_a,V_A,T_a) )
<=> ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,axiom,
! [V_a: $i,T_a: $i,V_A: $i] :
( ( c_Set_Oinsert(V_a,V_A,T_a) = V_A )
| ~ c_in(V_a,V_A,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
tff(22,plain,
! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ),
inference(modus_ponens,[status(thm)],[22,18]) ).
tff(24,plain,
! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ),
inference(modus_ponens,[status(thm)],[24,17]) ).
tff(26,plain,
( ( ~ ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent))),tc_Message_Omsg)
| ( c_Set_Oinsert(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent))),tc_Message_Omsg) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent))) ) )
<=> ( ~ ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent))),tc_Message_Omsg)
| ( c_Set_Oinsert(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent))),tc_Message_Omsg) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
( ~ ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent))),tc_Message_Omsg)
| ( c_Set_Oinsert(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent))),tc_Message_Omsg) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
( ~ ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent))),tc_Message_Omsg)
| ( c_Set_Oinsert(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent))),tc_Message_Omsg) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent))) ) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
c_Set_Oinsert(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent))),tc_Message_Omsg) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent))),
inference(unit_resolution,[status(thm)],[28,25,15]) ).
tff(30,plain,
c_Set_Oinsert(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent))),tc_Message_Omsg) = c_Message_Oparts(c_Set_Oinsert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg)),
inference(transitivity,[status(thm)],[29,12]) ).
tff(31,plain,
( c_lessequals(c_Set_Oinsert(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent))),tc_Message_Omsg),c_Lattices_Oupper__semilattice__class_Osup(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool)),tc_fun(tc_Message_Omsg,tc_bool))
<=> c_lessequals(c_Message_Oparts(c_Set_Oinsert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg)),c_Lattices_Oupper__semilattice__class_Osup(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool)),tc_fun(tc_Message_Omsg,tc_bool)) ),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
( c_lessequals(c_Message_Oparts(c_Set_Oinsert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg)),c_Lattices_Oupper__semilattice__class_Osup(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool)),tc_fun(tc_Message_Omsg,tc_bool))
<=> c_lessequals(c_Set_Oinsert(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent))),tc_Message_Omsg),c_Lattices_Oupper__semilattice__class_Osup(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool)),tc_fun(tc_Message_Omsg,tc_bool)) ),
inference(symmetry,[status(thm)],[31]) ).
tff(33,plain,
( c_in(v_X,c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg)
<=> c_in(v_X,c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,axiom,
c_in(v_X,c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(35,plain,
c_in(v_X,c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
^ [V_H: $i,V_X: $i] :
refl(( ( ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| c_lessequals(c_Message_Oparts(c_Set_Oinsert(V_X,V_H,tc_Message_Omsg)),c_Lattices_Oupper__semilattice__class_Osup(c_Message_Osynth(c_Message_Oanalz(V_H)),c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)),tc_fun(tc_Message_Omsg,tc_bool)) )
<=> ( ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| c_lessequals(c_Message_Oparts(c_Set_Oinsert(V_X,V_H,tc_Message_Omsg)),c_Lattices_Oupper__semilattice__class_Osup(c_Message_Osynth(c_Message_Oanalz(V_H)),c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)),tc_fun(tc_Message_Omsg,tc_bool)) ) )),
inference(bind,[status(th)],[]) ).
tff(37,plain,
( ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| c_lessequals(c_Message_Oparts(c_Set_Oinsert(V_X,V_H,tc_Message_Omsg)),c_Lattices_Oupper__semilattice__class_Osup(c_Message_Osynth(c_Message_Oanalz(V_H)),c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)),tc_fun(tc_Message_Omsg,tc_bool)) )
<=> ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| c_lessequals(c_Message_Oparts(c_Set_Oinsert(V_X,V_H,tc_Message_Omsg)),c_Lattices_Oupper__semilattice__class_Osup(c_Message_Osynth(c_Message_Oanalz(V_H)),c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)),tc_fun(tc_Message_Omsg,tc_bool)) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| c_lessequals(c_Message_Oparts(c_Set_Oinsert(V_X,V_H,tc_Message_Omsg)),c_Lattices_Oupper__semilattice__class_Osup(c_Message_Osynth(c_Message_Oanalz(V_H)),c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)),tc_fun(tc_Message_Omsg,tc_bool)) )
<=> ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| c_lessequals(c_Message_Oparts(c_Set_Oinsert(V_X,V_H,tc_Message_Omsg)),c_Lattices_Oupper__semilattice__class_Osup(c_Message_Osynth(c_Message_Oanalz(V_H)),c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)),tc_fun(tc_Message_Omsg,tc_bool)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,plain,
^ [V_H: $i,V_X: $i] :
rewrite(( ( c_lessequals(c_Message_Oparts(c_Set_Oinsert(V_X,V_H,tc_Message_Omsg)),c_Lattices_Oupper__semilattice__class_Osup(c_Message_Osynth(c_Message_Oanalz(V_H)),c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)),tc_fun(tc_Message_Omsg,tc_bool))
| ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg) )
<=> ( ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| c_lessequals(c_Message_Oparts(c_Set_Oinsert(V_X,V_H,tc_Message_Omsg)),c_Lattices_Oupper__semilattice__class_Osup(c_Message_Osynth(c_Message_Oanalz(V_H)),c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)),tc_fun(tc_Message_Omsg,tc_bool)) ) )),
inference(bind,[status(th)],[]) ).
tff(40,plain,
( ! [V_H: $i,V_X: $i] :
( c_lessequals(c_Message_Oparts(c_Set_Oinsert(V_X,V_H,tc_Message_Omsg)),c_Lattices_Oupper__semilattice__class_Osup(c_Message_Osynth(c_Message_Oanalz(V_H)),c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)),tc_fun(tc_Message_Omsg,tc_bool))
| ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg) )
<=> ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| c_lessequals(c_Message_Oparts(c_Set_Oinsert(V_X,V_H,tc_Message_Omsg)),c_Lattices_Oupper__semilattice__class_Osup(c_Message_Osynth(c_Message_Oanalz(V_H)),c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)),tc_fun(tc_Message_Omsg,tc_bool)) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,axiom,
! [V_H: $i,V_X: $i] :
( c_lessequals(c_Message_Oparts(c_Set_Oinsert(V_X,V_H,tc_Message_Omsg)),c_Lattices_Oupper__semilattice__class_Osup(c_Message_Osynth(c_Message_Oanalz(V_H)),c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)),tc_fun(tc_Message_Omsg,tc_bool))
| ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Fake__parts__insert_0) ).
tff(42,plain,
! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| c_lessequals(c_Message_Oparts(c_Set_Oinsert(V_X,V_H,tc_Message_Omsg)),c_Lattices_Oupper__semilattice__class_Osup(c_Message_Osynth(c_Message_Oanalz(V_H)),c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)),tc_fun(tc_Message_Omsg,tc_bool)) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| c_lessequals(c_Message_Oparts(c_Set_Oinsert(V_X,V_H,tc_Message_Omsg)),c_Lattices_Oupper__semilattice__class_Osup(c_Message_Osynth(c_Message_Oanalz(V_H)),c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)),tc_fun(tc_Message_Omsg,tc_bool)) ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| c_lessequals(c_Message_Oparts(c_Set_Oinsert(V_X,V_H,tc_Message_Omsg)),c_Lattices_Oupper__semilattice__class_Osup(c_Message_Osynth(c_Message_Oanalz(V_H)),c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)),tc_fun(tc_Message_Omsg,tc_bool)) ),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| c_lessequals(c_Message_Oparts(c_Set_Oinsert(V_X,V_H,tc_Message_Omsg)),c_Lattices_Oupper__semilattice__class_Osup(c_Message_Osynth(c_Message_Oanalz(V_H)),c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)),tc_fun(tc_Message_Omsg,tc_bool)) ),
inference(modus_ponens,[status(thm)],[44,37]) ).
tff(46,plain,
( ( ~ ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| c_lessequals(c_Message_Oparts(c_Set_Oinsert(V_X,V_H,tc_Message_Omsg)),c_Lattices_Oupper__semilattice__class_Osup(c_Message_Osynth(c_Message_Oanalz(V_H)),c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)),tc_fun(tc_Message_Omsg,tc_bool)) )
| ~ c_in(v_X,c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg)
| c_lessequals(c_Message_Oparts(c_Set_Oinsert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg)),c_Lattices_Oupper__semilattice__class_Osup(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool)),tc_fun(tc_Message_Omsg,tc_bool)) )
<=> ( ~ ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| c_lessequals(c_Message_Oparts(c_Set_Oinsert(V_X,V_H,tc_Message_Omsg)),c_Lattices_Oupper__semilattice__class_Osup(c_Message_Osynth(c_Message_Oanalz(V_H)),c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)),tc_fun(tc_Message_Omsg,tc_bool)) )
| ~ c_in(v_X,c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg)
| c_lessequals(c_Message_Oparts(c_Set_Oinsert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg)),c_Lattices_Oupper__semilattice__class_Osup(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool)),tc_fun(tc_Message_Omsg,tc_bool)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
( ~ ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| c_lessequals(c_Message_Oparts(c_Set_Oinsert(V_X,V_H,tc_Message_Omsg)),c_Lattices_Oupper__semilattice__class_Osup(c_Message_Osynth(c_Message_Oanalz(V_H)),c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)),tc_fun(tc_Message_Omsg,tc_bool)) )
| ~ c_in(v_X,c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg)
| c_lessequals(c_Message_Oparts(c_Set_Oinsert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg)),c_Lattices_Oupper__semilattice__class_Osup(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool)),tc_fun(tc_Message_Omsg,tc_bool)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
( ~ ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| c_lessequals(c_Message_Oparts(c_Set_Oinsert(V_X,V_H,tc_Message_Omsg)),c_Lattices_Oupper__semilattice__class_Osup(c_Message_Osynth(c_Message_Oanalz(V_H)),c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)),tc_fun(tc_Message_Omsg,tc_bool)) )
| ~ c_in(v_X,c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg)
| c_lessequals(c_Message_Oparts(c_Set_Oinsert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg)),c_Lattices_Oupper__semilattice__class_Osup(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool)),tc_fun(tc_Message_Omsg,tc_bool)) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
c_lessequals(c_Message_Oparts(c_Set_Oinsert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg)),c_Lattices_Oupper__semilattice__class_Osup(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool)),tc_fun(tc_Message_Omsg,tc_bool)),
inference(unit_resolution,[status(thm)],[48,45,35]) ).
tff(50,plain,
c_lessequals(c_Set_Oinsert(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent))),tc_Message_Omsg),c_Lattices_Oupper__semilattice__class_Osup(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool)),tc_fun(tc_Message_Omsg,tc_bool)),
inference(modus_ponens,[status(thm)],[49,32]) ).
tff(51,plain,
^ [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
refl(( ( ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool))
| c_in(V_x,V_B,T_a) )
<=> ( ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool))
| c_in(V_x,V_B,T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(52,plain,
( ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool))
| c_in(V_x,V_B,T_a) )
<=> ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool))
| c_in(V_x,V_B,T_a) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,plain,
( ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool))
| c_in(V_x,V_B,T_a) )
<=> ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool))
| c_in(V_x,V_B,T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,plain,
^ [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
rewrite(( ( c_in(V_x,V_B,T_a)
| ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) )
<=> ( ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool))
| c_in(V_x,V_B,T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(55,plain,
( ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_x,V_B,T_a)
| ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) )
<=> ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool))
| c_in(V_x,V_B,T_a) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,axiom,
! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_x,V_B,T_a)
| ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_0) ).
tff(57,plain,
! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool))
| c_in(V_x,V_B,T_a) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool))
| c_in(V_x,V_B,T_a) ),
inference(modus_ponens,[status(thm)],[57,53]) ).
tff(59,plain,
! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool))
| c_in(V_x,V_B,T_a) ),
inference(skolemize,[status(sab)],[58]) ).
tff(60,plain,
! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool))
| c_in(V_x,V_B,T_a) ),
inference(modus_ponens,[status(thm)],[59,52]) ).
tff(61,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool))
| c_in(V_x,V_B,T_a) )
| ~ c_lessequals(c_Set_Oinsert(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent))),tc_Message_Omsg),c_Lattices_Oupper__semilattice__class_Osup(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool)),tc_fun(tc_Message_Omsg,tc_bool))
| c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Lattices_Oupper__semilattice__class_Osup(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool))
| c_in(V_x,V_B,T_a) )
| ~ c_lessequals(c_Set_Oinsert(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent))),tc_Message_Omsg),c_Lattices_Oupper__semilattice__class_Osup(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool)),tc_fun(tc_Message_Omsg,tc_bool))
| c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Lattices_Oupper__semilattice__class_Osup(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,plain,
( ~ ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool))
| c_in(V_x,V_B,T_a) )
| ~ c_lessequals(c_Set_Oinsert(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent))),tc_Message_Omsg),c_Lattices_Oupper__semilattice__class_Osup(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool)),tc_fun(tc_Message_Omsg,tc_bool))
| c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Lattices_Oupper__semilattice__class_Osup(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],[]) ).
tff(63,plain,
( ~ ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool))
| c_in(V_x,V_B,T_a) )
| ~ c_lessequals(c_Set_Oinsert(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent))),tc_Message_Omsg),c_Lattices_Oupper__semilattice__class_Osup(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool)),tc_fun(tc_Message_Omsg,tc_bool))
| c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Lattices_Oupper__semilattice__class_Osup(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
( ~ c_lessequals(c_Set_Oinsert(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent))),tc_Message_Omsg),c_Lattices_Oupper__semilattice__class_Osup(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool)),tc_fun(tc_Message_Omsg,tc_bool))
| c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Lattices_Oupper__semilattice__class_Osup(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg) ),
inference(unit_resolution,[status(thm)],[63,60]) ).
tff(65,plain,
c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Lattices_Oupper__semilattice__class_Osup(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[64,50]) ).
tff(66,plain,
( ~ c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent))),tc_Message_Omsg)
<=> ~ c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent))),tc_Message_Omsg) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,axiom,
~ c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent))),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(68,plain,
~ c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent))),tc_Message_Omsg),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
^ [V_c: $i,V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
refl(( ( ~ c_in(V_c,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| c_in(V_c,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(V_A,V_B,V_X),V_evs,tc_Event_Oevent))),tc_Message_Omsg) )
<=> ( ~ c_in(V_c,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| c_in(V_c,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(V_A,V_B,V_X),V_evs,tc_Event_Oevent))),tc_Message_Omsg) ) )),
inference(bind,[status(th)],[]) ).
tff(70,plain,
( ! [V_c: $i,V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(V_c,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| c_in(V_c,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(V_A,V_B,V_X),V_evs,tc_Event_Oevent))),tc_Message_Omsg) )
<=> ! [V_c: $i,V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(V_c,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| c_in(V_c,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(V_A,V_B,V_X),V_evs,tc_Event_Oevent))),tc_Message_Omsg) ) ),
inference(quant_intro,[status(thm)],[69]) ).
tff(71,plain,
( ! [V_c: $i,V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(V_c,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| c_in(V_c,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(V_A,V_B,V_X),V_evs,tc_Event_Oevent))),tc_Message_Omsg) )
<=> ! [V_c: $i,V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(V_c,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| c_in(V_c,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(V_A,V_B,V_X),V_evs,tc_Event_Oevent))),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(72,axiom,
! [V_c: $i,V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(V_c,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| c_in(V_c,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(V_A,V_B,V_X),V_evs,tc_Event_Oevent))),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__mono__contra_I1_J_0) ).
tff(73,plain,
! [V_c: $i,V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(V_c,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| c_in(V_c,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(V_A,V_B,V_X),V_evs,tc_Event_Oevent))),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
! [V_c: $i,V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(V_c,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| c_in(V_c,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(V_A,V_B,V_X),V_evs,tc_Event_Oevent))),tc_Message_Omsg) ),
inference(skolemize,[status(sab)],[73]) ).
tff(75,plain,
! [V_c: $i,V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(V_c,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| c_in(V_c,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(V_A,V_B,V_X),V_evs,tc_Event_Oevent))),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[74,70]) ).
tff(76,plain,
( ( ~ ! [V_c: $i,V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(V_c,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| c_in(V_c,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(V_A,V_B,V_X),V_evs,tc_Event_Oevent))),tc_Message_Omsg) )
| ~ c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent))),tc_Message_Omsg) )
<=> ( ~ ! [V_c: $i,V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(V_c,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| c_in(V_c,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(V_A,V_B,V_X),V_evs,tc_Event_Oevent))),tc_Message_Omsg) )
| ~ c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent))),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(77,plain,
( ~ ! [V_c: $i,V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(V_c,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| c_in(V_c,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(V_A,V_B,V_X),V_evs,tc_Event_Oevent))),tc_Message_Omsg) )
| ~ c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent))),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],[]) ).
tff(78,plain,
( ~ ! [V_c: $i,V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(V_c,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| c_in(V_c,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(V_A,V_B,V_X),V_evs,tc_Event_Oevent))),tc_Message_Omsg) )
| ~ c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent))),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
~ c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[78,75,68]) ).
tff(80,plain,
( ( c_Message_Oagent_OServer != c_Message_Oagent_OSpy )
<=> ( c_Message_Oagent_OServer != c_Message_Oagent_OSpy ) ),
inference(rewrite,[status(thm)],[]) ).
tff(81,axiom,
c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_agent_Osimps_I4_J_0) ).
tff(82,plain,
c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
^ [V_agent2_H: $i,V_agent2: $i,V_agent1_H: $i,V_agent1: $i,V_msg_H: $i,V_msg: $i] :
refl(( ( ( c_Event_Oevent_OSays(V_agent1,V_agent2,V_msg) != c_Event_Oevent_OSays(V_agent1_H,V_agent2_H,V_msg_H) )
| ( V_agent1 = V_agent1_H ) )
<=> ( ( c_Event_Oevent_OSays(V_agent1,V_agent2,V_msg) != c_Event_Oevent_OSays(V_agent1_H,V_agent2_H,V_msg_H) )
| ( V_agent1 = V_agent1_H ) ) )),
inference(bind,[status(th)],[]) ).
tff(84,plain,
( ! [V_agent2_H: $i,V_agent2: $i,V_agent1_H: $i,V_agent1: $i,V_msg_H: $i,V_msg: $i] :
( ( c_Event_Oevent_OSays(V_agent1,V_agent2,V_msg) != c_Event_Oevent_OSays(V_agent1_H,V_agent2_H,V_msg_H) )
| ( V_agent1 = V_agent1_H ) )
<=> ! [V_agent2_H: $i,V_agent2: $i,V_agent1_H: $i,V_agent1: $i,V_msg_H: $i,V_msg: $i] :
( ( c_Event_Oevent_OSays(V_agent1,V_agent2,V_msg) != c_Event_Oevent_OSays(V_agent1_H,V_agent2_H,V_msg_H) )
| ( V_agent1 = V_agent1_H ) ) ),
inference(quant_intro,[status(thm)],[83]) ).
tff(85,plain,
( ! [V_agent2_H: $i,V_agent2: $i,V_agent1_H: $i,V_agent1: $i,V_msg_H: $i,V_msg: $i] :
( ( c_Event_Oevent_OSays(V_agent1,V_agent2,V_msg) != c_Event_Oevent_OSays(V_agent1_H,V_agent2_H,V_msg_H) )
| ( V_agent1 = V_agent1_H ) )
<=> ! [V_agent2_H: $i,V_agent2: $i,V_agent1_H: $i,V_agent1: $i,V_msg_H: $i,V_msg: $i] :
( ( c_Event_Oevent_OSays(V_agent1,V_agent2,V_msg) != c_Event_Oevent_OSays(V_agent1_H,V_agent2_H,V_msg_H) )
| ( V_agent1 = V_agent1_H ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(86,axiom,
! [V_agent2_H: $i,V_agent2: $i,V_agent1_H: $i,V_agent1: $i,V_msg_H: $i,V_msg: $i] :
( ( c_Event_Oevent_OSays(V_agent1,V_agent2,V_msg) != c_Event_Oevent_OSays(V_agent1_H,V_agent2_H,V_msg_H) )
| ( V_agent1 = V_agent1_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I1_J_0) ).
tff(87,plain,
! [V_agent2_H: $i,V_agent2: $i,V_agent1_H: $i,V_agent1: $i,V_msg_H: $i,V_msg: $i] :
( ( c_Event_Oevent_OSays(V_agent1,V_agent2,V_msg) != c_Event_Oevent_OSays(V_agent1_H,V_agent2_H,V_msg_H) )
| ( V_agent1 = V_agent1_H ) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
! [V_agent2_H: $i,V_agent2: $i,V_agent1_H: $i,V_agent1: $i,V_msg_H: $i,V_msg: $i] :
( ( c_Event_Oevent_OSays(V_agent1,V_agent2,V_msg) != c_Event_Oevent_OSays(V_agent1_H,V_agent2_H,V_msg_H) )
| ( V_agent1 = V_agent1_H ) ),
inference(skolemize,[status(sab)],[87]) ).
tff(89,plain,
! [V_agent2_H: $i,V_agent2: $i,V_agent1_H: $i,V_agent1: $i,V_msg_H: $i,V_msg: $i] :
( ( c_Event_Oevent_OSays(V_agent1,V_agent2,V_msg) != c_Event_Oevent_OSays(V_agent1_H,V_agent2_H,V_msg_H) )
| ( V_agent1 = V_agent1_H ) ),
inference(modus_ponens,[status(thm)],[88,84]) ).
tff(90,plain,
( ( ~ ! [V_agent2_H: $i,V_agent2: $i,V_agent1_H: $i,V_agent1: $i,V_msg_H: $i,V_msg: $i] :
( ( c_Event_Oevent_OSays(V_agent1,V_agent2,V_msg) != c_Event_Oevent_OSays(V_agent1_H,V_agent2_H,V_msg_H) )
| ( V_agent1 = V_agent1_H ) )
| ( c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))) != c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X) )
| ( c_Message_Oagent_OServer = c_Message_Oagent_OSpy ) )
<=> ( ~ ! [V_agent2_H: $i,V_agent2: $i,V_agent1_H: $i,V_agent1: $i,V_msg_H: $i,V_msg: $i] :
( ( c_Event_Oevent_OSays(V_agent1,V_agent2,V_msg) != c_Event_Oevent_OSays(V_agent1_H,V_agent2_H,V_msg_H) )
| ( V_agent1 = V_agent1_H ) )
| ( c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))) != c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X) )
| ( c_Message_Oagent_OServer = c_Message_Oagent_OSpy ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(91,plain,
( ~ ! [V_agent2_H: $i,V_agent2: $i,V_agent1_H: $i,V_agent1: $i,V_msg_H: $i,V_msg: $i] :
( ( c_Event_Oevent_OSays(V_agent1,V_agent2,V_msg) != c_Event_Oevent_OSays(V_agent1_H,V_agent2_H,V_msg_H) )
| ( V_agent1 = V_agent1_H ) )
| ( c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))) != c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X) )
| ( c_Message_Oagent_OServer = c_Message_Oagent_OSpy ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(92,plain,
( ~ ! [V_agent2_H: $i,V_agent2: $i,V_agent1_H: $i,V_agent1: $i,V_msg_H: $i,V_msg: $i] :
( ( c_Event_Oevent_OSays(V_agent1,V_agent2,V_msg) != c_Event_Oevent_OSays(V_agent1_H,V_agent2_H,V_msg_H) )
| ( V_agent1 = V_agent1_H ) )
| ( c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))) != c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X) )
| ( c_Message_Oagent_OServer = c_Message_Oagent_OSpy ) ),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))) != c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),
inference(unit_resolution,[status(thm)],[92,89,82]) ).
tff(94,plain,
( c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent)
<=> c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent) ),
inference(rewrite,[status(thm)],[]) ).
tff(95,axiom,
c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
tff(96,plain,
c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent),
inference(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
^ [V_x: $i,V_xs: $i,T_a: $i,V_y: $i] :
refl(( ( ( V_y = V_x )
| ~ c_in(V_y,c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a),T_a)
| c_in(V_y,c_List_Oset(V_xs,T_a),T_a) )
<=> ( ( V_y = V_x )
| ~ c_in(V_y,c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a),T_a)
| c_in(V_y,c_List_Oset(V_xs,T_a),T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(98,plain,
( ! [V_x: $i,V_xs: $i,T_a: $i,V_y: $i] :
( ( V_y = V_x )
| ~ c_in(V_y,c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a),T_a)
| c_in(V_y,c_List_Oset(V_xs,T_a),T_a) )
<=> ! [V_x: $i,V_xs: $i,T_a: $i,V_y: $i] :
( ( V_y = V_x )
| ~ c_in(V_y,c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a),T_a)
| c_in(V_y,c_List_Oset(V_xs,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[97]) ).
tff(99,plain,
( ! [V_x: $i,V_xs: $i,T_a: $i,V_y: $i] :
( ( V_y = V_x )
| ~ c_in(V_y,c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a),T_a)
| c_in(V_y,c_List_Oset(V_xs,T_a),T_a) )
<=> ! [V_x: $i,V_xs: $i,T_a: $i,V_y: $i] :
( ( V_y = V_x )
| ~ c_in(V_y,c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a),T_a)
| c_in(V_y,c_List_Oset(V_xs,T_a),T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(100,plain,
^ [V_x: $i,V_xs: $i,T_a: $i,V_y: $i] :
trans(monotonicity(rewrite(( ( c_in(V_y,c_List_Oset(V_xs,T_a),T_a)
| ( V_y = V_x ) )
<=> ( ( V_y = V_x )
| c_in(V_y,c_List_Oset(V_xs,T_a),T_a) ) )),
( ( c_in(V_y,c_List_Oset(V_xs,T_a),T_a)
| ( V_y = V_x )
| ~ c_in(V_y,c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a),T_a) )
<=> ( ( V_y = V_x )
| c_in(V_y,c_List_Oset(V_xs,T_a),T_a)
| ~ c_in(V_y,c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a),T_a) ) )),
rewrite(( ( ( V_y = V_x )
| c_in(V_y,c_List_Oset(V_xs,T_a),T_a)
| ~ c_in(V_y,c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a),T_a) )
<=> ( ( V_y = V_x )
| ~ c_in(V_y,c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a),T_a)
| c_in(V_y,c_List_Oset(V_xs,T_a),T_a) ) )),
( ( c_in(V_y,c_List_Oset(V_xs,T_a),T_a)
| ( V_y = V_x )
| ~ c_in(V_y,c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a),T_a) )
<=> ( ( V_y = V_x )
| ~ c_in(V_y,c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a),T_a)
| c_in(V_y,c_List_Oset(V_xs,T_a),T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(101,plain,
( ! [V_x: $i,V_xs: $i,T_a: $i,V_y: $i] :
( c_in(V_y,c_List_Oset(V_xs,T_a),T_a)
| ( V_y = V_x )
| ~ c_in(V_y,c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a),T_a) )
<=> ! [V_x: $i,V_xs: $i,T_a: $i,V_y: $i] :
( ( V_y = V_x )
| ~ c_in(V_y,c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a),T_a)
| c_in(V_y,c_List_Oset(V_xs,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[100]) ).
tff(102,axiom,
! [V_x: $i,V_xs: $i,T_a: $i,V_y: $i] :
( c_in(V_y,c_List_Oset(V_xs,T_a),T_a)
| ( V_y = V_x )
| ~ c_in(V_y,c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__ConsD_0) ).
tff(103,plain,
! [V_x: $i,V_xs: $i,T_a: $i,V_y: $i] :
( ( V_y = V_x )
| ~ c_in(V_y,c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a),T_a)
| c_in(V_y,c_List_Oset(V_xs,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[102,101]) ).
tff(104,plain,
! [V_x: $i,V_xs: $i,T_a: $i,V_y: $i] :
( ( V_y = V_x )
| ~ c_in(V_y,c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a),T_a)
| c_in(V_y,c_List_Oset(V_xs,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[103,99]) ).
tff(105,plain,
! [V_x: $i,V_xs: $i,T_a: $i,V_y: $i] :
( ( V_y = V_x )
| ~ c_in(V_y,c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a),T_a)
| c_in(V_y,c_List_Oset(V_xs,T_a),T_a) ),
inference(skolemize,[status(sab)],[104]) ).
tff(106,plain,
! [V_x: $i,V_xs: $i,T_a: $i,V_y: $i] :
( ( V_y = V_x )
| ~ c_in(V_y,c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a),T_a)
| c_in(V_y,c_List_Oset(V_xs,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[105,98]) ).
tff(107,plain,
( ( ~ ! [V_x: $i,V_xs: $i,T_a: $i,V_y: $i] :
( ( V_y = V_x )
| ~ c_in(V_y,c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a),T_a)
| c_in(V_y,c_List_Oset(V_xs,T_a),T_a) )
| c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent)
| ( c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))) = c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X) ) )
<=> ( ~ ! [V_x: $i,V_xs: $i,T_a: $i,V_y: $i] :
( ( V_y = V_x )
| ~ c_in(V_y,c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a),T_a)
| c_in(V_y,c_List_Oset(V_xs,T_a),T_a) )
| c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent)
| ( c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))) = c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(108,plain,
( ( ( c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))) = c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X) )
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent)
| c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent) )
<=> ( c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent)
| ( c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))) = c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(109,plain,
( ( ~ ! [V_x: $i,V_xs: $i,T_a: $i,V_y: $i] :
( ( V_y = V_x )
| ~ c_in(V_y,c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a),T_a)
| c_in(V_y,c_List_Oset(V_xs,T_a),T_a) )
| ( c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))) = c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X) )
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent)
| c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent) )
<=> ( ~ ! [V_x: $i,V_xs: $i,T_a: $i,V_y: $i] :
( ( V_y = V_x )
| ~ c_in(V_y,c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a),T_a)
| c_in(V_y,c_List_Oset(V_xs,T_a),T_a) )
| c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent)
| ( c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))) = c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X) ) ) ),
inference(monotonicity,[status(thm)],[108]) ).
tff(110,plain,
( ( ~ ! [V_x: $i,V_xs: $i,T_a: $i,V_y: $i] :
( ( V_y = V_x )
| ~ c_in(V_y,c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a),T_a)
| c_in(V_y,c_List_Oset(V_xs,T_a),T_a) )
| ( c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))) = c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X) )
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent)
| c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent) )
<=> ( ~ ! [V_x: $i,V_xs: $i,T_a: $i,V_y: $i] :
( ( V_y = V_x )
| ~ c_in(V_y,c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a),T_a)
| c_in(V_y,c_List_Oset(V_xs,T_a),T_a) )
| c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent)
| ( c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))) = c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X) ) ) ),
inference(transitivity,[status(thm)],[109,107]) ).
tff(111,plain,
( ~ ! [V_x: $i,V_xs: $i,T_a: $i,V_y: $i] :
( ( V_y = V_x )
| ~ c_in(V_y,c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a),T_a)
| c_in(V_y,c_List_Oset(V_xs,T_a),T_a) )
| ( c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))) = c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X) )
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent)
| c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent) ),
inference(quant_inst,[status(thm)],[]) ).
tff(112,plain,
( ~ ! [V_x: $i,V_xs: $i,T_a: $i,V_y: $i] :
( ( V_y = V_x )
| ~ c_in(V_y,c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a),T_a)
| c_in(V_y,c_List_Oset(V_xs,T_a),T_a) )
| c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent)
| ( c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))) = c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X) ) ),
inference(modus_ponens,[status(thm)],[111,110]) ).
tff(113,plain,
( c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent)
| ( c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))) = c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X) ) ),
inference(unit_resolution,[status(thm)],[112,106,96]) ).
tff(114,plain,
c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent),
inference(unit_resolution,[status(thm)],[113,93]) ).
tff(115,plain,
^ [V_x: $i,V_xs: $i,T_a: $i] :
refl(( ( c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_Set_Oinsert(V_x,c_List_Oset(V_xs,T_a),T_a) )
<=> ( c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_Set_Oinsert(V_x,c_List_Oset(V_xs,T_a),T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(116,plain,
( ! [V_x: $i,V_xs: $i,T_a: $i] : ( c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_Set_Oinsert(V_x,c_List_Oset(V_xs,T_a),T_a) )
<=> ! [V_x: $i,V_xs: $i,T_a: $i] : ( c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_Set_Oinsert(V_x,c_List_Oset(V_xs,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[115]) ).
tff(117,plain,
( ! [V_x: $i,V_xs: $i,T_a: $i] : ( c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_Set_Oinsert(V_x,c_List_Oset(V_xs,T_a),T_a) )
<=> ! [V_x: $i,V_xs: $i,T_a: $i] : ( c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_Set_Oinsert(V_x,c_List_Oset(V_xs,T_a),T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(118,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] : ( c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_Set_Oinsert(V_x,c_List_Oset(V_xs,T_a),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset_Osimps_I2_J_0) ).
tff(119,plain,
! [V_x: $i,V_xs: $i,T_a: $i] : ( c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_Set_Oinsert(V_x,c_List_Oset(V_xs,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[118,117]) ).
tff(120,plain,
! [V_x: $i,V_xs: $i,T_a: $i] : ( c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_Set_Oinsert(V_x,c_List_Oset(V_xs,T_a),T_a) ),
inference(skolemize,[status(sab)],[119]) ).
tff(121,plain,
! [V_x: $i,V_xs: $i,T_a: $i] : ( c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_Set_Oinsert(V_x,c_List_Oset(V_xs,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[120,116]) ).
tff(122,plain,
( ~ ! [V_x: $i,V_xs: $i,T_a: $i] : ( c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_Set_Oinsert(V_x,c_List_Oset(V_xs,T_a),T_a) )
| ( c_List_Oset(c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent),tc_Event_Oevent) = c_Set_Oinsert(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(123,plain,
c_List_Oset(c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent),tc_Event_Oevent) = c_Set_Oinsert(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent),
inference(unit_resolution,[status(thm)],[122,121]) ).
tff(124,plain,
c_Set_Oinsert(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent) = c_List_Oset(c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent),tc_Event_Oevent),
inference(symmetry,[status(thm)],[123]) ).
tff(125,plain,
( c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_Set_Oinsert(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent)
<=> c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent) ),
inference(monotonicity,[status(thm)],[124]) ).
tff(126,plain,
( c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent)
<=> c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_Set_Oinsert(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent) ),
inference(symmetry,[status(thm)],[125]) ).
tff(127,plain,
( ~ c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent)
<=> ~ c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_Set_Oinsert(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent) ),
inference(monotonicity,[status(thm)],[126]) ).
tff(128,plain,
( ~ c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent)
<=> ~ c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent) ),
inference(rewrite,[status(thm)],[]) ).
tff(129,axiom,
~ c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).
tff(130,plain,
~ c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),v_evsf,tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent),
inference(modus_ponens,[status(thm)],[129,128]) ).
tff(131,plain,
~ c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_Set_Oinsert(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent),
inference(modus_ponens,[status(thm)],[130,127]) ).
tff(132,plain,
^ [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
refl(( ( ~ c_in(V_a,V_A,T_a)
| c_in(V_a,c_Set_Oinsert(V_b,V_A,T_a),T_a) )
<=> ( ~ c_in(V_a,V_A,T_a)
| c_in(V_a,c_Set_Oinsert(V_b,V_A,T_a),T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(133,plain,
( ! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| c_in(V_a,c_Set_Oinsert(V_b,V_A,T_a),T_a) )
<=> ! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| c_in(V_a,c_Set_Oinsert(V_b,V_A,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[132]) ).
tff(134,plain,
( ! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| c_in(V_a,c_Set_Oinsert(V_b,V_A,T_a),T_a) )
<=> ! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| c_in(V_a,c_Set_Oinsert(V_b,V_A,T_a),T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(135,plain,
^ [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
rewrite(( ( c_in(V_a,c_Set_Oinsert(V_b,V_A,T_a),T_a)
| ~ c_in(V_a,V_A,T_a) )
<=> ( ~ c_in(V_a,V_A,T_a)
| c_in(V_a,c_Set_Oinsert(V_b,V_A,T_a),T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(136,plain,
( ! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( c_in(V_a,c_Set_Oinsert(V_b,V_A,T_a),T_a)
| ~ c_in(V_a,V_A,T_a) )
<=> ! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| c_in(V_a,c_Set_Oinsert(V_b,V_A,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[135]) ).
tff(137,axiom,
! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( c_in(V_a,c_Set_Oinsert(V_b,V_A,T_a),T_a)
| ~ c_in(V_a,V_A,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_2) ).
tff(138,plain,
! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| c_in(V_a,c_Set_Oinsert(V_b,V_A,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[137,136]) ).
tff(139,plain,
! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| c_in(V_a,c_Set_Oinsert(V_b,V_A,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[138,134]) ).
tff(140,plain,
! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| c_in(V_a,c_Set_Oinsert(V_b,V_A,T_a),T_a) ),
inference(skolemize,[status(sab)],[139]) ).
tff(141,plain,
! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| c_in(V_a,c_Set_Oinsert(V_b,V_A,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[140,133]) ).
tff(142,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| c_in(V_a,c_Set_Oinsert(V_b,V_A,T_a),T_a) )
| ~ c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent)
| c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_Set_Oinsert(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| c_in(V_a,c_Set_Oinsert(V_b,V_A,T_a),T_a) )
| ~ c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent)
| c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_Set_Oinsert(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(143,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| c_in(V_a,c_Set_Oinsert(V_b,V_A,T_a),T_a) )
| ~ c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent)
| c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_Set_Oinsert(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent) ),
inference(quant_inst,[status(thm)],[]) ).
tff(144,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| c_in(V_a,c_Set_Oinsert(V_b,V_A,T_a),T_a) )
| ~ c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent)
| c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_Set_Oinsert(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent) ),
inference(modus_ponens,[status(thm)],[143,142]) ).
tff(145,plain,
( ~ c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent)
| c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_Set_Oinsert(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,v_Ba,v_X),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent) ),
inference(unit_resolution,[status(thm)],[144,141]) ).
tff(146,plain,
~ c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent),
inference(unit_resolution,[status(thm)],[145,131]) ).
tff(147,plain,
( ( c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent)
| c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg) )
<=> ( c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent)
| c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(148,plain,
( ( c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent)
| c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg) )
<=> ( c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent)
| c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(149,plain,
( ( c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent) )
<=> ( c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(150,plain,
( ( c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg) )
<=> ( c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(151,plain,
( ( c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent) )
<=> ( c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent) ) ),
inference(monotonicity,[status(thm)],[150]) ).
tff(152,plain,
( ( c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent) )
<=> ( c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent) ) ),
inference(transitivity,[status(thm)],[151,149]) ).
tff(153,plain,
( ( c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent)
| c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg) )
<=> ( c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent)
| c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg) ) ),
inference(monotonicity,[status(thm)],[152]) ).
tff(154,plain,
( ( c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent)
| c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg) )
<=> ( c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent)
| c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg) ) ),
inference(transitivity,[status(thm)],[153,148]) ).
tff(155,axiom,
( c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent)
| c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_7) ).
tff(156,plain,
( c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent)
| c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[155,154]) ).
tff(157,plain,
( c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent)
| c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[156,147]) ).
tff(158,plain,
( c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent)
| c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[157,147]) ).
tff(159,plain,
( c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent)
| c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[158,147]) ).
tff(160,plain,
( c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evsf,tc_Event_Oevent),tc_Event_Oevent)
| c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[159,147]) ).
tff(161,plain,
~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[160,146,114,79]) ).
tff(162,plain,
^ [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
refl(( ( c_in(V_c,V_B,T_a)
| c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) )
<=> ( c_in(V_c,V_B,T_a)
| c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(163,plain,
( ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) )
<=> ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ) ),
inference(quant_intro,[status(thm)],[162]) ).
tff(164,plain,
( ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) )
<=> ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(165,plain,
^ [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
trans(monotonicity(rewrite(( ( c_in(V_c,V_B,T_a)
| c_in(V_c,V_A,T_a) )
<=> ( c_in(V_c,V_B,T_a)
| c_in(V_c,V_A,T_a) ) )),
( ( c_in(V_c,V_B,T_a)
| c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) )
<=> ( c_in(V_c,V_B,T_a)
| c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ) )),
rewrite(( ( c_in(V_c,V_B,T_a)
| c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) )
<=> ( c_in(V_c,V_B,T_a)
| c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ) )),
( ( c_in(V_c,V_B,T_a)
| c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) )
<=> ( c_in(V_c,V_B,T_a)
| c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(166,plain,
( ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) )
<=> ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ) ),
inference(quant_intro,[status(thm)],[165]) ).
tff(167,axiom,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnE_0) ).
tff(168,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ),
inference(modus_ponens,[status(thm)],[167,166]) ).
tff(169,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ),
inference(modus_ponens,[status(thm)],[168,164]) ).
tff(170,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ),
inference(skolemize,[status(sab)],[169]) ).
tff(171,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ),
inference(modus_ponens,[status(thm)],[170,163]) ).
tff(172,plain,
( ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) )
| c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Lattices_Oupper__semilattice__class_Osup(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg) )
<=> ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) )
| c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Lattices_Oupper__semilattice__class_Osup(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(173,plain,
( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) )
| c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Lattices_Oupper__semilattice__class_Osup(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],[]) ).
tff(174,plain,
( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) )
| c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Lattices_Oupper__semilattice__class_Osup(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[173,172]) ).
tff(175,plain,
c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[174,171,161,65]) ).
tff(176,plain,
^ [V_H: $i,V_X: $i] :
refl(( ( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg) )
<=> ( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg) ) )),
inference(bind,[status(th)],[]) ).
tff(177,plain,
( ! [V_H: $i,V_X: $i] :
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg) )
<=> ! [V_H: $i,V_X: $i] :
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg) ) ),
inference(quant_intro,[status(thm)],[176]) ).
tff(178,plain,
( ! [V_H: $i,V_X: $i] :
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg) )
<=> ! [V_H: $i,V_X: $i] :
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(179,axiom,
! [V_H: $i,V_X: $i] :
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__conj__parts_0) ).
tff(180,plain,
! [V_H: $i,V_X: $i] :
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[179,178]) ).
tff(181,plain,
! [V_H: $i,V_X: $i] :
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg) ),
inference(skolemize,[status(sab)],[180]) ).
tff(182,plain,
! [V_H: $i,V_X: $i] :
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[181,177]) ).
tff(183,plain,
( ( ~ ! [V_H: $i,V_X: $i] :
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg) )
| c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg) )
<=> ( ~ ! [V_H: $i,V_X: $i] :
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg) )
| c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(184,plain,
( ~ ! [V_H: $i,V_X: $i] :
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg) )
| c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],[]) ).
tff(185,plain,
( ~ ! [V_H: $i,V_X: $i] :
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg) )
| c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[184,183]) ).
tff(186,plain,
~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[185,182,161]) ).
tff(187,plain,
^ [V_H: $i,V_X: $i,V_K: $i] :
refl(( ( c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(hAPP(c_Message_Omsg_OKey,V_K),V_H,tc_Message_Omsg) )
<=> ( c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(hAPP(c_Message_Omsg_OKey,V_K),V_H,tc_Message_Omsg) ) )),
inference(bind,[status(th)],[]) ).
tff(188,plain,
( ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(hAPP(c_Message_Omsg_OKey,V_K),V_H,tc_Message_Omsg) )
<=> ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(hAPP(c_Message_Omsg_OKey,V_K),V_H,tc_Message_Omsg) ) ),
inference(quant_intro,[status(thm)],[187]) ).
tff(189,plain,
( ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(hAPP(c_Message_Omsg_OKey,V_K),V_H,tc_Message_Omsg) )
<=> ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(hAPP(c_Message_Omsg_OKey,V_K),V_H,tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(190,plain,
^ [V_H: $i,V_X: $i,V_K: $i] :
trans(monotonicity(rewrite(( ( c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Osynth(V_H),tc_Message_Omsg) )
<=> ( c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Osynth(V_H),tc_Message_Omsg) ) )),
( ( c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(hAPP(c_Message_Omsg_OKey,V_K),V_H,tc_Message_Omsg) )
<=> ( c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(hAPP(c_Message_Omsg_OKey,V_K),V_H,tc_Message_Omsg) ) )),
rewrite(( ( c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(hAPP(c_Message_Omsg_OKey,V_K),V_H,tc_Message_Omsg) )
<=> ( c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(hAPP(c_Message_Omsg_OKey,V_K),V_H,tc_Message_Omsg) ) )),
( ( c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(hAPP(c_Message_Omsg_OKey,V_K),V_H,tc_Message_Omsg) )
<=> ( c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(hAPP(c_Message_Omsg_OKey,V_K),V_H,tc_Message_Omsg) ) )),
inference(bind,[status(th)],[]) ).
tff(191,plain,
( ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(hAPP(c_Message_Omsg_OKey,V_K),V_H,tc_Message_Omsg) )
<=> ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(hAPP(c_Message_Omsg_OKey,V_K),V_H,tc_Message_Omsg) ) ),
inference(quant_intro,[status(thm)],[190]) ).
tff(192,axiom,
! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(hAPP(c_Message_Omsg_OKey,V_K),V_H,tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Crypt__synth__eq_0) ).
tff(193,plain,
! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(hAPP(c_Message_Omsg_OKey,V_K),V_H,tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[192,191]) ).
tff(194,plain,
! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(hAPP(c_Message_Omsg_OKey,V_K),V_H,tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[193,189]) ).
tff(195,plain,
! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(hAPP(c_Message_Omsg_OKey,V_K),V_H,tc_Message_Omsg) ),
inference(skolemize,[status(sab)],[194]) ).
tff(196,plain,
! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(hAPP(c_Message_Omsg_OKey,V_K),V_H,tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[195,188]) ).
tff(197,plain,
( ( ~ ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(hAPP(c_Message_Omsg_OKey,V_K),V_H,tc_Message_Omsg) )
| c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg) )
<=> ( ~ ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(hAPP(c_Message_Omsg_OKey,V_K),V_H,tc_Message_Omsg) )
| c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(198,plain,
( ( c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg)
| c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg) )
<=> ( c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(199,plain,
( ( ~ ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(hAPP(c_Message_Omsg_OKey,V_K),V_H,tc_Message_Omsg) )
| c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg)
| c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg) )
<=> ( ~ ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(hAPP(c_Message_Omsg_OKey,V_K),V_H,tc_Message_Omsg) )
| c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg) ) ),
inference(monotonicity,[status(thm)],[198]) ).
tff(200,plain,
( ( ~ ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(hAPP(c_Message_Omsg_OKey,V_K),V_H,tc_Message_Omsg) )
| c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg)
| c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg) )
<=> ( ~ ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(hAPP(c_Message_Omsg_OKey,V_K),V_H,tc_Message_Omsg) )
| c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg) ) ),
inference(transitivity,[status(thm)],[199,197]) ).
tff(201,plain,
( ~ ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(hAPP(c_Message_Omsg_OKey,V_K),V_H,tc_Message_Omsg) )
| c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg)
| c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],[]) ).
tff(202,plain,
( ~ ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(hAPP(c_Message_Omsg_OKey,V_K),V_H,tc_Message_Omsg) )
| c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[201,200]) ).
tff(203,plain,
( c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg) ),
inference(unit_resolution,[status(thm)],[202,196,79]) ).
tff(204,plain,
$false,
inference(unit_resolution,[status(thm)],[203,186,175]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.14 % Problem : SWV767-1 : TPTP v9.0.0. Released v4.1.0.
% 0.14/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n001.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Jun 20 10:54:05 EDT 2025
% 0.14/0.36 % CPUTime :
% 103.75/103.92 % SZS status Unsatisfiable
% 103.75/103.92 % SZS output start Proof
% See solution above
% 104.17/104.31 % E exiting
%------------------------------------------------------------------------------