% TIMEFORMAT='%3R'; { time (exec 2>&1; /home/martin/bin/satallax -E /home/martin/.isabelle/contrib/e-2.5-1/x86_64-linux/eprover -p tstp -t 5 /home/martin/judgement-day/tptp-thf/tptp/NS_Shared/prob_499__5233372_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:25:16.144

% Could-be-implicit typings (12)
thf(ty_n_t__List__Olist_It__List__Olist_It__Event__Oevent_J_J, type,
    list_list_event : $tType).
thf(ty_n_t__Set__Oset_It__List__Olist_It__Event__Oevent_J_J, type,
    set_list_event : $tType).
thf(ty_n_t__List__Olist_It__Message__Oagent_J, type,
    list_agent : $tType).
thf(ty_n_t__Set__Oset_It__Message__Oagent_J, type,
    set_agent : $tType).
thf(ty_n_t__List__Olist_It__Message__Omsg_J, type,
    list_msg : $tType).
thf(ty_n_t__List__Olist_It__Event__Oevent_J, type,
    list_event : $tType).
thf(ty_n_t__Set__Oset_It__Message__Omsg_J, type,
    set_msg : $tType).
thf(ty_n_t__Set__Oset_It__Event__Oevent_J, type,
    set_event : $tType).
thf(ty_n_t__Message__Oagent, type,
    agent : $tType).
thf(ty_n_t__Message__Omsg, type,
    msg : $tType).
thf(ty_n_t__Event__Oevent, type,
    event : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (56)
thf(sy_c_Event_Obad, type,
    bad : set_agent).
thf(sy_c_Event_Oevent_OGets, type,
    gets : agent > msg > event).
thf(sy_c_Event_Oevent_ONotes, type,
    notes : agent > msg > event).
thf(sy_c_Event_Oevent_OSays, type,
    says : agent > agent > msg > event).
thf(sy_c_Event_OinitState, type,
    initState : agent > set_msg).
thf(sy_c_Event_Oknows, type,
    knows : agent > list_event > set_msg).
thf(sy_c_Event_Oused, type,
    used : list_event > set_msg).
thf(sy_c_List_Ocan__select_001t__Event__Oevent, type,
    can_select_event : (event > $o) > set_event > $o).
thf(sy_c_List_Ocan__select_001t__List__Olist_It__Event__Oevent_J, type,
    can_se1625331413_event : (list_event > $o) > set_list_event > $o).
thf(sy_c_List_Ocan__select_001t__Message__Oagent, type,
    can_select_agent : (agent > $o) > set_agent > $o).
thf(sy_c_List_Ocan__select_001t__Message__Omsg, type,
    can_select_msg : (msg > $o) > set_msg > $o).
thf(sy_c_List_Olist_ONil_001t__Event__Oevent, type,
    nil_event : list_event).
thf(sy_c_List_Olist_Oset_001t__Event__Oevent, type,
    set_event2 : list_event > set_event).
thf(sy_c_List_Olist_Oset_001t__List__Olist_It__Event__Oevent_J, type,
    set_list_event2 : list_list_event > set_list_event).
thf(sy_c_List_Olist_Oset_001t__Message__Oagent, type,
    set_agent2 : list_agent > set_agent).
thf(sy_c_List_Olist_Oset_001t__Message__Omsg, type,
    set_msg2 : list_msg > set_msg).
thf(sy_c_List_Olist__ex1_001t__Event__Oevent, type,
    list_ex1_event : (event > $o) > list_event > $o).
thf(sy_c_List_Olist__ex1_001t__List__Olist_It__Event__Oevent_J, type,
    list_ex1_list_event : (list_event > $o) > list_list_event > $o).
thf(sy_c_List_Olist__ex1_001t__Message__Oagent, type,
    list_ex1_agent : (agent > $o) > list_agent > $o).
thf(sy_c_List_Olist__ex1_001t__Message__Omsg, type,
    list_ex1_msg : (msg > $o) > list_msg > $o).
thf(sy_c_List_Orev_001t__Event__Oevent, type,
    rev_event : list_event > list_event).
thf(sy_c_List_OtakeWhile_001t__Event__Oevent, type,
    takeWhile_event : (event > $o) > list_event > list_event).
thf(sy_c_List_OtakeWhile_001t__List__Olist_It__Event__Oevent_J, type,
    takeWhile_list_event : (list_event > $o) > list_list_event > list_list_event).
thf(sy_c_List_OtakeWhile_001t__Message__Oagent, type,
    takeWhile_agent : (agent > $o) > list_agent > list_agent).
thf(sy_c_List_OtakeWhile_001t__Message__Omsg, type,
    takeWhile_msg : (msg > $o) > list_msg > list_msg).
thf(sy_c_Message_Oagent_OSpy, type,
    spy : agent).
thf(sy_c_Message_Oanalz, type,
    analz : set_msg > set_msg).
thf(sy_c_Message_OinvKey, type,
    invKey : nat > nat).
thf(sy_c_Message_Omsg_OCrypt, type,
    crypt : nat > msg > msg).
thf(sy_c_Message_Omsg_OKey, type,
    key : nat > msg).
thf(sy_c_Message_Omsg_OMPair, type,
    mPair : msg > msg > msg).
thf(sy_c_Message_Omsg_ONonce, type,
    nonce : nat > msg).
thf(sy_c_Message_Oparts, type,
    parts : set_msg > set_msg).
thf(sy_c_NS__Shared__Mirabelle__xwdrtqxrux_OIssues, type,
    nS_Sha1425748201Issues : agent > agent > msg > list_event > $o).
thf(sy_c_NS__Shared__Mirabelle__xwdrtqxrux_Ons__shared, type,
    nS_Sha1061662329shared : set_list_event).
thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Event__Oevent_M_Eo_J, type,
    ord_less_eq_event_o : (event > $o) > (event > $o) > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__List__Olist_It__Event__Oevent_J_M_Eo_J, type,
    ord_le1505328861vent_o : (list_event > $o) > (list_event > $o) > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Message__Oagent_M_Eo_J, type,
    ord_less_eq_agent_o : (agent > $o) > (agent > $o) > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Message__Omsg_M_Eo_J, type,
    ord_less_eq_msg_o : (msg > $o) > (msg > $o) > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat, type,
    ord_less_eq_nat : nat > nat > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Event__Oevent_J, type,
    ord_le152226328_event : set_event > set_event > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__List__Olist_It__Event__Oevent_J_J, type,
    ord_le119303592_event : set_list_event > set_list_event > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Message__Oagent_J, type,
    ord_le722097072_agent : set_agent > set_agent > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Message__Omsg_J, type,
    ord_less_eq_set_msg : set_msg > set_msg > $o).
thf(sy_c_Set_OCollect_001t__Event__Oevent, type,
    collect_event : (event > $o) > set_event).
thf(sy_c_Set_OCollect_001t__List__Olist_It__Event__Oevent_J, type,
    collect_list_event : (list_event > $o) > set_list_event).
thf(sy_c_Set_OCollect_001t__Message__Oagent, type,
    collect_agent : (agent > $o) > set_agent).
thf(sy_c_Set_OCollect_001t__Message__Omsg, type,
    collect_msg : (msg > $o) > set_msg).
thf(sy_c_member_001t__Event__Oevent, type,
    member_event : event > set_event > $o).
thf(sy_c_member_001t__List__Olist_It__Event__Oevent_J, type,
    member_list_event : list_event > set_list_event > $o).
thf(sy_c_member_001t__Message__Oagent, type,
    member_agent : agent > set_agent > $o).
thf(sy_c_member_001t__Message__Omsg, type,
    member_msg : msg > set_msg > $o).
thf(sy_v_A, type,
    a : agent).
thf(sy_v_B, type,
    b : agent).
thf(sy_v_K, type,
    k : nat).
thf(sy_v_NB, type,
    nb : nat).

% Relevant facts (204)
thf(fact_0_spies__evs__rev, axiom,
    ((![Evs : list_event]: ((knows @ spy @ Evs) = (knows @ spy @ (rev_event @ Evs)))))). % spies_evs_rev
thf(fact_1_NS3__msg__in__parts__spies, axiom,
    ((![S : agent, A : agent, KA : nat, N : msg, B : msg, K : msg, X : msg, Evs : list_event]: ((member_event @ (says @ S @ A @ (crypt @ KA @ (mPair @ N @ (mPair @ B @ (mPair @ K @ X))))) @ (set_event2 @ Evs)) => (member_msg @ X @ (parts @ (knows @ spy @ Evs))))))). % NS3_msg_in_parts_spies
thf(fact_2_Spy__in__bad, axiom,
    ((member_agent @ spy @ bad))). % Spy_in_bad
thf(fact_3_Says__imp__analz__Spy, axiom,
    ((![A : agent, B : agent, X : msg, Evs : list_event]: ((member_event @ (says @ A @ B @ X) @ (set_event2 @ Evs)) => (member_msg @ X @ (analz @ (knows @ spy @ Evs))))))). % Says_imp_analz_Spy
thf(fact_4_takeWhile__eq__all__conv, axiom,
    ((![P : event > $o, Xs : list_event]: (((takeWhile_event @ P @ Xs) = Xs) = (![X2 : event]: (((member_event @ X2 @ (set_event2 @ Xs))) => ((P @ X2)))))))). % takeWhile_eq_all_conv
thf(fact_5_analz__parts, axiom,
    ((![H : set_msg]: ((analz @ (parts @ H)) = (parts @ H))))). % analz_parts
thf(fact_6_parts__analz, axiom,
    ((![H : set_msg]: ((parts @ (analz @ H)) = (parts @ H))))). % parts_analz
thf(fact_7_analz__conj__parts, axiom,
    ((![X : msg, H : set_msg]: ((((member_msg @ X @ (analz @ H))) & ((member_msg @ X @ (parts @ H)))) = (member_msg @ X @ (analz @ H)))))). % analz_conj_parts
thf(fact_8_analz__disj__parts, axiom,
    ((![X : msg, H : set_msg]: ((((member_msg @ X @ (analz @ H))) | ((member_msg @ X @ (parts @ H)))) = (member_msg @ X @ (parts @ H)))))). % analz_disj_parts
thf(fact_9_set__rev, axiom,
    ((![Xs : list_event]: ((set_event2 @ (rev_event @ Xs)) = (set_event2 @ Xs))))). % set_rev
thf(fact_10_Nil__is__rev__conv, axiom,
    ((![Xs : list_event]: ((nil_event = (rev_event @ Xs)) = (Xs = nil_event))))). % Nil_is_rev_conv
thf(fact_11_rev__is__Nil__conv, axiom,
    ((![Xs : list_event]: (((rev_event @ Xs) = nil_event) = (Xs = nil_event))))). % rev_is_Nil_conv
thf(fact_12_Says__imp__knows__Spy, axiom,
    ((![A : agent, B : agent, X : msg, Evs : list_event]: ((member_event @ (says @ A @ B @ X) @ (set_event2 @ Evs)) => (member_msg @ X @ (knows @ spy @ Evs)))))). % Says_imp_knows_Spy
thf(fact_13_Says__imp__knows, axiom,
    ((![A : agent, B : agent, X : msg, Evs : list_event]: ((member_event @ (says @ A @ B @ X) @ (set_event2 @ Evs)) => (member_msg @ X @ (knows @ A @ Evs)))))). % Says_imp_knows
thf(fact_14_msg_Oinject_I6_J, axiom,
    ((![X61 : msg, X62 : msg, Y61 : msg, Y62 : msg]: (((mPair @ X61 @ X62) = (mPair @ Y61 @ Y62)) = (((X61 = Y61)) & ((X62 = Y62))))))). % msg.inject(6)
thf(fact_15_analz__idem, axiom,
    ((![H : set_msg]: ((analz @ (analz @ H)) = (analz @ H))))). % analz_idem
thf(fact_16_msg_Oinject_I4_J, axiom,
    ((![X4 : nat, Y4 : nat]: (((key @ X4) = (key @ Y4)) = (X4 = Y4))))). % msg.inject(4)
thf(fact_17_parts__idem, axiom,
    ((![H : set_msg]: ((parts @ (parts @ H)) = (parts @ H))))). % parts_idem
thf(fact_18_msg_Oinject_I7_J, axiom,
    ((![X71 : nat, X72 : msg, Y71 : nat, Y72 : msg]: (((crypt @ X71 @ X72) = (crypt @ Y71 @ Y72)) = (((X71 = Y71)) & ((X72 = Y72))))))). % msg.inject(7)
thf(fact_19_msg_Oinject_I3_J, axiom,
    ((![X3 : nat, Y3 : nat]: (((nonce @ X3) = (nonce @ Y3)) = (X3 = Y3))))). % msg.inject(3)
thf(fact_20_rev__is__rev__conv, axiom,
    ((![Xs : list_event, Ys : list_event]: (((rev_event @ Xs) = (rev_event @ Ys)) = (Xs = Ys))))). % rev_is_rev_conv
thf(fact_21_rev__rev__ident, axiom,
    ((![Xs : list_event]: ((rev_event @ (rev_event @ Xs)) = Xs)))). % rev_rev_ident
thf(fact_22_event_Oinject_I1_J, axiom,
    ((![X11 : agent, X12 : agent, X13 : msg, Y11 : agent, Y12 : agent, Y13 : msg]: (((says @ X11 @ X12 @ X13) = (says @ Y11 @ Y12 @ Y13)) = (((X11 = Y11)) & ((((X12 = Y12)) & ((X13 = Y13))))))))). % event.inject(1)
thf(fact_23_takeWhile__idem, axiom,
    ((![P : event > $o, Xs : list_event]: ((takeWhile_event @ P @ (takeWhile_event @ P @ Xs)) = (takeWhile_event @ P @ Xs))))). % takeWhile_idem
thf(fact_24_analz__analzD, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ (analz @ (analz @ H))) => (member_msg @ X @ (analz @ H)))))). % analz_analzD
thf(fact_25_analz_OInj, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ H) => (member_msg @ X @ (analz @ H)))))). % analz.Inj
thf(fact_26_parts__partsD, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ (parts @ (parts @ H))) => (member_msg @ X @ (parts @ H)))))). % parts_partsD
thf(fact_27_parts_OInj, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ H) => (member_msg @ X @ (parts @ H)))))). % parts.Inj
thf(fact_28_rev__swap, axiom,
    ((![Xs : list_event, Ys : list_event]: (((rev_event @ Xs) = Ys) = (Xs = (rev_event @ Ys)))))). % rev_swap
thf(fact_29_MPair__analz, axiom,
    ((![X : msg, Y : msg, H : set_msg]: ((member_msg @ (mPair @ X @ Y) @ (analz @ H)) => (~ (((member_msg @ X @ (analz @ H)) => (~ ((member_msg @ Y @ (analz @ H))))))))))). % MPair_analz
thf(fact_30_analz_OSnd, axiom,
    ((![X : msg, Y : msg, H : set_msg]: ((member_msg @ (mPair @ X @ Y) @ (analz @ H)) => (member_msg @ Y @ (analz @ H)))))). % analz.Snd
thf(fact_31_analz_OFst, axiom,
    ((![X : msg, Y : msg, H : set_msg]: ((member_msg @ (mPair @ X @ Y) @ (analz @ H)) => (member_msg @ X @ (analz @ H)))))). % analz.Fst
thf(fact_32_rev_Osimps_I1_J, axiom,
    (((rev_event @ nil_event) = nil_event))). % rev.simps(1)
thf(fact_33_msg_Odistinct_I33_J, axiom,
    ((![X4 : nat, X61 : msg, X62 : msg]: (~ (((key @ X4) = (mPair @ X61 @ X62))))))). % msg.distinct(33)
thf(fact_34_MPair__parts, axiom,
    ((![X : msg, Y : msg, H : set_msg]: ((member_msg @ (mPair @ X @ Y) @ (parts @ H)) => (~ (((member_msg @ X @ (parts @ H)) => (~ ((member_msg @ Y @ (parts @ H))))))))))). % MPair_parts
thf(fact_35_parts_OSnd, axiom,
    ((![X : msg, Y : msg, H : set_msg]: ((member_msg @ (mPair @ X @ Y) @ (parts @ H)) => (member_msg @ Y @ (parts @ H)))))). % parts.Snd
thf(fact_36_parts_OFst, axiom,
    ((![X : msg, Y : msg, H : set_msg]: ((member_msg @ (mPair @ X @ Y) @ (parts @ H)) => (member_msg @ X @ (parts @ H)))))). % parts.Fst
thf(fact_37_not__parts__not__analz, axiom,
    ((![C : msg, H : set_msg]: ((~ ((member_msg @ C @ (parts @ H)))) => (~ ((member_msg @ C @ (analz @ H)))))))). % not_parts_not_analz
thf(fact_38_analz__into__parts, axiom,
    ((![C : msg, H : set_msg]: ((member_msg @ C @ (analz @ H)) => (member_msg @ C @ (parts @ H)))))). % analz_into_parts
thf(fact_39_msg_Odistinct_I41_J, axiom,
    ((![X61 : msg, X62 : msg, X71 : nat, X72 : msg]: (~ (((mPair @ X61 @ X62) = (crypt @ X71 @ X72))))))). % msg.distinct(41)
thf(fact_40_msg_Odistinct_I35_J, axiom,
    ((![X4 : nat, X71 : nat, X72 : msg]: (~ (((key @ X4) = (crypt @ X71 @ X72))))))). % msg.distinct(35)
thf(fact_41_parts_OBody, axiom,
    ((![K : nat, X : msg, H : set_msg]: ((member_msg @ (crypt @ K @ X) @ (parts @ H)) => (member_msg @ X @ (parts @ H)))))). % parts.Body
thf(fact_42_takeWhile_Osimps_I1_J, axiom,
    ((![P : event > $o]: ((takeWhile_event @ P @ nil_event) = nil_event)))). % takeWhile.simps(1)
thf(fact_43_msg_Odistinct_I27_J, axiom,
    ((![X3 : nat, X61 : msg, X62 : msg]: (~ (((nonce @ X3) = (mPair @ X61 @ X62))))))). % msg.distinct(27)
thf(fact_44_mem__Collect__eq, axiom,
    ((![A2 : agent, P : agent > $o]: ((member_agent @ A2 @ (collect_agent @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_45_mem__Collect__eq, axiom,
    ((![A2 : msg, P : msg > $o]: ((member_msg @ A2 @ (collect_msg @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_46_mem__Collect__eq, axiom,
    ((![A2 : event, P : event > $o]: ((member_event @ A2 @ (collect_event @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_47_mem__Collect__eq, axiom,
    ((![A2 : list_event, P : list_event > $o]: ((member_list_event @ A2 @ (collect_list_event @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_48_Collect__mem__eq, axiom,
    ((![A : set_agent]: ((collect_agent @ (^[X2 : agent]: (member_agent @ X2 @ A))) = A)))). % Collect_mem_eq
thf(fact_49_Collect__mem__eq, axiom,
    ((![A : set_msg]: ((collect_msg @ (^[X2 : msg]: (member_msg @ X2 @ A))) = A)))). % Collect_mem_eq
thf(fact_50_Collect__mem__eq, axiom,
    ((![A : set_event]: ((collect_event @ (^[X2 : event]: (member_event @ X2 @ A))) = A)))). % Collect_mem_eq
thf(fact_51_Collect__mem__eq, axiom,
    ((![A : set_list_event]: ((collect_list_event @ (^[X2 : list_event]: (member_list_event @ X2 @ A))) = A)))). % Collect_mem_eq
thf(fact_52_takeWhile__cong, axiom,
    ((![L : list_agent, K2 : list_agent, P : agent > $o, Q : agent > $o]: ((L = K2) => ((![X5 : agent]: ((member_agent @ X5 @ (set_agent2 @ L)) => ((P @ X5) = (Q @ X5)))) => ((takeWhile_agent @ P @ L) = (takeWhile_agent @ Q @ K2))))))). % takeWhile_cong
thf(fact_53_takeWhile__cong, axiom,
    ((![L : list_msg, K2 : list_msg, P : msg > $o, Q : msg > $o]: ((L = K2) => ((![X5 : msg]: ((member_msg @ X5 @ (set_msg2 @ L)) => ((P @ X5) = (Q @ X5)))) => ((takeWhile_msg @ P @ L) = (takeWhile_msg @ Q @ K2))))))). % takeWhile_cong
thf(fact_54_takeWhile__cong, axiom,
    ((![L : list_list_event, K2 : list_list_event, P : list_event > $o, Q : list_event > $o]: ((L = K2) => ((![X5 : list_event]: ((member_list_event @ X5 @ (set_list_event2 @ L)) => ((P @ X5) = (Q @ X5)))) => ((takeWhile_list_event @ P @ L) = (takeWhile_list_event @ Q @ K2))))))). % takeWhile_cong
thf(fact_55_takeWhile__cong, axiom,
    ((![L : list_event, K2 : list_event, P : event > $o, Q : event > $o]: ((L = K2) => ((![X5 : event]: ((member_event @ X5 @ (set_event2 @ L)) => ((P @ X5) = (Q @ X5)))) => ((takeWhile_event @ P @ L) = (takeWhile_event @ Q @ K2))))))). % takeWhile_cong
thf(fact_56_set__takeWhileD, axiom,
    ((![X6 : agent, P : agent > $o, Xs : list_agent]: ((member_agent @ X6 @ (set_agent2 @ (takeWhile_agent @ P @ Xs))) => ((member_agent @ X6 @ (set_agent2 @ Xs)) & (P @ X6)))))). % set_takeWhileD
thf(fact_57_set__takeWhileD, axiom,
    ((![X6 : msg, P : msg > $o, Xs : list_msg]: ((member_msg @ X6 @ (set_msg2 @ (takeWhile_msg @ P @ Xs))) => ((member_msg @ X6 @ (set_msg2 @ Xs)) & (P @ X6)))))). % set_takeWhileD
thf(fact_58_set__takeWhileD, axiom,
    ((![X6 : list_event, P : list_event > $o, Xs : list_list_event]: ((member_list_event @ X6 @ (set_list_event2 @ (takeWhile_list_event @ P @ Xs))) => ((member_list_event @ X6 @ (set_list_event2 @ Xs)) & (P @ X6)))))). % set_takeWhileD
thf(fact_59_set__takeWhileD, axiom,
    ((![X6 : event, P : event > $o, Xs : list_event]: ((member_event @ X6 @ (set_event2 @ (takeWhile_event @ P @ Xs))) => ((member_event @ X6 @ (set_event2 @ Xs)) & (P @ X6)))))). % set_takeWhileD
thf(fact_60_msg_Odistinct_I23_J, axiom,
    ((![X3 : nat, X4 : nat]: (~ (((nonce @ X3) = (key @ X4))))))). % msg.distinct(23)
thf(fact_61_msg_Odistinct_I29_J, axiom,
    ((![X3 : nat, X71 : nat, X72 : msg]: (~ (((nonce @ X3) = (crypt @ X71 @ X72))))))). % msg.distinct(29)
thf(fact_62_analz__trivial, axiom,
    ((![H : set_msg]: ((![X7 : msg, Y2 : msg]: (~ ((member_msg @ (mPair @ X7 @ Y2) @ H)))) => ((![X7 : msg, K3 : nat]: (~ ((member_msg @ (crypt @ K3 @ X7) @ H)))) => ((analz @ H) = H)))))). % analz_trivial
thf(fact_63_parts_Oinducts, axiom,
    ((![X6 : msg, H : set_msg, P : msg > $o]: ((member_msg @ X6 @ (parts @ H)) => ((![X7 : msg]: ((member_msg @ X7 @ H) => (P @ X7))) => ((![X7 : msg, Y2 : msg]: ((member_msg @ (mPair @ X7 @ Y2) @ (parts @ H)) => ((P @ (mPair @ X7 @ Y2)) => (P @ X7)))) => ((![X7 : msg, Y2 : msg]: ((member_msg @ (mPair @ X7 @ Y2) @ (parts @ H)) => ((P @ (mPair @ X7 @ Y2)) => (P @ Y2)))) => ((![K3 : nat, X7 : msg]: ((member_msg @ (crypt @ K3 @ X7) @ (parts @ H)) => ((P @ (crypt @ K3 @ X7)) => (P @ X7)))) => (P @ X6))))))))). % parts.inducts
thf(fact_64_parts_Osimps, axiom,
    ((![A2 : msg, H : set_msg]: ((member_msg @ A2 @ (parts @ H)) = (((?[X8 : msg]: (((A2 = X8)) & ((member_msg @ X8 @ H))))) | ((((?[X8 : msg]: (?[Y5 : msg]: (((A2 = X8)) & ((member_msg @ (mPair @ X8 @ Y5) @ (parts @ H))))))) | ((((?[X8 : msg]: (?[Y5 : msg]: (((A2 = Y5)) & ((member_msg @ (mPair @ X8 @ Y5) @ (parts @ H))))))) | ((?[K4 : nat]: (?[X8 : msg]: (((A2 = X8)) & ((member_msg @ (crypt @ K4 @ X8) @ (parts @ H)))))))))))))))). % parts.simps
thf(fact_65_parts_Ocases, axiom,
    ((![A2 : msg, H : set_msg]: ((member_msg @ A2 @ (parts @ H)) => ((~ ((member_msg @ A2 @ H))) => ((![Y2 : msg]: (~ ((member_msg @ (mPair @ A2 @ Y2) @ (parts @ H))))) => ((![X7 : msg]: (~ ((member_msg @ (mPair @ X7 @ A2) @ (parts @ H))))) => (~ ((![K3 : nat]: (~ ((member_msg @ (crypt @ K3 @ A2) @ (parts @ H)))))))))))))). % parts.cases
thf(fact_66_analz__impI, axiom,
    ((![Y : msg, Evs : list_event, Q : $o]: (((~ ((member_msg @ Y @ (analz @ (knows @ spy @ Evs))))) => Q) => ((~ ((member_msg @ Y @ (analz @ (knows @ spy @ Evs))))) => Q))))). % analz_impI
thf(fact_67_B__Issues__A, axiom,
    ((![B : agent, A : agent, K : nat, Nb : nat, Evs : list_event]: ((member_event @ (says @ B @ A @ (crypt @ K @ (nonce @ Nb))) @ (set_event2 @ Evs)) => ((~ ((member_msg @ (key @ K) @ (analz @ (knows @ spy @ Evs))))) => ((~ ((member_agent @ A @ bad))) => ((~ ((member_agent @ B @ bad))) => ((member_list_event @ Evs @ nS_Sha1061662329shared) => (nS_Sha1425748201Issues @ B @ A @ (crypt @ K @ (nonce @ Nb)) @ Evs))))))))). % B_Issues_A
thf(fact_68_Notes__imp__knows__Spy, axiom,
    ((![A : agent, X : msg, Evs : list_event]: ((member_event @ (notes @ A @ X) @ (set_event2 @ Evs)) => ((member_agent @ A @ bad) => (member_msg @ X @ (knows @ spy @ Evs))))))). % Notes_imp_knows_Spy
thf(fact_69_parts__spies__takeWhile__mono, axiom,
    ((![P : event > $o, Evs : list_event]: (ord_less_eq_set_msg @ (parts @ (knows @ spy @ (takeWhile_event @ P @ Evs))) @ (parts @ (knows @ spy @ Evs)))))). % parts_spies_takeWhile_mono
thf(fact_70_parts__spies__evs__revD2, axiom,
    ((![Evs : list_event]: (ord_less_eq_set_msg @ (parts @ (knows @ spy @ (rev_event @ Evs))) @ (parts @ (knows @ spy @ Evs)))))). % parts_spies_evs_revD2
thf(fact_71_Gets__imp__knows__agents, axiom,
    ((![A : agent, X : msg, Evs : list_event]: ((~ ((A = spy))) => ((member_event @ (gets @ A @ X) @ (set_event2 @ Evs)) => (member_msg @ X @ (knows @ A @ Evs))))))). % Gets_imp_knows_agents
thf(fact_72_list__ex1__simps_I1_J, axiom,
    ((![P : event > $o]: (~ ((list_ex1_event @ P @ nil_event)))))). % list_ex1_simps(1)
thf(fact_73_analz_Oinducts, axiom,
    ((![X6 : msg, H : set_msg, P : msg > $o]: ((member_msg @ X6 @ (analz @ H)) => ((![X7 : msg]: ((member_msg @ X7 @ H) => (P @ X7))) => ((![X7 : msg, Y2 : msg]: ((member_msg @ (mPair @ X7 @ Y2) @ (analz @ H)) => ((P @ (mPair @ X7 @ Y2)) => (P @ X7)))) => ((![X7 : msg, Y2 : msg]: ((member_msg @ (mPair @ X7 @ Y2) @ (analz @ H)) => ((P @ (mPair @ X7 @ Y2)) => (P @ Y2)))) => ((![K3 : nat, X7 : msg]: ((member_msg @ (crypt @ K3 @ X7) @ (analz @ H)) => ((P @ (crypt @ K3 @ X7)) => ((member_msg @ (key @ (invKey @ K3)) @ (analz @ H)) => ((P @ (key @ (invKey @ K3))) => (P @ X7)))))) => (P @ X6))))))))). % analz.inducts
thf(fact_74_analz_Osimps, axiom,
    ((![A2 : msg, H : set_msg]: ((member_msg @ A2 @ (analz @ H)) = (((?[X8 : msg]: (((A2 = X8)) & ((member_msg @ X8 @ H))))) | ((((?[X8 : msg]: (?[Y5 : msg]: (((A2 = X8)) & ((member_msg @ (mPair @ X8 @ Y5) @ (analz @ H))))))) | ((((?[X8 : msg]: (?[Y5 : msg]: (((A2 = Y5)) & ((member_msg @ (mPair @ X8 @ Y5) @ (analz @ H))))))) | ((?[K4 : nat]: (?[X8 : msg]: (((A2 = X8)) & ((((member_msg @ (crypt @ K4 @ X8) @ (analz @ H))) & ((member_msg @ (key @ (invKey @ K4)) @ (analz @ H)))))))))))))))))). % analz.simps
thf(fact_75_analz_Ocases, axiom,
    ((![A2 : msg, H : set_msg]: ((member_msg @ A2 @ (analz @ H)) => ((~ ((member_msg @ A2 @ H))) => ((![Y2 : msg]: (~ ((member_msg @ (mPair @ A2 @ Y2) @ (analz @ H))))) => ((![X7 : msg]: (~ ((member_msg @ (mPair @ X7 @ A2) @ (analz @ H))))) => (~ ((![K3 : nat]: ((member_msg @ (crypt @ K3 @ A2) @ (analz @ H)) => (~ ((member_msg @ (key @ (invKey @ K3)) @ (analz @ H))))))))))))))). % analz.cases
thf(fact_76_usedI, axiom,
    ((![C : msg, Evs : list_event]: ((member_msg @ C @ (parts @ (knows @ spy @ Evs))) => (member_msg @ C @ (used @ Evs)))))). % usedI
thf(fact_77_invKey, axiom,
    ((![K : nat]: ((invKey @ (invKey @ K)) = K)))). % invKey
thf(fact_78_invKey__eq, axiom,
    ((![K : nat, K5 : nat]: (((invKey @ K) = (invKey @ K5)) = (K = K5))))). % invKey_eq
thf(fact_79_event_Oinject_I3_J, axiom,
    ((![X31 : agent, X32 : msg, Y31 : agent, Y32 : msg]: (((notes @ X31 @ X32) = (notes @ Y31 @ Y32)) = (((X31 = Y31)) & ((X32 = Y32))))))). % event.inject(3)
thf(fact_80_event_Oinject_I2_J, axiom,
    ((![X21 : agent, X22 : msg, Y21 : agent, Y22 : msg]: (((gets @ X21 @ X22) = (gets @ Y21 @ Y22)) = (((X21 = Y21)) & ((X22 = Y22))))))). % event.inject(2)
thf(fact_81_analz__subset__iff, axiom,
    ((![G : set_msg, H : set_msg]: ((ord_less_eq_set_msg @ (analz @ G) @ (analz @ H)) = (ord_less_eq_set_msg @ G @ (analz @ H)))))). % analz_subset_iff
thf(fact_82_parts__subset__iff, axiom,
    ((![G : set_msg, H : set_msg]: ((ord_less_eq_set_msg @ (parts @ G) @ (parts @ H)) = (ord_less_eq_set_msg @ G @ (parts @ H)))))). % parts_subset_iff
thf(fact_83_event_Odistinct_I5_J, axiom,
    ((![X21 : agent, X22 : msg, X31 : agent, X32 : msg]: (~ (((gets @ X21 @ X22) = (notes @ X31 @ X32))))))). % event.distinct(5)
thf(fact_84_Notes__imp__used, axiom,
    ((![A : agent, X : msg, Evs : list_event]: ((member_event @ (notes @ A @ X) @ (set_event2 @ Evs)) => (member_msg @ X @ (used @ Evs)))))). % Notes_imp_used
thf(fact_85_used__nil__subset, axiom,
    ((![Evs : list_event]: (ord_less_eq_set_msg @ (used @ nil_event) @ (used @ Evs))))). % used_nil_subset
thf(fact_86_event_Oinduct, axiom,
    ((![P : event > $o, Event : event]: ((![X1 : agent, X23 : agent, X33 : msg]: (P @ (says @ X1 @ X23 @ X33))) => ((![X1 : agent, X23 : msg]: (P @ (gets @ X1 @ X23))) => ((![X1 : agent, X23 : msg]: (P @ (notes @ X1 @ X23))) => (P @ Event))))))). % event.induct
thf(fact_87_event_Oexhaust, axiom,
    ((![Y6 : event]: ((![X112 : agent, X122 : agent, X132 : msg]: (~ ((Y6 = (says @ X112 @ X122 @ X132))))) => ((![X212 : agent, X222 : msg]: (~ ((Y6 = (gets @ X212 @ X222))))) => (~ ((![X312 : agent, X322 : msg]: (~ ((Y6 = (notes @ X312 @ X322)))))))))))). % event.exhaust
thf(fact_88_subset__code_I1_J, axiom,
    ((![Xs : list_agent, B : set_agent]: ((ord_le722097072_agent @ (set_agent2 @ Xs) @ B) = (![X2 : agent]: (((member_agent @ X2 @ (set_agent2 @ Xs))) => ((member_agent @ X2 @ B)))))))). % subset_code(1)
thf(fact_89_subset__code_I1_J, axiom,
    ((![Xs : list_list_event, B : set_list_event]: ((ord_le119303592_event @ (set_list_event2 @ Xs) @ B) = (![X2 : list_event]: (((member_list_event @ X2 @ (set_list_event2 @ Xs))) => ((member_list_event @ X2 @ B)))))))). % subset_code(1)
thf(fact_90_subset__code_I1_J, axiom,
    ((![Xs : list_event, B : set_event]: ((ord_le152226328_event @ (set_event2 @ Xs) @ B) = (![X2 : event]: (((member_event @ X2 @ (set_event2 @ Xs))) => ((member_event @ X2 @ B)))))))). % subset_code(1)
thf(fact_91_subset__code_I1_J, axiom,
    ((![Xs : list_msg, B : set_msg]: ((ord_less_eq_set_msg @ (set_msg2 @ Xs) @ B) = (![X2 : msg]: (((member_msg @ X2 @ (set_msg2 @ Xs))) => ((member_msg @ X2 @ B)))))))). % subset_code(1)
thf(fact_92_analz__mono, axiom,
    ((![G : set_msg, H : set_msg]: ((ord_less_eq_set_msg @ G @ H) => (ord_less_eq_set_msg @ (analz @ G) @ (analz @ H)))))). % analz_mono
thf(fact_93_analz__trans, axiom,
    ((![X : msg, G : set_msg, H : set_msg]: ((member_msg @ X @ (analz @ G)) => ((ord_less_eq_set_msg @ G @ (analz @ H)) => (member_msg @ X @ (analz @ H))))))). % analz_trans
thf(fact_94_analz__increasing, axiom,
    ((![H : set_msg]: (ord_less_eq_set_msg @ H @ (analz @ H))))). % analz_increasing
thf(fact_95_parts__mono, axiom,
    ((![G : set_msg, H : set_msg]: ((ord_less_eq_set_msg @ G @ H) => (ord_less_eq_set_msg @ (parts @ G) @ (parts @ H)))))). % parts_mono
thf(fact_96_parts__trans, axiom,
    ((![X : msg, G : set_msg, H : set_msg]: ((member_msg @ X @ (parts @ G)) => ((ord_less_eq_set_msg @ G @ (parts @ H)) => (member_msg @ X @ (parts @ H))))))). % parts_trans
thf(fact_97_parts__increasing, axiom,
    ((![H : set_msg]: (ord_less_eq_set_msg @ H @ (parts @ H))))). % parts_increasing
thf(fact_98_event_Odistinct_I3_J, axiom,
    ((![X11 : agent, X12 : agent, X13 : msg, X31 : agent, X32 : msg]: (~ (((says @ X11 @ X12 @ X13) = (notes @ X31 @ X32))))))). % event.distinct(3)
thf(fact_99_parts__knows__Spy__subset__used, axiom,
    ((![Evs : list_event]: (ord_less_eq_set_msg @ (parts @ (knows @ spy @ Evs)) @ (used @ Evs))))). % parts_knows_Spy_subset_used
thf(fact_100_event_Odistinct_I1_J, axiom,
    ((![X11 : agent, X12 : agent, X13 : msg, X21 : agent, X22 : msg]: (~ (((says @ X11 @ X12 @ X13) = (gets @ X21 @ X22))))))). % event.distinct(1)
thf(fact_101_ns__shared_ONil, axiom,
    ((member_list_event @ nil_event @ nS_Sha1061662329shared))). % ns_shared.Nil
thf(fact_102_analz__subset__parts, axiom,
    ((![H : set_msg]: (ord_less_eq_set_msg @ (analz @ H) @ (parts @ H))))). % analz_subset_parts
thf(fact_103_Says__imp__used, axiom,
    ((![A : agent, B : agent, X : msg, Evs : list_event]: ((member_event @ (says @ A @ B @ X) @ (set_event2 @ Evs)) => (member_msg @ X @ (used @ Evs)))))). % Says_imp_used
thf(fact_104_list__ex1__iff, axiom,
    ((list_ex1_agent = (^[P2 : agent > $o]: (^[Xs2 : list_agent]: (?[X2 : agent]: (((((member_agent @ X2 @ (set_agent2 @ Xs2))) & ((P2 @ X2)))) & ((![Y7 : agent]: (((((member_agent @ Y7 @ (set_agent2 @ Xs2))) & ((P2 @ Y7)))) => ((Y7 = X2)))))))))))). % list_ex1_iff
thf(fact_105_list__ex1__iff, axiom,
    ((list_ex1_msg = (^[P2 : msg > $o]: (^[Xs2 : list_msg]: (?[X2 : msg]: (((((member_msg @ X2 @ (set_msg2 @ Xs2))) & ((P2 @ X2)))) & ((![Y7 : msg]: (((((member_msg @ Y7 @ (set_msg2 @ Xs2))) & ((P2 @ Y7)))) => ((Y7 = X2)))))))))))). % list_ex1_iff
thf(fact_106_list__ex1__iff, axiom,
    ((list_ex1_list_event = (^[P2 : list_event > $o]: (^[Xs2 : list_list_event]: (?[X2 : list_event]: (((((member_list_event @ X2 @ (set_list_event2 @ Xs2))) & ((P2 @ X2)))) & ((![Y7 : list_event]: (((((member_list_event @ Y7 @ (set_list_event2 @ Xs2))) & ((P2 @ Y7)))) => ((Y7 = X2)))))))))))). % list_ex1_iff
thf(fact_107_list__ex1__iff, axiom,
    ((list_ex1_event = (^[P2 : event > $o]: (^[Xs2 : list_event]: (?[X2 : event]: (((((member_event @ X2 @ (set_event2 @ Xs2))) & ((P2 @ X2)))) & ((![Y7 : event]: (((((member_event @ Y7 @ (set_event2 @ Xs2))) & ((P2 @ Y7)))) => ((Y7 = X2)))))))))))). % list_ex1_iff
thf(fact_108_Notes__imp__knows, axiom,
    ((![A : agent, X : msg, Evs : list_event]: ((member_event @ (notes @ A @ X) @ (set_event2 @ Evs)) => (member_msg @ X @ (knows @ A @ Evs)))))). % Notes_imp_knows
thf(fact_109_analz_ODecrypt, axiom,
    ((![K : nat, X : msg, H : set_msg]: ((member_msg @ (crypt @ K @ X) @ (analz @ H)) => ((member_msg @ (key @ (invKey @ K)) @ (analz @ H)) => (member_msg @ X @ (analz @ H))))))). % analz.Decrypt
thf(fact_110_spies__takeWhile, axiom,
    ((![P : event > $o, Evs : list_event]: (ord_less_eq_set_msg @ (knows @ spy @ (takeWhile_event @ P @ Evs)) @ (knows @ spy @ Evs))))). % spies_takeWhile
thf(fact_111_Nonce__notin__used__empty, axiom,
    ((![N : nat]: (~ ((member_msg @ (nonce @ N) @ (used @ nil_event))))))). % Nonce_notin_used_empty
thf(fact_112_Crypt__notin__used__empty, axiom,
    ((![K : nat, X : msg]: (~ ((member_msg @ (crypt @ K @ X) @ (used @ nil_event))))))). % Crypt_notin_used_empty
thf(fact_113_knows__imp__Says__Gets__Notes__initState, axiom,
    ((![X : msg, A : agent, Evs : list_event]: ((member_msg @ X @ (knows @ A @ Evs)) => ((~ ((A = spy))) => (?[B2 : agent]: ((member_event @ (says @ A @ B2 @ X) @ (set_event2 @ Evs)) | ((member_event @ (gets @ A @ X) @ (set_event2 @ Evs)) | ((member_event @ (notes @ A @ X) @ (set_event2 @ Evs)) | (member_msg @ X @ (initState @ A))))))))))). % knows_imp_Says_Gets_Notes_initState
thf(fact_114_can__select__set__list__ex1, axiom,
    ((![P : event > $o, A : list_event]: ((can_select_event @ P @ (set_event2 @ A)) = (list_ex1_event @ P @ A))))). % can_select_set_list_ex1
thf(fact_115_knows__Spy__imp__Says__Notes__initState, axiom,
    ((![X : msg, Evs : list_event]: ((member_msg @ X @ (knows @ spy @ Evs)) => (?[A3 : agent, B2 : agent]: ((member_event @ (says @ A3 @ B2 @ X) @ (set_event2 @ Evs)) | ((member_event @ (notes @ A3 @ X) @ (set_event2 @ Evs)) | (member_msg @ X @ (initState @ spy))))))))). % knows_Spy_imp_Says_Notes_initState
thf(fact_116_can__select__def, axiom,
    ((can_select_agent = (^[P2 : agent > $o]: (^[A4 : set_agent]: (?[X2 : agent]: (((((member_agent @ X2 @ A4)) & ((P2 @ X2)))) & ((![Y7 : agent]: (((((member_agent @ Y7 @ A4)) & ((P2 @ Y7)))) => ((Y7 = X2)))))))))))). % can_select_def
thf(fact_117_can__select__def, axiom,
    ((can_select_msg = (^[P2 : msg > $o]: (^[A4 : set_msg]: (?[X2 : msg]: (((((member_msg @ X2 @ A4)) & ((P2 @ X2)))) & ((![Y7 : msg]: (((((member_msg @ Y7 @ A4)) & ((P2 @ Y7)))) => ((Y7 = X2)))))))))))). % can_select_def
thf(fact_118_can__select__def, axiom,
    ((can_select_event = (^[P2 : event > $o]: (^[A4 : set_event]: (?[X2 : event]: (((((member_event @ X2 @ A4)) & ((P2 @ X2)))) & ((![Y7 : event]: (((((member_event @ Y7 @ A4)) & ((P2 @ Y7)))) => ((Y7 = X2)))))))))))). % can_select_def
thf(fact_119_can__select__def, axiom,
    ((can_se1625331413_event = (^[P2 : list_event > $o]: (^[A4 : set_list_event]: (?[X2 : list_event]: (((((member_list_event @ X2 @ A4)) & ((P2 @ X2)))) & ((![Y7 : list_event]: (((((member_list_event @ Y7 @ A4)) & ((P2 @ Y7)))) => ((Y7 = X2)))))))))))). % can_select_def
thf(fact_120_Crypt__notin__initState, axiom,
    ((![K : nat, X : msg, B : agent]: (~ ((member_msg @ (crypt @ K @ X) @ (parts @ (initState @ B)))))))). % Crypt_notin_initState
thf(fact_121_Nonce__notin__initState, axiom,
    ((![N : nat, B : agent]: (~ ((member_msg @ (nonce @ N) @ (parts @ (initState @ B)))))))). % Nonce_notin_initState
thf(fact_122_initState__subset__knows, axiom,
    ((![A : agent, Evs : list_event]: (ord_less_eq_set_msg @ (initState @ A) @ (knows @ A @ Evs))))). % initState_subset_knows
thf(fact_123_initState__into__used, axiom,
    ((![X : msg, B : agent, Evs : list_event]: ((member_msg @ X @ (parts @ (initState @ B))) => (member_msg @ X @ (used @ Evs)))))). % initState_into_used
thf(fact_124_knows__Nil, axiom,
    ((![A : agent]: ((knows @ A @ nil_event) = (initState @ A))))). % knows_Nil
thf(fact_125_MPair__used__D, axiom,
    ((![X : msg, Y : msg, H : list_event]: ((member_msg @ (mPair @ X @ Y) @ (used @ H)) => ((member_msg @ X @ (used @ H)) & (member_msg @ Y @ (used @ H))))))). % MPair_used_D
thf(fact_126_MPair__used, axiom,
    ((![X : msg, Y : msg, H : list_event]: ((member_msg @ (mPair @ X @ Y) @ (used @ H)) => (~ (((member_msg @ X @ (used @ H)) => (~ ((member_msg @ Y @ (used @ H))))))))))). % MPair_used
thf(fact_127_Nonce__supply1, axiom,
    ((![Evs : list_event]: (?[N2 : nat]: (~ ((member_msg @ (nonce @ N2) @ (used @ Evs)))))))). % Nonce_supply1
thf(fact_128_subsetI, axiom,
    ((![A : set_agent, B : set_agent]: ((![X5 : agent]: ((member_agent @ X5 @ A) => (member_agent @ X5 @ B))) => (ord_le722097072_agent @ A @ B))))). % subsetI
thf(fact_129_subsetI, axiom,
    ((![A : set_event, B : set_event]: ((![X5 : event]: ((member_event @ X5 @ A) => (member_event @ X5 @ B))) => (ord_le152226328_event @ A @ B))))). % subsetI
thf(fact_130_subsetI, axiom,
    ((![A : set_list_event, B : set_list_event]: ((![X5 : list_event]: ((member_list_event @ X5 @ A) => (member_list_event @ X5 @ B))) => (ord_le119303592_event @ A @ B))))). % subsetI
thf(fact_131_subsetI, axiom,
    ((![A : set_msg, B : set_msg]: ((![X5 : msg]: ((member_msg @ X5 @ A) => (member_msg @ X5 @ B))) => (ord_less_eq_set_msg @ A @ B))))). % subsetI
thf(fact_132_subset__antisym, axiom,
    ((![A : set_msg, B : set_msg]: ((ord_less_eq_set_msg @ A @ B) => ((ord_less_eq_set_msg @ B @ A) => (A = B)))))). % subset_antisym
thf(fact_133_order__refl, axiom,
    ((![X6 : set_msg]: (ord_less_eq_set_msg @ X6 @ X6)))). % order_refl
thf(fact_134_order__refl, axiom,
    ((![X6 : nat]: (ord_less_eq_nat @ X6 @ X6)))). % order_refl
thf(fact_135_less__eq__set__def, axiom,
    ((ord_le722097072_agent = (^[A4 : set_agent]: (^[B3 : set_agent]: (ord_less_eq_agent_o @ (^[X2 : agent]: (member_agent @ X2 @ A4)) @ (^[X2 : agent]: (member_agent @ X2 @ B3)))))))). % less_eq_set_def
thf(fact_136_less__eq__set__def, axiom,
    ((ord_le152226328_event = (^[A4 : set_event]: (^[B3 : set_event]: (ord_less_eq_event_o @ (^[X2 : event]: (member_event @ X2 @ A4)) @ (^[X2 : event]: (member_event @ X2 @ B3)))))))). % less_eq_set_def
thf(fact_137_less__eq__set__def, axiom,
    ((ord_le119303592_event = (^[A4 : set_list_event]: (^[B3 : set_list_event]: (ord_le1505328861vent_o @ (^[X2 : list_event]: (member_list_event @ X2 @ A4)) @ (^[X2 : list_event]: (member_list_event @ X2 @ B3)))))))). % less_eq_set_def
thf(fact_138_less__eq__set__def, axiom,
    ((ord_less_eq_set_msg = (^[A4 : set_msg]: (^[B3 : set_msg]: (ord_less_eq_msg_o @ (^[X2 : msg]: (member_msg @ X2 @ A4)) @ (^[X2 : msg]: (member_msg @ X2 @ B3)))))))). % less_eq_set_def
thf(fact_139_Nonce__supply__lemma, axiom,
    ((![Evs : list_event]: (?[N2 : nat]: (![N3 : nat]: ((ord_less_eq_nat @ N2 @ N3) => (~ ((member_msg @ (nonce @ N3) @ (used @ Evs)))))))))). % Nonce_supply_lemma
thf(fact_140_dual__order_Oantisym, axiom,
    ((![B4 : set_msg, A2 : set_msg]: ((ord_less_eq_set_msg @ B4 @ A2) => ((ord_less_eq_set_msg @ A2 @ B4) => (A2 = B4)))))). % dual_order.antisym
thf(fact_141_dual__order_Oantisym, axiom,
    ((![B4 : nat, A2 : nat]: ((ord_less_eq_nat @ B4 @ A2) => ((ord_less_eq_nat @ A2 @ B4) => (A2 = B4)))))). % dual_order.antisym
thf(fact_142_dual__order_Oeq__iff, axiom,
    (((^[Y8 : set_msg]: (^[Z : set_msg]: (Y8 = Z))) = (^[A5 : set_msg]: (^[B5 : set_msg]: (((ord_less_eq_set_msg @ B5 @ A5)) & ((ord_less_eq_set_msg @ A5 @ B5)))))))). % dual_order.eq_iff
thf(fact_143_dual__order_Oeq__iff, axiom,
    (((^[Y8 : nat]: (^[Z : nat]: (Y8 = Z))) = (^[A5 : nat]: (^[B5 : nat]: (((ord_less_eq_nat @ B5 @ A5)) & ((ord_less_eq_nat @ A5 @ B5)))))))). % dual_order.eq_iff
thf(fact_144_dual__order_Otrans, axiom,
    ((![B4 : set_msg, A2 : set_msg, C : set_msg]: ((ord_less_eq_set_msg @ B4 @ A2) => ((ord_less_eq_set_msg @ C @ B4) => (ord_less_eq_set_msg @ C @ A2)))))). % dual_order.trans
thf(fact_145_dual__order_Otrans, axiom,
    ((![B4 : nat, A2 : nat, C : nat]: ((ord_less_eq_nat @ B4 @ A2) => ((ord_less_eq_nat @ C @ B4) => (ord_less_eq_nat @ C @ A2)))))). % dual_order.trans
thf(fact_146_linorder__wlog, axiom,
    ((![P : nat > nat > $o, A2 : nat, B4 : nat]: ((![A6 : nat, B6 : nat]: ((ord_less_eq_nat @ A6 @ B6) => (P @ A6 @ B6))) => ((![A6 : nat, B6 : nat]: ((P @ B6 @ A6) => (P @ A6 @ B6))) => (P @ A2 @ B4)))))). % linorder_wlog
thf(fact_147_dual__order_Orefl, axiom,
    ((![A2 : set_msg]: (ord_less_eq_set_msg @ A2 @ A2)))). % dual_order.refl
thf(fact_148_dual__order_Orefl, axiom,
    ((![A2 : nat]: (ord_less_eq_nat @ A2 @ A2)))). % dual_order.refl
thf(fact_149_order__trans, axiom,
    ((![X6 : set_msg, Y6 : set_msg, Z2 : set_msg]: ((ord_less_eq_set_msg @ X6 @ Y6) => ((ord_less_eq_set_msg @ Y6 @ Z2) => (ord_less_eq_set_msg @ X6 @ Z2)))))). % order_trans
thf(fact_150_order__trans, axiom,
    ((![X6 : nat, Y6 : nat, Z2 : nat]: ((ord_less_eq_nat @ X6 @ Y6) => ((ord_less_eq_nat @ Y6 @ Z2) => (ord_less_eq_nat @ X6 @ Z2)))))). % order_trans
thf(fact_151_order__class_Oorder_Oantisym, axiom,
    ((![A2 : set_msg, B4 : set_msg]: ((ord_less_eq_set_msg @ A2 @ B4) => ((ord_less_eq_set_msg @ B4 @ A2) => (A2 = B4)))))). % order_class.order.antisym
thf(fact_152_order__class_Oorder_Oantisym, axiom,
    ((![A2 : nat, B4 : nat]: ((ord_less_eq_nat @ A2 @ B4) => ((ord_less_eq_nat @ B4 @ A2) => (A2 = B4)))))). % order_class.order.antisym
thf(fact_153_ord__le__eq__trans, axiom,
    ((![A2 : set_msg, B4 : set_msg, C : set_msg]: ((ord_less_eq_set_msg @ A2 @ B4) => ((B4 = C) => (ord_less_eq_set_msg @ A2 @ C)))))). % ord_le_eq_trans
thf(fact_154_ord__le__eq__trans, axiom,
    ((![A2 : nat, B4 : nat, C : nat]: ((ord_less_eq_nat @ A2 @ B4) => ((B4 = C) => (ord_less_eq_nat @ A2 @ C)))))). % ord_le_eq_trans
thf(fact_155_ord__eq__le__trans, axiom,
    ((![A2 : set_msg, B4 : set_msg, C : set_msg]: ((A2 = B4) => ((ord_less_eq_set_msg @ B4 @ C) => (ord_less_eq_set_msg @ A2 @ C)))))). % ord_eq_le_trans
thf(fact_156_ord__eq__le__trans, axiom,
    ((![A2 : nat, B4 : nat, C : nat]: ((A2 = B4) => ((ord_less_eq_nat @ B4 @ C) => (ord_less_eq_nat @ A2 @ C)))))). % ord_eq_le_trans
thf(fact_157_order__class_Oorder_Oeq__iff, axiom,
    (((^[Y8 : set_msg]: (^[Z : set_msg]: (Y8 = Z))) = (^[A5 : set_msg]: (^[B5 : set_msg]: (((ord_less_eq_set_msg @ A5 @ B5)) & ((ord_less_eq_set_msg @ B5 @ A5)))))))). % order_class.order.eq_iff
thf(fact_158_order__class_Oorder_Oeq__iff, axiom,
    (((^[Y8 : nat]: (^[Z : nat]: (Y8 = Z))) = (^[A5 : nat]: (^[B5 : nat]: (((ord_less_eq_nat @ A5 @ B5)) & ((ord_less_eq_nat @ B5 @ A5)))))))). % order_class.order.eq_iff
thf(fact_159_antisym__conv, axiom,
    ((![Y6 : set_msg, X6 : set_msg]: ((ord_less_eq_set_msg @ Y6 @ X6) => ((ord_less_eq_set_msg @ X6 @ Y6) = (X6 = Y6)))))). % antisym_conv
thf(fact_160_antisym__conv, axiom,
    ((![Y6 : nat, X6 : nat]: ((ord_less_eq_nat @ Y6 @ X6) => ((ord_less_eq_nat @ X6 @ Y6) = (X6 = Y6)))))). % antisym_conv
thf(fact_161_le__cases3, axiom,
    ((![X6 : nat, Y6 : nat, Z2 : nat]: (((ord_less_eq_nat @ X6 @ Y6) => (~ ((ord_less_eq_nat @ Y6 @ Z2)))) => (((ord_less_eq_nat @ Y6 @ X6) => (~ ((ord_less_eq_nat @ X6 @ Z2)))) => (((ord_less_eq_nat @ X6 @ Z2) => (~ ((ord_less_eq_nat @ Z2 @ Y6)))) => (((ord_less_eq_nat @ Z2 @ Y6) => (~ ((ord_less_eq_nat @ Y6 @ X6)))) => (((ord_less_eq_nat @ Y6 @ Z2) => (~ ((ord_less_eq_nat @ Z2 @ X6)))) => (~ (((ord_less_eq_nat @ Z2 @ X6) => (~ ((ord_less_eq_nat @ X6 @ Y6)))))))))))))). % le_cases3
thf(fact_162_order_Otrans, axiom,
    ((![A2 : set_msg, B4 : set_msg, C : set_msg]: ((ord_less_eq_set_msg @ A2 @ B4) => ((ord_less_eq_set_msg @ B4 @ C) => (ord_less_eq_set_msg @ A2 @ C)))))). % order.trans
thf(fact_163_order_Otrans, axiom,
    ((![A2 : nat, B4 : nat, C : nat]: ((ord_less_eq_nat @ A2 @ B4) => ((ord_less_eq_nat @ B4 @ C) => (ord_less_eq_nat @ A2 @ C)))))). % order.trans
thf(fact_164_le__cases, axiom,
    ((![X6 : nat, Y6 : nat]: ((~ ((ord_less_eq_nat @ X6 @ Y6))) => (ord_less_eq_nat @ Y6 @ X6))))). % le_cases
thf(fact_165_eq__refl, axiom,
    ((![X6 : set_msg, Y6 : set_msg]: ((X6 = Y6) => (ord_less_eq_set_msg @ X6 @ Y6))))). % eq_refl
thf(fact_166_eq__refl, axiom,
    ((![X6 : nat, Y6 : nat]: ((X6 = Y6) => (ord_less_eq_nat @ X6 @ Y6))))). % eq_refl
thf(fact_167_linear, axiom,
    ((![X6 : nat, Y6 : nat]: ((ord_less_eq_nat @ X6 @ Y6) | (ord_less_eq_nat @ Y6 @ X6))))). % linear
thf(fact_168_antisym, axiom,
    ((![X6 : set_msg, Y6 : set_msg]: ((ord_less_eq_set_msg @ X6 @ Y6) => ((ord_less_eq_set_msg @ Y6 @ X6) => (X6 = Y6)))))). % antisym
thf(fact_169_antisym, axiom,
    ((![X6 : nat, Y6 : nat]: ((ord_less_eq_nat @ X6 @ Y6) => ((ord_less_eq_nat @ Y6 @ X6) => (X6 = Y6)))))). % antisym
thf(fact_170_eq__iff, axiom,
    (((^[Y8 : set_msg]: (^[Z : set_msg]: (Y8 = Z))) = (^[X2 : set_msg]: (^[Y7 : set_msg]: (((ord_less_eq_set_msg @ X2 @ Y7)) & ((ord_less_eq_set_msg @ Y7 @ X2)))))))). % eq_iff
thf(fact_171_eq__iff, axiom,
    (((^[Y8 : nat]: (^[Z : nat]: (Y8 = Z))) = (^[X2 : nat]: (^[Y7 : nat]: (((ord_less_eq_nat @ X2 @ Y7)) & ((ord_less_eq_nat @ Y7 @ X2)))))))). % eq_iff
thf(fact_172_ord__le__eq__subst, axiom,
    ((![A2 : set_msg, B4 : set_msg, F : set_msg > set_msg, C : set_msg]: ((ord_less_eq_set_msg @ A2 @ B4) => (((F @ B4) = C) => ((![X5 : set_msg, Y9 : set_msg]: ((ord_less_eq_set_msg @ X5 @ Y9) => (ord_less_eq_set_msg @ (F @ X5) @ (F @ Y9)))) => (ord_less_eq_set_msg @ (F @ A2) @ C))))))). % ord_le_eq_subst
thf(fact_173_ord__le__eq__subst, axiom,
    ((![A2 : set_msg, B4 : set_msg, F : set_msg > nat, C : nat]: ((ord_less_eq_set_msg @ A2 @ B4) => (((F @ B4) = C) => ((![X5 : set_msg, Y9 : set_msg]: ((ord_less_eq_set_msg @ X5 @ Y9) => (ord_less_eq_nat @ (F @ X5) @ (F @ Y9)))) => (ord_less_eq_nat @ (F @ A2) @ C))))))). % ord_le_eq_subst
thf(fact_174_ord__le__eq__subst, axiom,
    ((![A2 : nat, B4 : nat, F : nat > set_msg, C : set_msg]: ((ord_less_eq_nat @ A2 @ B4) => (((F @ B4) = C) => ((![X5 : nat, Y9 : nat]: ((ord_less_eq_nat @ X5 @ Y9) => (ord_less_eq_set_msg @ (F @ X5) @ (F @ Y9)))) => (ord_less_eq_set_msg @ (F @ A2) @ C))))))). % ord_le_eq_subst
thf(fact_175_ord__le__eq__subst, axiom,
    ((![A2 : nat, B4 : nat, F : nat > nat, C : nat]: ((ord_less_eq_nat @ A2 @ B4) => (((F @ B4) = C) => ((![X5 : nat, Y9 : nat]: ((ord_less_eq_nat @ X5 @ Y9) => (ord_less_eq_nat @ (F @ X5) @ (F @ Y9)))) => (ord_less_eq_nat @ (F @ A2) @ C))))))). % ord_le_eq_subst
thf(fact_176_ord__eq__le__subst, axiom,
    ((![A2 : set_msg, F : set_msg > set_msg, B4 : set_msg, C : set_msg]: ((A2 = (F @ B4)) => ((ord_less_eq_set_msg @ B4 @ C) => ((![X5 : set_msg, Y9 : set_msg]: ((ord_less_eq_set_msg @ X5 @ Y9) => (ord_less_eq_set_msg @ (F @ X5) @ (F @ Y9)))) => (ord_less_eq_set_msg @ A2 @ (F @ C)))))))). % ord_eq_le_subst
thf(fact_177_ord__eq__le__subst, axiom,
    ((![A2 : nat, F : set_msg > nat, B4 : set_msg, C : set_msg]: ((A2 = (F @ B4)) => ((ord_less_eq_set_msg @ B4 @ C) => ((![X5 : set_msg, Y9 : set_msg]: ((ord_less_eq_set_msg @ X5 @ Y9) => (ord_less_eq_nat @ (F @ X5) @ (F @ Y9)))) => (ord_less_eq_nat @ A2 @ (F @ C)))))))). % ord_eq_le_subst
thf(fact_178_ord__eq__le__subst, axiom,
    ((![A2 : set_msg, F : nat > set_msg, B4 : nat, C : nat]: ((A2 = (F @ B4)) => ((ord_less_eq_nat @ B4 @ C) => ((![X5 : nat, Y9 : nat]: ((ord_less_eq_nat @ X5 @ Y9) => (ord_less_eq_set_msg @ (F @ X5) @ (F @ Y9)))) => (ord_less_eq_set_msg @ A2 @ (F @ C)))))))). % ord_eq_le_subst
thf(fact_179_ord__eq__le__subst, axiom,
    ((![A2 : nat, F : nat > nat, B4 : nat, C : nat]: ((A2 = (F @ B4)) => ((ord_less_eq_nat @ B4 @ C) => ((![X5 : nat, Y9 : nat]: ((ord_less_eq_nat @ X5 @ Y9) => (ord_less_eq_nat @ (F @ X5) @ (F @ Y9)))) => (ord_less_eq_nat @ A2 @ (F @ C)))))))). % ord_eq_le_subst
thf(fact_180_order__subst2, axiom,
    ((![A2 : set_msg, B4 : set_msg, F : set_msg > set_msg, C : set_msg]: ((ord_less_eq_set_msg @ A2 @ B4) => ((ord_less_eq_set_msg @ (F @ B4) @ C) => ((![X5 : set_msg, Y9 : set_msg]: ((ord_less_eq_set_msg @ X5 @ Y9) => (ord_less_eq_set_msg @ (F @ X5) @ (F @ Y9)))) => (ord_less_eq_set_msg @ (F @ A2) @ C))))))). % order_subst2
thf(fact_181_order__subst2, axiom,
    ((![A2 : set_msg, B4 : set_msg, F : set_msg > nat, C : nat]: ((ord_less_eq_set_msg @ A2 @ B4) => ((ord_less_eq_nat @ (F @ B4) @ C) => ((![X5 : set_msg, Y9 : set_msg]: ((ord_less_eq_set_msg @ X5 @ Y9) => (ord_less_eq_nat @ (F @ X5) @ (F @ Y9)))) => (ord_less_eq_nat @ (F @ A2) @ C))))))). % order_subst2
thf(fact_182_order__subst2, axiom,
    ((![A2 : nat, B4 : nat, F : nat > set_msg, C : set_msg]: ((ord_less_eq_nat @ A2 @ B4) => ((ord_less_eq_set_msg @ (F @ B4) @ C) => ((![X5 : nat, Y9 : nat]: ((ord_less_eq_nat @ X5 @ Y9) => (ord_less_eq_set_msg @ (F @ X5) @ (F @ Y9)))) => (ord_less_eq_set_msg @ (F @ A2) @ C))))))). % order_subst2
thf(fact_183_order__subst2, axiom,
    ((![A2 : nat, B4 : nat, F : nat > nat, C : nat]: ((ord_less_eq_nat @ A2 @ B4) => ((ord_less_eq_nat @ (F @ B4) @ C) => ((![X5 : nat, Y9 : nat]: ((ord_less_eq_nat @ X5 @ Y9) => (ord_less_eq_nat @ (F @ X5) @ (F @ Y9)))) => (ord_less_eq_nat @ (F @ A2) @ C))))))). % order_subst2
thf(fact_184_order__subst1, axiom,
    ((![A2 : set_msg, F : set_msg > set_msg, B4 : set_msg, C : set_msg]: ((ord_less_eq_set_msg @ A2 @ (F @ B4)) => ((ord_less_eq_set_msg @ B4 @ C) => ((![X5 : set_msg, Y9 : set_msg]: ((ord_less_eq_set_msg @ X5 @ Y9) => (ord_less_eq_set_msg @ (F @ X5) @ (F @ Y9)))) => (ord_less_eq_set_msg @ A2 @ (F @ C)))))))). % order_subst1
thf(fact_185_order__subst1, axiom,
    ((![A2 : set_msg, F : nat > set_msg, B4 : nat, C : nat]: ((ord_less_eq_set_msg @ A2 @ (F @ B4)) => ((ord_less_eq_nat @ B4 @ C) => ((![X5 : nat, Y9 : nat]: ((ord_less_eq_nat @ X5 @ Y9) => (ord_less_eq_set_msg @ (F @ X5) @ (F @ Y9)))) => (ord_less_eq_set_msg @ A2 @ (F @ C)))))))). % order_subst1
thf(fact_186_order__subst1, axiom,
    ((![A2 : nat, F : set_msg > nat, B4 : set_msg, C : set_msg]: ((ord_less_eq_nat @ A2 @ (F @ B4)) => ((ord_less_eq_set_msg @ B4 @ C) => ((![X5 : set_msg, Y9 : set_msg]: ((ord_less_eq_set_msg @ X5 @ Y9) => (ord_less_eq_nat @ (F @ X5) @ (F @ Y9)))) => (ord_less_eq_nat @ A2 @ (F @ C)))))))). % order_subst1
thf(fact_187_order__subst1, axiom,
    ((![A2 : nat, F : nat > nat, B4 : nat, C : nat]: ((ord_less_eq_nat @ A2 @ (F @ B4)) => ((ord_less_eq_nat @ B4 @ C) => ((![X5 : nat, Y9 : nat]: ((ord_less_eq_nat @ X5 @ Y9) => (ord_less_eq_nat @ (F @ X5) @ (F @ Y9)))) => (ord_less_eq_nat @ A2 @ (F @ C)))))))). % order_subst1
thf(fact_188_Collect__mono__iff, axiom,
    ((![P : msg > $o, Q : msg > $o]: ((ord_less_eq_set_msg @ (collect_msg @ P) @ (collect_msg @ Q)) = (![X2 : msg]: (((P @ X2)) => ((Q @ X2)))))))). % Collect_mono_iff
thf(fact_189_set__eq__subset, axiom,
    (((^[Y8 : set_msg]: (^[Z : set_msg]: (Y8 = Z))) = (^[A4 : set_msg]: (^[B3 : set_msg]: (((ord_less_eq_set_msg @ A4 @ B3)) & ((ord_less_eq_set_msg @ B3 @ A4)))))))). % set_eq_subset
thf(fact_190_subset__trans, axiom,
    ((![A : set_msg, B : set_msg, C2 : set_msg]: ((ord_less_eq_set_msg @ A @ B) => ((ord_less_eq_set_msg @ B @ C2) => (ord_less_eq_set_msg @ A @ C2)))))). % subset_trans
thf(fact_191_Collect__mono, axiom,
    ((![P : msg > $o, Q : msg > $o]: ((![X5 : msg]: ((P @ X5) => (Q @ X5))) => (ord_less_eq_set_msg @ (collect_msg @ P) @ (collect_msg @ Q)))))). % Collect_mono
thf(fact_192_subset__refl, axiom,
    ((![A : set_msg]: (ord_less_eq_set_msg @ A @ A)))). % subset_refl
thf(fact_193_subset__iff, axiom,
    ((ord_le722097072_agent = (^[A4 : set_agent]: (^[B3 : set_agent]: (![T : agent]: (((member_agent @ T @ A4)) => ((member_agent @ T @ B3))))))))). % subset_iff
thf(fact_194_subset__iff, axiom,
    ((ord_le152226328_event = (^[A4 : set_event]: (^[B3 : set_event]: (![T : event]: (((member_event @ T @ A4)) => ((member_event @ T @ B3))))))))). % subset_iff
thf(fact_195_subset__iff, axiom,
    ((ord_le119303592_event = (^[A4 : set_list_event]: (^[B3 : set_list_event]: (![T : list_event]: (((member_list_event @ T @ A4)) => ((member_list_event @ T @ B3))))))))). % subset_iff
thf(fact_196_subset__iff, axiom,
    ((ord_less_eq_set_msg = (^[A4 : set_msg]: (^[B3 : set_msg]: (![T : msg]: (((member_msg @ T @ A4)) => ((member_msg @ T @ B3))))))))). % subset_iff
thf(fact_197_equalityD2, axiom,
    ((![A : set_msg, B : set_msg]: ((A = B) => (ord_less_eq_set_msg @ B @ A))))). % equalityD2
thf(fact_198_equalityD1, axiom,
    ((![A : set_msg, B : set_msg]: ((A = B) => (ord_less_eq_set_msg @ A @ B))))). % equalityD1
thf(fact_199_subset__eq, axiom,
    ((ord_le722097072_agent = (^[A4 : set_agent]: (^[B3 : set_agent]: (![X2 : agent]: (((member_agent @ X2 @ A4)) => ((member_agent @ X2 @ B3))))))))). % subset_eq
thf(fact_200_subset__eq, axiom,
    ((ord_le152226328_event = (^[A4 : set_event]: (^[B3 : set_event]: (![X2 : event]: (((member_event @ X2 @ A4)) => ((member_event @ X2 @ B3))))))))). % subset_eq
thf(fact_201_subset__eq, axiom,
    ((ord_le119303592_event = (^[A4 : set_list_event]: (^[B3 : set_list_event]: (![X2 : list_event]: (((member_list_event @ X2 @ A4)) => ((member_list_event @ X2 @ B3))))))))). % subset_eq
thf(fact_202_subset__eq, axiom,
    ((ord_less_eq_set_msg = (^[A4 : set_msg]: (^[B3 : set_msg]: (![X2 : msg]: (((member_msg @ X2 @ A4)) => ((member_msg @ X2 @ B3))))))))). % subset_eq
thf(fact_203_equalityE, axiom,
    ((![A : set_msg, B : set_msg]: ((A = B) => (~ (((ord_less_eq_set_msg @ A @ B) => (~ ((ord_less_eq_set_msg @ B @ A)))))))))). % equalityE

% Conjectures (3)
thf(conj_0, hypothesis,
    ((~ ((member_agent @ a @ bad))))).
thf(conj_1, hypothesis,
    ((~ ((member_agent @ b @ bad))))).
thf(conj_2, conjecture,
    (((member_msg @ (key @ k) @ (analz @ (knows @ spy @ nil_event))) | ((~ ((member_event @ (says @ a @ b @ (crypt @ k @ (mPair @ (nonce @ nb) @ (nonce @ nb)))) @ (set_event2 @ nil_event)))) | (~ ((member_msg @ (crypt @ k @ (mPair @ (nonce @ nb) @ (nonce @ nb))) @ (parts @ (knows @ spy @ (takeWhile_event @ (^[Z3 : event]: (~ ((Z3 = (says @ a @ b @ (crypt @ k @ (mPair @ (nonce @ nb) @ (nonce @ nb)))))))) @ (rev_event @ nil_event))))))))))).
