% 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_301__5230646_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:24:12.676

% Could-be-implicit typings (11)
thf(ty_n_t__Set__Oset_It__List__Olist_It__Event__Oevent_J_J, type,
    set_list_event : $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__Set__Oset_It__Nat__Onat_J, type,
    set_nat : $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 (59)
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_List_Olist_OCons_001t__Event__Oevent, type,
    cons_event : event > list_event > list_event).
thf(sy_c_List_Olist_OCons_001t__Message__Omsg, type,
    cons_msg : msg > list_msg > list_msg).
thf(sy_c_List_Olist_Oset_001t__Event__Oevent, type,
    set_event2 : list_event > set_event).
thf(sy_c_List_Olist_Oset_001t__Message__Omsg, type,
    set_msg2 : list_msg > set_msg).
thf(sy_c_Message_Oagent_OServer, type,
    server : agent).
thf(sy_c_Message_Oagent_OSpy, type,
    spy : agent).
thf(sy_c_Message_Oanalz, type,
    analz : set_msg > set_msg).
thf(sy_c_Message_Omsg_OAgent, type,
    agent2 : agent > msg).
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_Message_OsymKeys, type,
    symKeys : set_nat).
thf(sy_c_NS__Shared__Mirabelle__xwdrtqxrux_Ons__shared, type,
    nS_Sha1061662329shared : set_list_event).
thf(sy_c_NS__Shared__Mirabelle__xwdrtqxrux_Ons__sharedp, type,
    nS_Sha1092415543haredp : list_event > $o).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Event__Oevent_J, type,
    top_top_set_event : set_event).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__List__Olist_It__Event__Oevent_J_J, type,
    top_to1178833912_event : set_list_event).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Message__Oagent_J, type,
    top_top_set_agent : set_agent).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Message__Omsg_J, type,
    top_top_set_msg : set_msg).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Nat__Onat_J, type,
    top_top_set_nat : set_nat).
thf(sy_c_Public_OshrK, type,
    shrK : agent > nat).
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_Set_OCollect_001t__Nat__Onat, type,
    collect_nat : (nat > $o) > set_nat).
thf(sy_c_Set_Oimage_001t__Event__Oevent_001t__Message__Oagent, type,
    image_event_agent : (event > agent) > set_event > set_agent).
thf(sy_c_Set_Oimage_001t__Event__Oevent_001t__Message__Omsg, type,
    image_event_msg : (event > msg) > set_event > set_msg).
thf(sy_c_Set_Oimage_001t__List__Olist_It__Event__Oevent_J_001t__Message__Omsg, type,
    image_list_event_msg : (list_event > msg) > set_list_event > set_msg).
thf(sy_c_Set_Oimage_001t__Message__Oagent_001t__Event__Oevent, type,
    image_agent_event : (agent > event) > set_agent > set_event).
thf(sy_c_Set_Oimage_001t__Message__Oagent_001t__Message__Oagent, type,
    image_agent_agent : (agent > agent) > set_agent > set_agent).
thf(sy_c_Set_Oimage_001t__Message__Oagent_001t__Message__Omsg, type,
    image_agent_msg : (agent > msg) > set_agent > set_msg).
thf(sy_c_Set_Oimage_001t__Message__Oagent_001t__Nat__Onat, type,
    image_agent_nat : (agent > nat) > set_agent > set_nat).
thf(sy_c_Set_Oimage_001t__Message__Omsg_001t__Event__Oevent, type,
    image_msg_event : (msg > event) > set_msg > set_event).
thf(sy_c_Set_Oimage_001t__Message__Omsg_001t__Message__Oagent, type,
    image_msg_agent : (msg > agent) > set_msg > set_agent).
thf(sy_c_Set_Oimage_001t__Message__Omsg_001t__Message__Omsg, type,
    image_msg_msg : (msg > msg) > set_msg > set_msg).
thf(sy_c_Set_Oimage_001t__Message__Omsg_001t__Nat__Onat, type,
    image_msg_nat : (msg > nat) > set_msg > set_nat).
thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Message__Omsg, type,
    image_nat_msg : (nat > msg) > set_nat > set_msg).
thf(sy_c_Set_Oinsert_001t__Event__Oevent, type,
    insert_event : event > set_event > set_event).
thf(sy_c_Set_Oinsert_001t__List__Olist_It__Event__Oevent_J, type,
    insert_list_event : list_event > set_list_event > set_list_event).
thf(sy_c_Set_Oinsert_001t__Message__Oagent, type,
    insert_agent : agent > set_agent > set_agent).
thf(sy_c_Set_Oinsert_001t__Message__Omsg, type,
    insert_msg : msg > set_msg > set_msg).
thf(sy_c_Set_Oinsert_001t__Nat__Onat, type,
    insert_nat : nat > set_nat > set_nat).
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_c_member_001t__Nat__Onat, type,
    member_nat : nat > set_nat > $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_evs, type,
    evs : list_event).

% Relevant facts (231)
thf(fact_0_Spy__see__shrK, axiom,
    ((![Evs : list_event, A : agent]: ((member_list_event @ Evs @ nS_Sha1061662329shared) => ((member_msg @ (key @ (shrK @ A)) @ (parts @ (knows @ spy @ Evs))) = (member_agent @ A @ bad)))))). % Spy_see_shrK
thf(fact_1_A__trusts__NS2, axiom,
    ((![A : agent, NA : msg, B : agent, K : nat, X : msg, Evs : list_event]: ((member_msg @ (crypt @ (shrK @ A) @ (mPair @ NA @ (mPair @ (agent2 @ B) @ (mPair @ (key @ K) @ X)))) @ (parts @ (knows @ spy @ Evs))) => ((~ ((member_agent @ A @ bad))) => ((member_list_event @ Evs @ nS_Sha1061662329shared) => (member_event @ (says @ server @ A @ (crypt @ (shrK @ A) @ (mPair @ NA @ (mPair @ (agent2 @ B) @ (mPair @ (key @ K) @ X))))) @ (set_event2 @ Evs)))))))). % A_trusts_NS2
thf(fact_2_Oops__parts__spies, axiom,
    ((![A : agent, NA : msg, B : msg, K : msg, X : msg, Evs : list_event]: ((member_event @ (says @ server @ A @ (crypt @ (shrK @ A) @ (mPair @ NA @ (mPair @ B @ (mPair @ K @ X))))) @ (set_event2 @ Evs)) => (member_msg @ K @ (parts @ (knows @ spy @ Evs))))))). % Oops_parts_spies
thf(fact_3_unique__session__keys, axiom,
    ((![A : agent, NA : msg, B : agent, K : nat, X : msg, Evs : list_event, A2 : agent, NA2 : msg, B2 : agent, X2 : msg]: ((member_event @ (says @ server @ A @ (crypt @ (shrK @ A) @ (mPair @ NA @ (mPair @ (agent2 @ B) @ (mPair @ (key @ K) @ X))))) @ (set_event2 @ Evs)) => ((member_event @ (says @ server @ A2 @ (crypt @ (shrK @ A2) @ (mPair @ NA2 @ (mPair @ (agent2 @ B2) @ (mPair @ (key @ K) @ X2))))) @ (set_event2 @ Evs)) => ((member_list_event @ Evs @ nS_Sha1061662329shared) => ((A = A2) & ((NA = NA2) & ((B = B2) & (X = X2)))))))))). % unique_session_keys
thf(fact_4_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_5_Spy__spies__bad__shrK, axiom,
    ((![A : agent, Evs : list_event]: ((member_agent @ A @ bad) => (member_msg @ (key @ (shrK @ A)) @ (knows @ spy @ Evs)))))). % Spy_spies_bad_shrK
thf(fact_6_shrK__in__knows, axiom,
    ((![A : agent, Evs : list_event]: (member_msg @ (key @ (shrK @ A)) @ (knows @ A @ Evs))))). % shrK_in_knows
thf(fact_7_Spy__in__bad, axiom,
    ((member_agent @ spy @ bad))). % Spy_in_bad
thf(fact_8_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_9_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_10_parts_Ocases, axiom,
    ((![A3 : msg, H : set_msg]: ((member_msg @ A3 @ (parts @ H)) => ((~ ((member_msg @ A3 @ H))) => ((![Y : msg]: (~ ((member_msg @ (mPair @ A3 @ Y) @ (parts @ H))))) => ((![X3 : msg]: (~ ((member_msg @ (mPair @ X3 @ A3) @ (parts @ H))))) => (~ ((![K2 : nat]: (~ ((member_msg @ (crypt @ K2 @ A3) @ (parts @ H)))))))))))))). % parts.cases
thf(fact_11_parts_Osimps, axiom,
    ((![A3 : msg, H : set_msg]: ((member_msg @ A3 @ (parts @ H)) = (((?[X4 : msg]: (((A3 = X4)) & ((member_msg @ X4 @ H))))) | ((((?[X4 : msg]: (?[Y2 : msg]: (((A3 = X4)) & ((member_msg @ (mPair @ X4 @ Y2) @ (parts @ H))))))) | ((((?[X4 : msg]: (?[Y2 : msg]: (((A3 = Y2)) & ((member_msg @ (mPair @ X4 @ Y2) @ (parts @ H))))))) | ((?[K3 : nat]: (?[X4 : msg]: (((A3 = X4)) & ((member_msg @ (crypt @ K3 @ X4) @ (parts @ H)))))))))))))))). % parts.simps
thf(fact_12_parts_Oinducts, axiom,
    ((![X5 : msg, H : set_msg, P : msg > $o]: ((member_msg @ X5 @ (parts @ H)) => ((![X3 : msg]: ((member_msg @ X3 @ H) => (P @ X3))) => ((![X3 : msg, Y : msg]: ((member_msg @ (mPair @ X3 @ Y) @ (parts @ H)) => ((P @ (mPair @ X3 @ Y)) => (P @ X3)))) => ((![X3 : msg, Y : msg]: ((member_msg @ (mPair @ X3 @ Y) @ (parts @ H)) => ((P @ (mPair @ X3 @ Y)) => (P @ Y)))) => ((![K2 : nat, X3 : msg]: ((member_msg @ (crypt @ K2 @ X3) @ (parts @ H)) => ((P @ (crypt @ K2 @ X3)) => (P @ X3)))) => (P @ X5))))))))). % parts.inducts
thf(fact_13_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_14_shrK__injective, axiom,
    ((![X5 : agent, Y3 : agent]: (((shrK @ X5) = (shrK @ Y3)) = (X5 = Y3))))). % shrK_injective
thf(fact_15_msg_Oinject_I1_J, axiom,
    ((![X1 : agent, Y1 : agent]: (((agent2 @ X1) = (agent2 @ Y1)) = (X1 = Y1))))). % msg.inject(1)
thf(fact_16_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_17_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_18_msg_Oinject_I4_J, axiom,
    ((![X42 : nat, Y4 : nat]: (((key @ X42) = (key @ Y4)) = (X42 = Y4))))). % msg.inject(4)
thf(fact_19_parts__idem, axiom,
    ((![H : set_msg]: ((parts @ (parts @ H)) = (parts @ H))))). % parts_idem
thf(fact_20_parts__partsD, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ (parts @ (parts @ H))) => (member_msg @ X @ (parts @ H)))))). % parts_partsD
thf(fact_21_parts_OInj, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ H) => (member_msg @ X @ (parts @ H)))))). % parts.Inj
thf(fact_22_msg_Odistinct_I33_J, axiom,
    ((![X42 : nat, X61 : msg, X62 : msg]: (~ (((key @ X42) = (mPair @ X61 @ X62))))))). % msg.distinct(33)
thf(fact_23_MPair__parts, axiom,
    ((![X : msg, Y5 : msg, H : set_msg]: ((member_msg @ (mPair @ X @ Y5) @ (parts @ H)) => (~ (((member_msg @ X @ (parts @ H)) => (~ ((member_msg @ Y5 @ (parts @ H))))))))))). % MPair_parts
thf(fact_24_parts_OSnd, axiom,
    ((![X : msg, Y5 : msg, H : set_msg]: ((member_msg @ (mPair @ X @ Y5) @ (parts @ H)) => (member_msg @ Y5 @ (parts @ H)))))). % parts.Snd
thf(fact_25_parts_OFst, axiom,
    ((![X : msg, Y5 : msg, H : set_msg]: ((member_msg @ (mPair @ X @ Y5) @ (parts @ H)) => (member_msg @ X @ (parts @ H)))))). % parts.Fst
thf(fact_26_msg_Odistinct_I41_J, axiom,
    ((![X61 : msg, X62 : msg, X71 : nat, X72 : msg]: (~ (((mPair @ X61 @ X62) = (crypt @ X71 @ X72))))))). % msg.distinct(41)
thf(fact_27_msg_Odistinct_I35_J, axiom,
    ((![X42 : nat, X71 : nat, X72 : msg]: (~ (((key @ X42) = (crypt @ X71 @ X72))))))). % msg.distinct(35)
thf(fact_28_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_29_msg_Odistinct_I9_J, axiom,
    ((![X1 : agent, X61 : msg, X62 : msg]: (~ (((agent2 @ X1) = (mPair @ X61 @ X62))))))). % msg.distinct(9)
thf(fact_30_msg_Odistinct_I5_J, axiom,
    ((![X1 : agent, X42 : nat]: (~ (((agent2 @ X1) = (key @ X42))))))). % msg.distinct(5)
thf(fact_31_msg_Odistinct_I11_J, axiom,
    ((![X1 : agent, X71 : nat, X72 : msg]: (~ (((agent2 @ X1) = (crypt @ X71 @ X72))))))). % msg.distinct(11)
thf(fact_32_agent_Odistinct_I3_J, axiom,
    ((~ ((server = spy))))). % agent.distinct(3)
thf(fact_33_Server__not__bad, axiom,
    ((~ ((member_agent @ server @ bad))))). % Server_not_bad
thf(fact_34_Spy__analz__shrK, axiom,
    ((![Evs : list_event, A : agent]: ((member_list_event @ Evs @ nS_Sha1061662329shared) => ((member_msg @ (key @ (shrK @ A)) @ (analz @ (knows @ spy @ Evs))) = (member_agent @ A @ bad)))))). % Spy_analz_shrK
thf(fact_35_secrecy__lemma, axiom,
    ((![A : agent, NA : msg, B : agent, K : nat, Evs : list_event]: ((member_event @ (says @ server @ A @ (crypt @ (shrK @ A) @ (mPair @ NA @ (mPair @ (agent2 @ B) @ (mPair @ (key @ K) @ (crypt @ (shrK @ B) @ (mPair @ (key @ K) @ (agent2 @ A)))))))) @ (set_event2 @ Evs)) => ((~ ((member_agent @ A @ bad))) => ((~ ((member_agent @ B @ bad))) => ((member_list_event @ Evs @ nS_Sha1061662329shared) => ((![NB : msg]: (~ ((member_event @ (notes @ spy @ (mPair @ NA @ (mPair @ NB @ (key @ K)))) @ (set_event2 @ Evs))))) => (~ ((member_msg @ (key @ K) @ (analz @ (knows @ spy @ Evs))))))))))))). % secrecy_lemma
thf(fact_36_Spy__not__see__encrypted__key, axiom,
    ((![A : agent, K4 : nat, NA : msg, B : agent, K : nat, X : msg, Evs : list_event]: ((member_event @ (says @ server @ A @ (crypt @ K4 @ (mPair @ NA @ (mPair @ (agent2 @ B) @ (mPair @ (key @ K) @ X))))) @ (set_event2 @ Evs)) => ((![NB : msg]: (~ ((member_event @ (notes @ spy @ (mPair @ NA @ (mPair @ NB @ (key @ K)))) @ (set_event2 @ Evs))))) => ((~ ((member_agent @ A @ bad))) => ((~ ((member_agent @ B @ bad))) => ((member_list_event @ Evs @ nS_Sha1061662329shared) => (~ ((member_msg @ (key @ K) @ (analz @ (knows @ spy @ Evs))))))))))))). % Spy_not_see_encrypted_key
thf(fact_37_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_38_cert__A__form, axiom,
    ((![A : agent, NA : msg, B : agent, K : nat, X : msg, Evs : list_event]: ((member_msg @ (crypt @ (shrK @ A) @ (mPair @ NA @ (mPair @ (agent2 @ B) @ (mPair @ (key @ K) @ X)))) @ (parts @ (knows @ spy @ Evs))) => ((~ ((member_agent @ A @ bad))) => ((member_list_event @ Evs @ nS_Sha1061662329shared) => ((~ ((member_nat @ K @ (image_agent_nat @ shrK @ top_top_set_agent)))) & (X = (crypt @ (shrK @ B) @ (mPair @ (key @ K) @ (agent2 @ A))))))))))). % cert_A_form
thf(fact_39_Crypt__Spy__analz__bad, axiom,
    ((![A : agent, X : msg, Evs : list_event]: ((member_msg @ (crypt @ (shrK @ A) @ X) @ (analz @ (knows @ spy @ Evs))) => ((member_agent @ A @ bad) => (member_msg @ X @ (analz @ (knows @ spy @ Evs)))))))). % Crypt_Spy_analz_bad
thf(fact_40_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_41_Says__Server__message__form, axiom,
    ((![A : agent, K4 : nat, N : msg, B : agent, K : nat, X : msg, Evs : list_event]: ((member_event @ (says @ server @ A @ (crypt @ K4 @ (mPair @ N @ (mPair @ (agent2 @ B) @ (mPair @ (key @ K) @ X))))) @ (set_event2 @ Evs)) => ((member_list_event @ Evs @ nS_Sha1061662329shared) => ((~ ((member_nat @ K @ (image_agent_nat @ shrK @ top_top_set_agent)))) & ((X = (crypt @ (shrK @ B) @ (mPair @ (key @ K) @ (agent2 @ A)))) & (K4 = (shrK @ A))))))))). % Says_Server_message_form
thf(fact_42_ns__shared_ONS3, axiom,
    ((![Evs3 : list_event, A : agent, S : agent, NA : nat, B : agent, K : nat, X : msg]: ((member_list_event @ Evs3 @ nS_Sha1061662329shared) => ((~ ((A = server))) => ((member_event @ (says @ S @ A @ (crypt @ (shrK @ A) @ (mPair @ (nonce @ NA) @ (mPair @ (agent2 @ B) @ (mPair @ (key @ K) @ X))))) @ (set_event2 @ Evs3)) => ((member_event @ (says @ A @ server @ (mPair @ (agent2 @ A) @ (mPair @ (agent2 @ B) @ (nonce @ NA)))) @ (set_event2 @ Evs3)) => (member_list_event @ (cons_event @ (says @ A @ B @ X) @ Evs3) @ nS_Sha1061662329shared)))))))). % ns_shared.NS3
thf(fact_43_analz__idem, axiom,
    ((![H : set_msg]: ((analz @ (analz @ H)) = (analz @ H))))). % analz_idem
thf(fact_44_msg_Oinject_I3_J, axiom,
    ((![X32 : nat, Y32 : nat]: (((nonce @ X32) = (nonce @ Y32)) = (X32 = Y32))))). % msg.inject(3)
thf(fact_45_mem__Collect__eq, axiom,
    ((![A3 : msg, P : msg > $o]: ((member_msg @ A3 @ (collect_msg @ P)) = (P @ A3))))). % mem_Collect_eq
thf(fact_46_mem__Collect__eq, axiom,
    ((![A3 : agent, P : agent > $o]: ((member_agent @ A3 @ (collect_agent @ P)) = (P @ A3))))). % mem_Collect_eq
thf(fact_47_mem__Collect__eq, axiom,
    ((![A3 : list_event, P : list_event > $o]: ((member_list_event @ A3 @ (collect_list_event @ P)) = (P @ A3))))). % mem_Collect_eq
thf(fact_48_mem__Collect__eq, axiom,
    ((![A3 : event, P : event > $o]: ((member_event @ A3 @ (collect_event @ P)) = (P @ A3))))). % mem_Collect_eq
thf(fact_49_mem__Collect__eq, axiom,
    ((![A3 : nat, P : nat > $o]: ((member_nat @ A3 @ (collect_nat @ P)) = (P @ A3))))). % mem_Collect_eq
thf(fact_50_Collect__mem__eq, axiom,
    ((![A : set_msg]: ((collect_msg @ (^[X6 : msg]: (member_msg @ X6 @ A))) = A)))). % Collect_mem_eq
thf(fact_51_Collect__mem__eq, axiom,
    ((![A : set_agent]: ((collect_agent @ (^[X6 : agent]: (member_agent @ X6 @ A))) = A)))). % Collect_mem_eq
thf(fact_52_Collect__mem__eq, axiom,
    ((![A : set_list_event]: ((collect_list_event @ (^[X6 : list_event]: (member_list_event @ X6 @ A))) = A)))). % Collect_mem_eq
thf(fact_53_Collect__mem__eq, axiom,
    ((![A : set_event]: ((collect_event @ (^[X6 : event]: (member_event @ X6 @ A))) = A)))). % Collect_mem_eq
thf(fact_54_Collect__mem__eq, axiom,
    ((![A : set_nat]: ((collect_nat @ (^[X6 : nat]: (member_nat @ X6 @ A))) = A)))). % Collect_mem_eq
thf(fact_55_event_Oinject_I3_J, axiom,
    ((![X31 : agent, X322 : msg, Y31 : agent, Y322 : msg]: (((notes @ X31 @ X322) = (notes @ Y31 @ Y322)) = (((X31 = Y31)) & ((X322 = Y322))))))). % event.inject(3)
thf(fact_56_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_57_analz__parts, axiom,
    ((![H : set_msg]: ((analz @ (parts @ H)) = (parts @ H))))). % analz_parts
thf(fact_58_parts__analz, axiom,
    ((![H : set_msg]: ((parts @ (analz @ H)) = (parts @ H))))). % parts_analz
thf(fact_59_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_60_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_61_shrK__image__eq, axiom,
    ((![X5 : agent, AA : set_agent]: ((member_nat @ (shrK @ X5) @ (image_agent_nat @ shrK @ AA)) = (member_agent @ X5 @ AA))))). % shrK_image_eq
thf(fact_62_knows__Spy__Gets, axiom,
    ((![A : agent, X : msg, Evs : list_event]: ((knows @ spy @ (cons_event @ (gets @ A @ X) @ Evs)) = (knows @ spy @ Evs))))). % knows_Spy_Gets
thf(fact_63_event_Odistinct_I5_J, axiom,
    ((![X21 : agent, X22 : msg, X31 : agent, X322 : msg]: (~ (((gets @ X21 @ X22) = (notes @ X31 @ X322))))))). % event.distinct(5)
thf(fact_64_analz_OInj, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ H) => (member_msg @ X @ (analz @ H)))))). % analz.Inj
thf(fact_65_analz__analzD, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ (analz @ (analz @ H))) => (member_msg @ X @ (analz @ H)))))). % analz_analzD
thf(fact_66_analz__mono__contra_I2_J, axiom,
    ((![C : msg, A : agent, X : msg, Evs : list_event]: ((~ ((member_msg @ C @ (analz @ (knows @ spy @ (cons_event @ (notes @ A @ X) @ Evs)))))) => (~ ((member_msg @ C @ (analz @ (knows @ spy @ Evs))))))))). % analz_mono_contra(2)
thf(fact_67_analz__mono__contra_I3_J, axiom,
    ((![C : msg, A : agent, X : msg, Evs : list_event]: ((~ ((member_msg @ C @ (analz @ (knows @ spy @ (cons_event @ (gets @ A @ X) @ Evs)))))) => (~ ((member_msg @ C @ (analz @ (knows @ spy @ Evs))))))))). % analz_mono_contra(3)
thf(fact_68_event_Oinduct, axiom,
    ((![P : event > $o, Event : event]: ((![X14 : agent, X23 : agent, X33 : msg]: (P @ (says @ X14 @ X23 @ X33))) => ((![X14 : agent, X23 : msg]: (P @ (gets @ X14 @ X23))) => ((![X14 : agent, X23 : msg]: (P @ (notes @ X14 @ X23))) => (P @ Event))))))). % event.induct
thf(fact_69_event_Oexhaust, axiom,
    ((![Y3 : event]: ((![X112 : agent, X122 : agent, X132 : msg]: (~ ((Y3 = (says @ X112 @ X122 @ X132))))) => ((![X212 : agent, X222 : msg]: (~ ((Y3 = (gets @ X212 @ X222))))) => (~ ((![X312 : agent, X323 : msg]: (~ ((Y3 = (notes @ X312 @ X323)))))))))))). % event.exhaust
thf(fact_70_analz_OFst, axiom,
    ((![X : msg, Y5 : msg, H : set_msg]: ((member_msg @ (mPair @ X @ Y5) @ (analz @ H)) => (member_msg @ X @ (analz @ H)))))). % analz.Fst
thf(fact_71_analz_OSnd, axiom,
    ((![X : msg, Y5 : msg, H : set_msg]: ((member_msg @ (mPair @ X @ Y5) @ (analz @ H)) => (member_msg @ Y5 @ (analz @ H)))))). % analz.Snd
thf(fact_72_MPair__analz, axiom,
    ((![X : msg, Y5 : msg, H : set_msg]: ((member_msg @ (mPair @ X @ Y5) @ (analz @ H)) => (~ (((member_msg @ X @ (analz @ H)) => (~ ((member_msg @ Y5 @ (analz @ H))))))))))). % MPair_analz
thf(fact_73_analz__into__parts, axiom,
    ((![C : msg, H : set_msg]: ((member_msg @ C @ (analz @ H)) => (member_msg @ C @ (parts @ H)))))). % analz_into_parts
thf(fact_74_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_75_msg_Odistinct_I27_J, axiom,
    ((![X32 : nat, X61 : msg, X62 : msg]: (~ (((nonce @ X32) = (mPair @ X61 @ X62))))))). % msg.distinct(27)
thf(fact_76_msg_Odistinct_I23_J, axiom,
    ((![X32 : nat, X42 : nat]: (~ (((nonce @ X32) = (key @ X42))))))). % msg.distinct(23)
thf(fact_77_msg_Odistinct_I29_J, axiom,
    ((![X32 : nat, X71 : nat, X72 : msg]: (~ (((nonce @ X32) = (crypt @ X71 @ X72))))))). % msg.distinct(29)
thf(fact_78_msg_Odistinct_I3_J, axiom,
    ((![X1 : agent, X32 : nat]: (~ (((agent2 @ X1) = (nonce @ X32))))))). % msg.distinct(3)
thf(fact_79_analz__mono__contra_I1_J, axiom,
    ((![C : msg, A : agent, B : agent, X : msg, Evs : list_event]: ((~ ((member_msg @ C @ (analz @ (knows @ spy @ (cons_event @ (says @ A @ B @ X) @ Evs)))))) => (~ ((member_msg @ C @ (analz @ (knows @ spy @ Evs))))))))). % analz_mono_contra(1)
thf(fact_80_event_Odistinct_I3_J, axiom,
    ((![X11 : agent, X12 : agent, X13 : msg, X31 : agent, X322 : msg]: (~ (((says @ X11 @ X12 @ X13) = (notes @ X31 @ X322))))))). % event.distinct(3)
thf(fact_81_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_82_analz__trivial, axiom,
    ((![H : set_msg]: ((![X3 : msg, Y : msg]: (~ ((member_msg @ (mPair @ X3 @ Y) @ H)))) => ((![X3 : msg, K2 : nat]: (~ ((member_msg @ (crypt @ K2 @ X3) @ H)))) => ((analz @ H) = H)))))). % analz_trivial
thf(fact_83_analz__impI, axiom,
    ((![Y5 : msg, Evs : list_event, Q : $o]: (((~ ((member_msg @ Y5 @ (analz @ (knows @ spy @ Evs))))) => Q) => ((~ ((member_msg @ Y5 @ (analz @ (knows @ spy @ Evs))))) => Q))))). % analz_impI
thf(fact_84_Says__S__message__form, axiom,
    ((![S : agent, A : agent, NA : nat, B : agent, K : nat, X : msg, Evs : list_event]: ((member_event @ (says @ S @ A @ (crypt @ (shrK @ A) @ (mPair @ (nonce @ NA) @ (mPair @ (agent2 @ B) @ (mPair @ (key @ K) @ X))))) @ (set_event2 @ Evs)) => ((member_list_event @ Evs @ nS_Sha1061662329shared) => (((~ ((member_nat @ K @ (image_agent_nat @ shrK @ top_top_set_agent)))) & (X = (crypt @ (shrK @ B) @ (mPair @ (key @ K) @ (agent2 @ A))))) | (member_msg @ X @ (analz @ (knows @ spy @ Evs))))))))). % Says_S_message_form
thf(fact_85_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_86_analz__shrK__Decrypt, axiom,
    ((![A : agent, X : msg, H : set_msg]: ((member_msg @ (crypt @ (shrK @ A) @ X) @ (analz @ H)) => ((member_msg @ (key @ (shrK @ A)) @ (analz @ H)) => (member_msg @ X @ (analz @ H))))))). % analz_shrK_Decrypt
thf(fact_87_ns__shared_OOops, axiom,
    ((![Evso : list_event, B : agent, A : agent, K : nat, NB2 : nat, NA : nat, X : msg]: ((member_list_event @ Evso @ nS_Sha1061662329shared) => ((member_event @ (says @ B @ A @ (crypt @ K @ (nonce @ NB2))) @ (set_event2 @ Evso)) => ((member_event @ (says @ server @ A @ (crypt @ (shrK @ A) @ (mPair @ (nonce @ NA) @ (mPair @ (agent2 @ B) @ (mPair @ (key @ K) @ X))))) @ (set_event2 @ Evso)) => (member_list_event @ (cons_event @ (notes @ spy @ (mPair @ (nonce @ NA) @ (mPair @ (nonce @ NB2) @ (key @ K)))) @ Evso) @ nS_Sha1061662329shared))))))). % ns_shared.Oops
thf(fact_88_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_89_ns__sharedp_OOops, axiom,
    ((![Evso : list_event, B : agent, A : agent, K : nat, NB2 : nat, NA : nat, X : msg]: ((nS_Sha1092415543haredp @ Evso) => ((member_event @ (says @ B @ A @ (crypt @ K @ (nonce @ NB2))) @ (set_event2 @ Evso)) => ((member_event @ (says @ server @ A @ (crypt @ (shrK @ A) @ (mPair @ (nonce @ NA) @ (mPair @ (agent2 @ B) @ (mPair @ (key @ K) @ X))))) @ (set_event2 @ Evso)) => (nS_Sha1092415543haredp @ (cons_event @ (notes @ spy @ (mPair @ (nonce @ NA) @ (mPair @ (nonce @ NB2) @ (key @ K)))) @ Evso)))))))). % ns_sharedp.Oops
thf(fact_90_ns__shared_ONS5, axiom,
    ((![Evs5 : list_event, K : nat, B2 : agent, A : agent, NB2 : nat, S : agent, NA : nat, B : agent, X : msg]: ((member_list_event @ Evs5 @ nS_Sha1061662329shared) => ((member_nat @ K @ symKeys) => ((member_event @ (says @ B2 @ A @ (crypt @ K @ (nonce @ NB2))) @ (set_event2 @ Evs5)) => ((member_event @ (says @ S @ A @ (crypt @ (shrK @ A) @ (mPair @ (nonce @ NA) @ (mPair @ (agent2 @ B) @ (mPair @ (key @ K) @ X))))) @ (set_event2 @ Evs5)) => (member_list_event @ (cons_event @ (says @ A @ B @ (crypt @ K @ (mPair @ (nonce @ NB2) @ (nonce @ NB2)))) @ Evs5) @ nS_Sha1061662329shared)))))))). % ns_shared.NS5
thf(fact_91_ns__sharedp_ONS3, axiom,
    ((![Evs3 : list_event, A : agent, S : agent, NA : nat, B : agent, K : nat, X : msg]: ((nS_Sha1092415543haredp @ Evs3) => ((~ ((A = server))) => ((member_event @ (says @ S @ A @ (crypt @ (shrK @ A) @ (mPair @ (nonce @ NA) @ (mPair @ (agent2 @ B) @ (mPair @ (key @ K) @ X))))) @ (set_event2 @ Evs3)) => ((member_event @ (says @ A @ server @ (mPair @ (agent2 @ A) @ (mPair @ (agent2 @ B) @ (nonce @ NA)))) @ (set_event2 @ Evs3)) => (nS_Sha1092415543haredp @ (cons_event @ (says @ A @ B @ X) @ Evs3))))))))). % ns_sharedp.NS3
thf(fact_92_knows__imp__Says__Gets__Notes__initState, axiom,
    ((![X : msg, A : agent, Evs : list_event]: ((member_msg @ X @ (knows @ A @ Evs)) => ((~ ((A = spy))) => (?[B3 : agent]: ((member_event @ (says @ A @ B3 @ 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_93_analz__insert__freshK, axiom,
    ((![Evs : list_event, KAB : nat, K : nat]: ((member_list_event @ Evs @ nS_Sha1061662329shared) => ((~ ((member_nat @ KAB @ (image_agent_nat @ shrK @ top_top_set_agent)))) => ((member_msg @ (key @ K) @ (analz @ (insert_msg @ (key @ KAB) @ (knows @ spy @ Evs)))) = (((K = KAB)) | ((member_msg @ (key @ K) @ (analz @ (knows @ spy @ Evs))))))))))). % analz_insert_freshK
thf(fact_94_knows__Spy__imp__Says__Notes__initState, axiom,
    ((![X : msg, Evs : list_event]: ((member_msg @ X @ (knows @ spy @ Evs)) => (?[A4 : agent, B3 : agent]: ((member_event @ (says @ A4 @ B3 @ X) @ (set_event2 @ Evs)) | ((member_event @ (notes @ A4 @ X) @ (set_event2 @ Evs)) | (member_msg @ X @ (initState @ spy))))))))). % knows_Spy_imp_Says_Notes_initState
thf(fact_95_parts__cut__eq, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ (parts @ H)) => ((parts @ (insert_msg @ X @ H)) = (parts @ H)))))). % parts_cut_eq
thf(fact_96_sym__shrK, axiom,
    ((![X : agent]: (member_nat @ (shrK @ X) @ symKeys)))). % sym_shrK
thf(fact_97_analz__insert__MPair, axiom,
    ((![X : msg, Y5 : msg, H : set_msg]: ((analz @ (insert_msg @ (mPair @ X @ Y5) @ H)) = (insert_msg @ (mPair @ X @ Y5) @ (analz @ (insert_msg @ X @ (insert_msg @ Y5 @ H)))))))). % analz_insert_MPair
thf(fact_98_parts__insert__MPair, axiom,
    ((![X : msg, Y5 : msg, H : set_msg]: ((parts @ (insert_msg @ (mPair @ X @ Y5) @ H)) = (insert_msg @ (mPair @ X @ Y5) @ (parts @ (insert_msg @ X @ (insert_msg @ Y5 @ H)))))))). % parts_insert_MPair
thf(fact_99_parts__insert__Key, axiom,
    ((![K : nat, H : set_msg]: ((parts @ (insert_msg @ (key @ K) @ H)) = (insert_msg @ (key @ K) @ (parts @ H)))))). % parts_insert_Key
thf(fact_100_parts__insert__Crypt, axiom,
    ((![K : nat, X : msg, H : set_msg]: ((parts @ (insert_msg @ (crypt @ K @ X) @ H)) = (insert_msg @ (crypt @ K @ X) @ (parts @ (insert_msg @ X @ H))))))). % parts_insert_Crypt
thf(fact_101_analz__insert__Agent, axiom,
    ((![Agt : agent, H : set_msg]: ((analz @ (insert_msg @ (agent2 @ Agt) @ H)) = (insert_msg @ (agent2 @ Agt) @ (analz @ H)))))). % analz_insert_Agent
thf(fact_102_analz__insert__Nonce, axiom,
    ((![N : nat, H : set_msg]: ((analz @ (insert_msg @ (nonce @ N) @ H)) = (insert_msg @ (nonce @ N) @ (analz @ H)))))). % analz_insert_Nonce
thf(fact_103_parts__insert__Agent, axiom,
    ((![Agt : agent, H : set_msg]: ((parts @ (insert_msg @ (agent2 @ Agt) @ H)) = (insert_msg @ (agent2 @ Agt) @ (parts @ H)))))). % parts_insert_Agent
thf(fact_104_parts__insert__Nonce, axiom,
    ((![N : nat, H : set_msg]: ((parts @ (insert_msg @ (nonce @ N) @ H)) = (insert_msg @ (nonce @ N) @ (parts @ H)))))). % parts_insert_Nonce
thf(fact_105_shrK__in__initState, axiom,
    ((![A : agent]: (member_msg @ (key @ (shrK @ A)) @ (initState @ A))))). % shrK_in_initState
thf(fact_106_knows__Spy__Says, axiom,
    ((![A : agent, B : agent, X : msg, Evs : list_event]: ((knows @ spy @ (cons_event @ (says @ A @ B @ X) @ Evs)) = (insert_msg @ X @ (knows @ spy @ Evs)))))). % knows_Spy_Says
thf(fact_107_knows__Spy__Notes, axiom,
    ((![A : agent, X : msg, Evs : list_event]: (((member_agent @ A @ bad) => ((knows @ spy @ (cons_event @ (notes @ A @ X) @ Evs)) = (insert_msg @ X @ (knows @ spy @ Evs)))) & ((~ ((member_agent @ A @ bad))) => ((knows @ spy @ (cons_event @ (notes @ A @ X) @ Evs)) = (knows @ spy @ Evs))))))). % knows_Spy_Notes
thf(fact_108_symKeys__neq__imp__neq, axiom,
    ((![K : nat, K4 : nat]: ((~ (((member_nat @ K @ symKeys) = (member_nat @ K4 @ symKeys)))) => (~ ((K = K4))))))). % symKeys_neq_imp_neq
thf(fact_109_analz__insert__eq__I, axiom,
    ((![X : msg, H : set_msg]: ((![X7 : msg]: ((member_msg @ X7 @ (analz @ (insert_msg @ X @ H))) => (member_msg @ X7 @ (insert_msg @ X @ (analz @ H))))) => ((analz @ (insert_msg @ X @ H)) = (insert_msg @ X @ (analz @ H))))))). % analz_insert_eq_I
thf(fact_110_analz__insert__cong, axiom,
    ((![H : set_msg, H2 : set_msg, X : msg]: (((analz @ H) = (analz @ H2)) => ((analz @ (insert_msg @ X @ H)) = (analz @ (insert_msg @ X @ H2))))))). % analz_insert_cong
thf(fact_111_analz__insert__eq, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ (analz @ H)) => ((analz @ (insert_msg @ X @ H)) = (analz @ H)))))). % analz_insert_eq
thf(fact_112_analz__insertI, axiom,
    ((![C : msg, G : set_msg, A3 : msg]: ((member_msg @ C @ (analz @ G)) => (member_msg @ C @ (analz @ (insert_msg @ A3 @ G))))))). % analz_insertI
thf(fact_113_analz__cut, axiom,
    ((![Y5 : msg, X : msg, H : set_msg]: ((member_msg @ Y5 @ (analz @ (insert_msg @ X @ H))) => ((member_msg @ X @ (analz @ H)) => (member_msg @ Y5 @ (analz @ H))))))). % analz_cut
thf(fact_114_parts__insert__eq__I, axiom,
    ((![X : msg, H : set_msg]: ((![X7 : msg]: ((member_msg @ X7 @ (parts @ (insert_msg @ X @ H))) => (member_msg @ X7 @ (insert_msg @ X @ (parts @ H))))) => ((parts @ (insert_msg @ X @ H)) = (insert_msg @ X @ (parts @ H))))))). % parts_insert_eq_I
thf(fact_115_parts__insertI, axiom,
    ((![C : msg, G : set_msg, A3 : msg]: ((member_msg @ C @ (parts @ G)) => (member_msg @ C @ (parts @ (insert_msg @ A3 @ G))))))). % parts_insertI
thf(fact_116_ns__sharedp__ns__shared__eq, axiom,
    ((nS_Sha1092415543haredp = (^[X6 : list_event]: (member_list_event @ X6 @ nS_Sha1061662329shared))))). % ns_sharedp_ns_shared_eq
thf(fact_117_pushKeys_I5_J, axiom,
    ((![K : nat, X : msg, Y5 : msg, A : set_msg]: ((insert_msg @ (key @ K) @ (insert_msg @ (mPair @ X @ Y5) @ A)) = (insert_msg @ (mPair @ X @ Y5) @ (insert_msg @ (key @ K) @ A)))))). % pushKeys(5)
thf(fact_118_pushCrypts_I6_J, axiom,
    ((![X : nat, K : msg, X2 : msg, Y5 : msg, A : set_msg]: ((insert_msg @ (crypt @ X @ K) @ (insert_msg @ (mPair @ X2 @ Y5) @ A)) = (insert_msg @ (mPair @ X2 @ Y5) @ (insert_msg @ (crypt @ X @ K) @ A)))))). % pushCrypts(6)
thf(fact_119_pushKeys_I6_J, axiom,
    ((![K : nat, X : nat, K4 : msg, A : set_msg]: ((insert_msg @ (key @ K) @ (insert_msg @ (crypt @ X @ K4) @ A)) = (insert_msg @ (crypt @ X @ K4) @ (insert_msg @ (key @ K) @ A)))))). % pushKeys(6)
thf(fact_120_pushKeys_I1_J, axiom,
    ((![K : nat, C2 : agent, A : set_msg]: ((insert_msg @ (key @ K) @ (insert_msg @ (agent2 @ C2) @ A)) = (insert_msg @ (agent2 @ C2) @ (insert_msg @ (key @ K) @ A)))))). % pushKeys(1)
thf(fact_121_pushKeys_I2_J, axiom,
    ((![K : nat, N : nat, A : set_msg]: ((insert_msg @ (key @ K) @ (insert_msg @ (nonce @ N) @ A)) = (insert_msg @ (nonce @ N) @ (insert_msg @ (key @ K) @ A)))))). % pushKeys(2)
thf(fact_122_pushCrypts_I1_J, axiom,
    ((![X : nat, K : msg, C2 : agent, A : set_msg]: ((insert_msg @ (crypt @ X @ K) @ (insert_msg @ (agent2 @ C2) @ A)) = (insert_msg @ (agent2 @ C2) @ (insert_msg @ (crypt @ X @ K) @ A)))))). % pushCrypts(1)
thf(fact_123_pushCrypts_I3_J, axiom,
    ((![X : nat, K : msg, N : nat, A : set_msg]: ((insert_msg @ (crypt @ X @ K) @ (insert_msg @ (nonce @ N) @ A)) = (insert_msg @ (nonce @ N) @ (insert_msg @ (crypt @ X @ K) @ A)))))). % pushCrypts(3)
thf(fact_124_Crypt__notin__initState, axiom,
    ((![K : nat, X : msg, B : agent]: (~ ((member_msg @ (crypt @ K @ X) @ (parts @ (initState @ B)))))))). % Crypt_notin_initState
thf(fact_125_Nonce__notin__initState, axiom,
    ((![N : nat, B : agent]: (~ ((member_msg @ (nonce @ N) @ (parts @ (initState @ B)))))))). % Nonce_notin_initState
thf(fact_126_analz__symKeys__Decrypt, axiom,
    ((![K : nat, X : msg, H : set_msg]: ((member_msg @ (crypt @ K @ X) @ (analz @ H)) => ((member_nat @ K @ symKeys) => ((member_msg @ (key @ K) @ (analz @ H)) => (member_msg @ X @ (analz @ H)))))))). % analz_symKeys_Decrypt
thf(fact_127_ns__sharedp_ONS5, axiom,
    ((![Evs5 : list_event, K : nat, B2 : agent, A : agent, NB2 : nat, S : agent, NA : nat, B : agent, X : msg]: ((nS_Sha1092415543haredp @ Evs5) => ((member_nat @ K @ symKeys) => ((member_event @ (says @ B2 @ A @ (crypt @ K @ (nonce @ NB2))) @ (set_event2 @ Evs5)) => ((member_event @ (says @ S @ A @ (crypt @ (shrK @ A) @ (mPair @ (nonce @ NA) @ (mPair @ (agent2 @ B) @ (mPair @ (key @ K) @ X))))) @ (set_event2 @ Evs5)) => (nS_Sha1092415543haredp @ (cons_event @ (says @ A @ B @ (crypt @ K @ (mPair @ (nonce @ NB2) @ (nonce @ NB2)))) @ Evs5))))))))). % ns_sharedp.NS5
thf(fact_128_list_Osimps_I15_J, axiom,
    ((![X21 : msg, X22 : list_msg]: ((set_msg2 @ (cons_msg @ X21 @ X22)) = (insert_msg @ X21 @ (set_msg2 @ X22)))))). % list.simps(15)
thf(fact_129_list_Osimps_I15_J, axiom,
    ((![X21 : event, X22 : list_event]: ((set_event2 @ (cons_event @ X21 @ X22)) = (insert_event @ X21 @ (set_event2 @ X22)))))). % list.simps(15)
thf(fact_130_insert__image, axiom,
    ((![X5 : msg, A : set_msg, F : msg > msg]: ((member_msg @ X5 @ A) => ((insert_msg @ (F @ X5) @ (image_msg_msg @ F @ A)) = (image_msg_msg @ F @ A)))))). % insert_image
thf(fact_131_insert__image, axiom,
    ((![X5 : agent, A : set_agent, F : agent > nat]: ((member_agent @ X5 @ A) => ((insert_nat @ (F @ X5) @ (image_agent_nat @ F @ A)) = (image_agent_nat @ F @ A)))))). % insert_image
thf(fact_132_insert__image, axiom,
    ((![X5 : agent, A : set_agent, F : agent > msg]: ((member_agent @ X5 @ A) => ((insert_msg @ (F @ X5) @ (image_agent_msg @ F @ A)) = (image_agent_msg @ F @ A)))))). % insert_image
thf(fact_133_insert__image, axiom,
    ((![X5 : list_event, A : set_list_event, F : list_event > msg]: ((member_list_event @ X5 @ A) => ((insert_msg @ (F @ X5) @ (image_list_event_msg @ F @ A)) = (image_list_event_msg @ F @ A)))))). % insert_image
thf(fact_134_insert__image, axiom,
    ((![X5 : event, A : set_event, F : event > msg]: ((member_event @ X5 @ A) => ((insert_msg @ (F @ X5) @ (image_event_msg @ F @ A)) = (image_event_msg @ F @ A)))))). % insert_image
thf(fact_135_insert__image, axiom,
    ((![X5 : nat, A : set_nat, F : nat > msg]: ((member_nat @ X5 @ A) => ((insert_msg @ (F @ X5) @ (image_nat_msg @ F @ A)) = (image_nat_msg @ F @ A)))))). % insert_image
thf(fact_136_image__insert, axiom,
    ((![F : agent > nat, A3 : agent, B : set_agent]: ((image_agent_nat @ F @ (insert_agent @ A3 @ B)) = (insert_nat @ (F @ A3) @ (image_agent_nat @ F @ B)))))). % image_insert
thf(fact_137_image__insert, axiom,
    ((![F : nat > msg, A3 : nat, B : set_nat]: ((image_nat_msg @ F @ (insert_nat @ A3 @ B)) = (insert_msg @ (F @ A3) @ (image_nat_msg @ F @ B)))))). % image_insert
thf(fact_138_image__insert, axiom,
    ((![F : msg > msg, A3 : msg, B : set_msg]: ((image_msg_msg @ F @ (insert_msg @ A3 @ B)) = (insert_msg @ (F @ A3) @ (image_msg_msg @ F @ B)))))). % image_insert
thf(fact_139_image__eqI, axiom,
    ((![B4 : msg, F : msg > msg, X5 : msg, A : set_msg]: ((B4 = (F @ X5)) => ((member_msg @ X5 @ A) => (member_msg @ B4 @ (image_msg_msg @ F @ A))))))). % image_eqI
thf(fact_140_image__eqI, axiom,
    ((![B4 : agent, F : msg > agent, X5 : msg, A : set_msg]: ((B4 = (F @ X5)) => ((member_msg @ X5 @ A) => (member_agent @ B4 @ (image_msg_agent @ F @ A))))))). % image_eqI
thf(fact_141_image__eqI, axiom,
    ((![B4 : event, F : msg > event, X5 : msg, A : set_msg]: ((B4 = (F @ X5)) => ((member_msg @ X5 @ A) => (member_event @ B4 @ (image_msg_event @ F @ A))))))). % image_eqI
thf(fact_142_image__eqI, axiom,
    ((![B4 : nat, F : msg > nat, X5 : msg, A : set_msg]: ((B4 = (F @ X5)) => ((member_msg @ X5 @ A) => (member_nat @ B4 @ (image_msg_nat @ F @ A))))))). % image_eqI
thf(fact_143_image__eqI, axiom,
    ((![B4 : msg, F : agent > msg, X5 : agent, A : set_agent]: ((B4 = (F @ X5)) => ((member_agent @ X5 @ A) => (member_msg @ B4 @ (image_agent_msg @ F @ A))))))). % image_eqI
thf(fact_144_image__eqI, axiom,
    ((![B4 : agent, F : agent > agent, X5 : agent, A : set_agent]: ((B4 = (F @ X5)) => ((member_agent @ X5 @ A) => (member_agent @ B4 @ (image_agent_agent @ F @ A))))))). % image_eqI
thf(fact_145_image__eqI, axiom,
    ((![B4 : event, F : agent > event, X5 : agent, A : set_agent]: ((B4 = (F @ X5)) => ((member_agent @ X5 @ A) => (member_event @ B4 @ (image_agent_event @ F @ A))))))). % image_eqI
thf(fact_146_image__eqI, axiom,
    ((![B4 : nat, F : agent > nat, X5 : agent, A : set_agent]: ((B4 = (F @ X5)) => ((member_agent @ X5 @ A) => (member_nat @ B4 @ (image_agent_nat @ F @ A))))))). % image_eqI
thf(fact_147_image__eqI, axiom,
    ((![B4 : msg, F : event > msg, X5 : event, A : set_event]: ((B4 = (F @ X5)) => ((member_event @ X5 @ A) => (member_msg @ B4 @ (image_event_msg @ F @ A))))))). % image_eqI
thf(fact_148_image__eqI, axiom,
    ((![B4 : agent, F : event > agent, X5 : event, A : set_event]: ((B4 = (F @ X5)) => ((member_event @ X5 @ A) => (member_agent @ B4 @ (image_event_agent @ F @ A))))))). % image_eqI
thf(fact_149_list_Oinject, axiom,
    ((![X21 : event, X22 : list_event, Y21 : event, Y22 : list_event]: (((cons_event @ X21 @ X22) = (cons_event @ Y21 @ Y22)) = (((X21 = Y21)) & ((X22 = Y22))))))). % list.inject
thf(fact_150_insert__absorb2, axiom,
    ((![X5 : msg, A : set_msg]: ((insert_msg @ X5 @ (insert_msg @ X5 @ A)) = (insert_msg @ X5 @ A))))). % insert_absorb2
thf(fact_151_insert__iff, axiom,
    ((![A3 : msg, B4 : msg, A : set_msg]: ((member_msg @ A3 @ (insert_msg @ B4 @ A)) = (((A3 = B4)) | ((member_msg @ A3 @ A))))))). % insert_iff
thf(fact_152_insert__iff, axiom,
    ((![A3 : agent, B4 : agent, A : set_agent]: ((member_agent @ A3 @ (insert_agent @ B4 @ A)) = (((A3 = B4)) | ((member_agent @ A3 @ A))))))). % insert_iff
thf(fact_153_insert__iff, axiom,
    ((![A3 : list_event, B4 : list_event, A : set_list_event]: ((member_list_event @ A3 @ (insert_list_event @ B4 @ A)) = (((A3 = B4)) | ((member_list_event @ A3 @ A))))))). % insert_iff
thf(fact_154_insert__iff, axiom,
    ((![A3 : event, B4 : event, A : set_event]: ((member_event @ A3 @ (insert_event @ B4 @ A)) = (((A3 = B4)) | ((member_event @ A3 @ A))))))). % insert_iff
thf(fact_155_insert__iff, axiom,
    ((![A3 : nat, B4 : nat, A : set_nat]: ((member_nat @ A3 @ (insert_nat @ B4 @ A)) = (((A3 = B4)) | ((member_nat @ A3 @ A))))))). % insert_iff
thf(fact_156_insertCI, axiom,
    ((![A3 : msg, B : set_msg, B4 : msg]: (((~ ((member_msg @ A3 @ B))) => (A3 = B4)) => (member_msg @ A3 @ (insert_msg @ B4 @ B)))))). % insertCI
thf(fact_157_insertCI, axiom,
    ((![A3 : agent, B : set_agent, B4 : agent]: (((~ ((member_agent @ A3 @ B))) => (A3 = B4)) => (member_agent @ A3 @ (insert_agent @ B4 @ B)))))). % insertCI
thf(fact_158_insertCI, axiom,
    ((![A3 : list_event, B : set_list_event, B4 : list_event]: (((~ ((member_list_event @ A3 @ B))) => (A3 = B4)) => (member_list_event @ A3 @ (insert_list_event @ B4 @ B)))))). % insertCI
thf(fact_159_insertCI, axiom,
    ((![A3 : event, B : set_event, B4 : event]: (((~ ((member_event @ A3 @ B))) => (A3 = B4)) => (member_event @ A3 @ (insert_event @ B4 @ B)))))). % insertCI
thf(fact_160_insertCI, axiom,
    ((![A3 : nat, B : set_nat, B4 : nat]: (((~ ((member_nat @ A3 @ B))) => (A3 = B4)) => (member_nat @ A3 @ (insert_nat @ B4 @ B)))))). % insertCI
thf(fact_161_UNIV__I, axiom,
    ((![X5 : msg]: (member_msg @ X5 @ top_top_set_msg)))). % UNIV_I
thf(fact_162_UNIV__I, axiom,
    ((![X5 : list_event]: (member_list_event @ X5 @ top_to1178833912_event)))). % UNIV_I
thf(fact_163_UNIV__I, axiom,
    ((![X5 : event]: (member_event @ X5 @ top_top_set_event)))). % UNIV_I
thf(fact_164_UNIV__I, axiom,
    ((![X5 : nat]: (member_nat @ X5 @ top_top_set_nat)))). % UNIV_I
thf(fact_165_UNIV__I, axiom,
    ((![X5 : agent]: (member_agent @ X5 @ top_top_set_agent)))). % UNIV_I
thf(fact_166_Key__image__eq, axiom,
    ((![X5 : nat, A : set_nat]: ((member_msg @ (key @ X5) @ (image_nat_msg @ key @ A)) = (member_nat @ X5 @ A))))). % Key_image_eq
thf(fact_167_analz__image__Key, axiom,
    ((![N : set_nat]: ((analz @ (image_nat_msg @ key @ N)) = (image_nat_msg @ key @ N))))). % analz_image_Key
thf(fact_168_parts__image__Key, axiom,
    ((![N : set_nat]: ((parts @ (image_nat_msg @ key @ N)) = (image_nat_msg @ key @ N))))). % parts_image_Key
thf(fact_169_Crypt__notin__image__Key, axiom,
    ((![K : nat, X : msg, A : set_nat]: (~ ((member_msg @ (crypt @ K @ X) @ (image_nat_msg @ key @ A))))))). % Crypt_notin_image_Key
thf(fact_170_Nonce__Key__image__eq, axiom,
    ((![X5 : nat, A : set_nat]: (~ ((member_msg @ (nonce @ X5) @ (image_nat_msg @ key @ A))))))). % Nonce_Key_image_eq
thf(fact_171_rev__image__eqI, axiom,
    ((![X5 : msg, A : set_msg, B4 : msg, F : msg > msg]: ((member_msg @ X5 @ A) => ((B4 = (F @ X5)) => (member_msg @ B4 @ (image_msg_msg @ F @ A))))))). % rev_image_eqI
thf(fact_172_rev__image__eqI, axiom,
    ((![X5 : msg, A : set_msg, B4 : agent, F : msg > agent]: ((member_msg @ X5 @ A) => ((B4 = (F @ X5)) => (member_agent @ B4 @ (image_msg_agent @ F @ A))))))). % rev_image_eqI
thf(fact_173_rev__image__eqI, axiom,
    ((![X5 : msg, A : set_msg, B4 : event, F : msg > event]: ((member_msg @ X5 @ A) => ((B4 = (F @ X5)) => (member_event @ B4 @ (image_msg_event @ F @ A))))))). % rev_image_eqI
thf(fact_174_rev__image__eqI, axiom,
    ((![X5 : msg, A : set_msg, B4 : nat, F : msg > nat]: ((member_msg @ X5 @ A) => ((B4 = (F @ X5)) => (member_nat @ B4 @ (image_msg_nat @ F @ A))))))). % rev_image_eqI
thf(fact_175_rev__image__eqI, axiom,
    ((![X5 : agent, A : set_agent, B4 : msg, F : agent > msg]: ((member_agent @ X5 @ A) => ((B4 = (F @ X5)) => (member_msg @ B4 @ (image_agent_msg @ F @ A))))))). % rev_image_eqI
thf(fact_176_rev__image__eqI, axiom,
    ((![X5 : agent, A : set_agent, B4 : agent, F : agent > agent]: ((member_agent @ X5 @ A) => ((B4 = (F @ X5)) => (member_agent @ B4 @ (image_agent_agent @ F @ A))))))). % rev_image_eqI
thf(fact_177_rev__image__eqI, axiom,
    ((![X5 : agent, A : set_agent, B4 : event, F : agent > event]: ((member_agent @ X5 @ A) => ((B4 = (F @ X5)) => (member_event @ B4 @ (image_agent_event @ F @ A))))))). % rev_image_eqI
thf(fact_178_rev__image__eqI, axiom,
    ((![X5 : agent, A : set_agent, B4 : nat, F : agent > nat]: ((member_agent @ X5 @ A) => ((B4 = (F @ X5)) => (member_nat @ B4 @ (image_agent_nat @ F @ A))))))). % rev_image_eqI
thf(fact_179_rev__image__eqI, axiom,
    ((![X5 : event, A : set_event, B4 : msg, F : event > msg]: ((member_event @ X5 @ A) => ((B4 = (F @ X5)) => (member_msg @ B4 @ (image_event_msg @ F @ A))))))). % rev_image_eqI
thf(fact_180_rev__image__eqI, axiom,
    ((![X5 : event, A : set_event, B4 : agent, F : event > agent]: ((member_event @ X5 @ A) => ((B4 = (F @ X5)) => (member_agent @ B4 @ (image_event_agent @ F @ A))))))). % rev_image_eqI
thf(fact_181_ball__imageD, axiom,
    ((![F : agent > nat, A : set_agent, P : nat > $o]: ((![X7 : nat]: ((member_nat @ X7 @ (image_agent_nat @ F @ A)) => (P @ X7))) => (![X8 : agent]: ((member_agent @ X8 @ A) => (P @ (F @ X8)))))))). % ball_imageD
thf(fact_182_ball__imageD, axiom,
    ((![F : nat > msg, A : set_nat, P : msg > $o]: ((![X7 : msg]: ((member_msg @ X7 @ (image_nat_msg @ F @ A)) => (P @ X7))) => (![X8 : nat]: ((member_nat @ X8 @ A) => (P @ (F @ X8)))))))). % ball_imageD
thf(fact_183_image__cong, axiom,
    ((![M : set_agent, N : set_agent, F : agent > nat, G2 : agent > nat]: ((M = N) => ((![X7 : agent]: ((member_agent @ X7 @ N) => ((F @ X7) = (G2 @ X7)))) => ((image_agent_nat @ F @ M) = (image_agent_nat @ G2 @ N))))))). % image_cong
thf(fact_184_image__cong, axiom,
    ((![M : set_nat, N : set_nat, F : nat > msg, G2 : nat > msg]: ((M = N) => ((![X7 : nat]: ((member_nat @ X7 @ N) => ((F @ X7) = (G2 @ X7)))) => ((image_nat_msg @ F @ M) = (image_nat_msg @ G2 @ N))))))). % image_cong
thf(fact_185_bex__imageD, axiom,
    ((![F : agent > nat, A : set_agent, P : nat > $o]: ((?[X8 : nat]: ((member_nat @ X8 @ (image_agent_nat @ F @ A)) & (P @ X8))) => (?[X7 : agent]: ((member_agent @ X7 @ A) & (P @ (F @ X7)))))))). % bex_imageD
thf(fact_186_bex__imageD, axiom,
    ((![F : nat > msg, A : set_nat, P : msg > $o]: ((?[X8 : msg]: ((member_msg @ X8 @ (image_nat_msg @ F @ A)) & (P @ X8))) => (?[X7 : nat]: ((member_nat @ X7 @ A) & (P @ (F @ X7)))))))). % bex_imageD
thf(fact_187_image__iff, axiom,
    ((![Z : msg, F : nat > msg, A : set_nat]: ((member_msg @ Z @ (image_nat_msg @ F @ A)) = (?[X6 : nat]: (((member_nat @ X6 @ A)) & ((Z = (F @ X6))))))))). % image_iff
thf(fact_188_image__iff, axiom,
    ((![Z : nat, F : agent > nat, A : set_agent]: ((member_nat @ Z @ (image_agent_nat @ F @ A)) = (?[X6 : agent]: (((member_agent @ X6 @ A)) & ((Z = (F @ X6))))))))). % image_iff
thf(fact_189_imageI, axiom,
    ((![X5 : msg, A : set_msg, F : msg > msg]: ((member_msg @ X5 @ A) => (member_msg @ (F @ X5) @ (image_msg_msg @ F @ A)))))). % imageI
thf(fact_190_imageI, axiom,
    ((![X5 : msg, A : set_msg, F : msg > agent]: ((member_msg @ X5 @ A) => (member_agent @ (F @ X5) @ (image_msg_agent @ F @ A)))))). % imageI
thf(fact_191_imageI, axiom,
    ((![X5 : msg, A : set_msg, F : msg > event]: ((member_msg @ X5 @ A) => (member_event @ (F @ X5) @ (image_msg_event @ F @ A)))))). % imageI
thf(fact_192_imageI, axiom,
    ((![X5 : msg, A : set_msg, F : msg > nat]: ((member_msg @ X5 @ A) => (member_nat @ (F @ X5) @ (image_msg_nat @ F @ A)))))). % imageI
thf(fact_193_imageI, axiom,
    ((![X5 : agent, A : set_agent, F : agent > msg]: ((member_agent @ X5 @ A) => (member_msg @ (F @ X5) @ (image_agent_msg @ F @ A)))))). % imageI
thf(fact_194_imageI, axiom,
    ((![X5 : agent, A : set_agent, F : agent > agent]: ((member_agent @ X5 @ A) => (member_agent @ (F @ X5) @ (image_agent_agent @ F @ A)))))). % imageI
thf(fact_195_imageI, axiom,
    ((![X5 : agent, A : set_agent, F : agent > event]: ((member_agent @ X5 @ A) => (member_event @ (F @ X5) @ (image_agent_event @ F @ A)))))). % imageI
thf(fact_196_imageI, axiom,
    ((![X5 : agent, A : set_agent, F : agent > nat]: ((member_agent @ X5 @ A) => (member_nat @ (F @ X5) @ (image_agent_nat @ F @ A)))))). % imageI
thf(fact_197_imageI, axiom,
    ((![X5 : event, A : set_event, F : event > msg]: ((member_event @ X5 @ A) => (member_msg @ (F @ X5) @ (image_event_msg @ F @ A)))))). % imageI
thf(fact_198_imageI, axiom,
    ((![X5 : event, A : set_event, F : event > agent]: ((member_event @ X5 @ A) => (member_agent @ (F @ X5) @ (image_event_agent @ F @ A)))))). % imageI
thf(fact_199_not__Cons__self2, axiom,
    ((![X5 : event, Xs : list_event]: (~ (((cons_event @ X5 @ Xs) = Xs)))))). % not_Cons_self2
thf(fact_200_mk__disjoint__insert, axiom,
    ((![A3 : msg, A : set_msg]: ((member_msg @ A3 @ A) => (?[B3 : set_msg]: ((A = (insert_msg @ A3 @ B3)) & (~ ((member_msg @ A3 @ B3))))))))). % mk_disjoint_insert
thf(fact_201_mk__disjoint__insert, axiom,
    ((![A3 : agent, A : set_agent]: ((member_agent @ A3 @ A) => (?[B3 : set_agent]: ((A = (insert_agent @ A3 @ B3)) & (~ ((member_agent @ A3 @ B3))))))))). % mk_disjoint_insert
thf(fact_202_mk__disjoint__insert, axiom,
    ((![A3 : list_event, A : set_list_event]: ((member_list_event @ A3 @ A) => (?[B3 : set_list_event]: ((A = (insert_list_event @ A3 @ B3)) & (~ ((member_list_event @ A3 @ B3))))))))). % mk_disjoint_insert
thf(fact_203_mk__disjoint__insert, axiom,
    ((![A3 : event, A : set_event]: ((member_event @ A3 @ A) => (?[B3 : set_event]: ((A = (insert_event @ A3 @ B3)) & (~ ((member_event @ A3 @ B3))))))))). % mk_disjoint_insert
thf(fact_204_mk__disjoint__insert, axiom,
    ((![A3 : nat, A : set_nat]: ((member_nat @ A3 @ A) => (?[B3 : set_nat]: ((A = (insert_nat @ A3 @ B3)) & (~ ((member_nat @ A3 @ B3))))))))). % mk_disjoint_insert
thf(fact_205_insert__commute, axiom,
    ((![X5 : msg, Y3 : msg, A : set_msg]: ((insert_msg @ X5 @ (insert_msg @ Y3 @ A)) = (insert_msg @ Y3 @ (insert_msg @ X5 @ A)))))). % insert_commute
thf(fact_206_insert__eq__iff, axiom,
    ((![A3 : msg, A : set_msg, B4 : msg, B : set_msg]: ((~ ((member_msg @ A3 @ A))) => ((~ ((member_msg @ B4 @ B))) => (((insert_msg @ A3 @ A) = (insert_msg @ B4 @ B)) = (((((A3 = B4)) => ((A = B)))) & ((((~ ((A3 = B4)))) => ((?[C3 : set_msg]: (((A = (insert_msg @ B4 @ C3))) & ((((~ ((member_msg @ B4 @ C3)))) & ((((B = (insert_msg @ A3 @ C3))) & ((~ ((member_msg @ A3 @ C3)))))))))))))))))))). % insert_eq_iff
thf(fact_207_insert__eq__iff, axiom,
    ((![A3 : agent, A : set_agent, B4 : agent, B : set_agent]: ((~ ((member_agent @ A3 @ A))) => ((~ ((member_agent @ B4 @ B))) => (((insert_agent @ A3 @ A) = (insert_agent @ B4 @ B)) = (((((A3 = B4)) => ((A = B)))) & ((((~ ((A3 = B4)))) => ((?[C3 : set_agent]: (((A = (insert_agent @ B4 @ C3))) & ((((~ ((member_agent @ B4 @ C3)))) & ((((B = (insert_agent @ A3 @ C3))) & ((~ ((member_agent @ A3 @ C3)))))))))))))))))))). % insert_eq_iff
thf(fact_208_insert__eq__iff, axiom,
    ((![A3 : list_event, A : set_list_event, B4 : list_event, B : set_list_event]: ((~ ((member_list_event @ A3 @ A))) => ((~ ((member_list_event @ B4 @ B))) => (((insert_list_event @ A3 @ A) = (insert_list_event @ B4 @ B)) = (((((A3 = B4)) => ((A = B)))) & ((((~ ((A3 = B4)))) => ((?[C3 : set_list_event]: (((A = (insert_list_event @ B4 @ C3))) & ((((~ ((member_list_event @ B4 @ C3)))) & ((((B = (insert_list_event @ A3 @ C3))) & ((~ ((member_list_event @ A3 @ C3)))))))))))))))))))). % insert_eq_iff
thf(fact_209_insert__eq__iff, axiom,
    ((![A3 : event, A : set_event, B4 : event, B : set_event]: ((~ ((member_event @ A3 @ A))) => ((~ ((member_event @ B4 @ B))) => (((insert_event @ A3 @ A) = (insert_event @ B4 @ B)) = (((((A3 = B4)) => ((A = B)))) & ((((~ ((A3 = B4)))) => ((?[C3 : set_event]: (((A = (insert_event @ B4 @ C3))) & ((((~ ((member_event @ B4 @ C3)))) & ((((B = (insert_event @ A3 @ C3))) & ((~ ((member_event @ A3 @ C3)))))))))))))))))))). % insert_eq_iff
thf(fact_210_insert__eq__iff, axiom,
    ((![A3 : nat, A : set_nat, B4 : nat, B : set_nat]: ((~ ((member_nat @ A3 @ A))) => ((~ ((member_nat @ B4 @ B))) => (((insert_nat @ A3 @ A) = (insert_nat @ B4 @ B)) = (((((A3 = B4)) => ((A = B)))) & ((((~ ((A3 = B4)))) => ((?[C3 : set_nat]: (((A = (insert_nat @ B4 @ C3))) & ((((~ ((member_nat @ B4 @ C3)))) & ((((B = (insert_nat @ A3 @ C3))) & ((~ ((member_nat @ A3 @ C3)))))))))))))))))))). % insert_eq_iff
thf(fact_211_insert__absorb, axiom,
    ((![A3 : msg, A : set_msg]: ((member_msg @ A3 @ A) => ((insert_msg @ A3 @ A) = A))))). % insert_absorb
thf(fact_212_insert__absorb, axiom,
    ((![A3 : agent, A : set_agent]: ((member_agent @ A3 @ A) => ((insert_agent @ A3 @ A) = A))))). % insert_absorb
thf(fact_213_insert__absorb, axiom,
    ((![A3 : list_event, A : set_list_event]: ((member_list_event @ A3 @ A) => ((insert_list_event @ A3 @ A) = A))))). % insert_absorb
thf(fact_214_insert__absorb, axiom,
    ((![A3 : event, A : set_event]: ((member_event @ A3 @ A) => ((insert_event @ A3 @ A) = A))))). % insert_absorb
thf(fact_215_insert__absorb, axiom,
    ((![A3 : nat, A : set_nat]: ((member_nat @ A3 @ A) => ((insert_nat @ A3 @ A) = A))))). % insert_absorb
thf(fact_216_insert__ident, axiom,
    ((![X5 : msg, A : set_msg, B : set_msg]: ((~ ((member_msg @ X5 @ A))) => ((~ ((member_msg @ X5 @ B))) => (((insert_msg @ X5 @ A) = (insert_msg @ X5 @ B)) = (A = B))))))). % insert_ident
thf(fact_217_insert__ident, axiom,
    ((![X5 : agent, A : set_agent, B : set_agent]: ((~ ((member_agent @ X5 @ A))) => ((~ ((member_agent @ X5 @ B))) => (((insert_agent @ X5 @ A) = (insert_agent @ X5 @ B)) = (A = B))))))). % insert_ident
thf(fact_218_insert__ident, axiom,
    ((![X5 : list_event, A : set_list_event, B : set_list_event]: ((~ ((member_list_event @ X5 @ A))) => ((~ ((member_list_event @ X5 @ B))) => (((insert_list_event @ X5 @ A) = (insert_list_event @ X5 @ B)) = (A = B))))))). % insert_ident
thf(fact_219_insert__ident, axiom,
    ((![X5 : event, A : set_event, B : set_event]: ((~ ((member_event @ X5 @ A))) => ((~ ((member_event @ X5 @ B))) => (((insert_event @ X5 @ A) = (insert_event @ X5 @ B)) = (A = B))))))). % insert_ident
thf(fact_220_insert__ident, axiom,
    ((![X5 : nat, A : set_nat, B : set_nat]: ((~ ((member_nat @ X5 @ A))) => ((~ ((member_nat @ X5 @ B))) => (((insert_nat @ X5 @ A) = (insert_nat @ X5 @ B)) = (A = B))))))). % insert_ident
thf(fact_221_Set_Oset__insert, axiom,
    ((![X5 : msg, A : set_msg]: ((member_msg @ X5 @ A) => (~ ((![B3 : set_msg]: ((A = (insert_msg @ X5 @ B3)) => (member_msg @ X5 @ B3))))))))). % Set.set_insert
thf(fact_222_Set_Oset__insert, axiom,
    ((![X5 : agent, A : set_agent]: ((member_agent @ X5 @ A) => (~ ((![B3 : set_agent]: ((A = (insert_agent @ X5 @ B3)) => (member_agent @ X5 @ B3))))))))). % Set.set_insert
thf(fact_223_Set_Oset__insert, axiom,
    ((![X5 : list_event, A : set_list_event]: ((member_list_event @ X5 @ A) => (~ ((![B3 : set_list_event]: ((A = (insert_list_event @ X5 @ B3)) => (member_list_event @ X5 @ B3))))))))). % Set.set_insert
thf(fact_224_Set_Oset__insert, axiom,
    ((![X5 : event, A : set_event]: ((member_event @ X5 @ A) => (~ ((![B3 : set_event]: ((A = (insert_event @ X5 @ B3)) => (member_event @ X5 @ B3))))))))). % Set.set_insert
thf(fact_225_Set_Oset__insert, axiom,
    ((![X5 : nat, A : set_nat]: ((member_nat @ X5 @ A) => (~ ((![B3 : set_nat]: ((A = (insert_nat @ X5 @ B3)) => (member_nat @ X5 @ B3))))))))). % Set.set_insert
thf(fact_226_insertI2, axiom,
    ((![A3 : msg, B : set_msg, B4 : msg]: ((member_msg @ A3 @ B) => (member_msg @ A3 @ (insert_msg @ B4 @ B)))))). % insertI2
thf(fact_227_insertI2, axiom,
    ((![A3 : agent, B : set_agent, B4 : agent]: ((member_agent @ A3 @ B) => (member_agent @ A3 @ (insert_agent @ B4 @ B)))))). % insertI2
thf(fact_228_insertI2, axiom,
    ((![A3 : list_event, B : set_list_event, B4 : list_event]: ((member_list_event @ A3 @ B) => (member_list_event @ A3 @ (insert_list_event @ B4 @ B)))))). % insertI2
thf(fact_229_insertI2, axiom,
    ((![A3 : event, B : set_event, B4 : event]: ((member_event @ A3 @ B) => (member_event @ A3 @ (insert_event @ B4 @ B)))))). % insertI2
thf(fact_230_insertI2, axiom,
    ((![A3 : nat, B : set_nat, B4 : nat]: ((member_nat @ A3 @ B) => (member_nat @ A3 @ (insert_nat @ B4 @ B)))))). % insertI2

% Conjectures (4)
thf(conj_0, hypothesis,
    ((member_msg @ (crypt @ (shrK @ b) @ (mPair @ (key @ k) @ (agent2 @ a))) @ (parts @ (knows @ spy @ evs))))).
thf(conj_1, hypothesis,
    ((~ ((member_agent @ b @ bad))))).
thf(conj_2, hypothesis,
    ((member_list_event @ evs @ nS_Sha1061662329shared))).
thf(conj_3, conjecture,
    ((?[NA3 : msg]: (member_event @ (says @ server @ a @ (crypt @ (shrK @ a) @ (mPair @ NA3 @ (mPair @ (agent2 @ b) @ (mPair @ (key @ k) @ (crypt @ (shrK @ b) @ (mPair @ (key @ k) @ (agent2 @ a)))))))) @ (set_event2 @ evs))))).
