% 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_432__5232484_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:24:46.884

% Could-be-implicit typings (13)
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__Public__Okeymode, type,
    keymode : $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 (45)
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__List__Olist_It__Event__Oevent_J, type,
    cons_list_event : list_event > list_list_event > list_list_event).
thf(sy_c_List_Olist_OCons_001t__Message__Oagent, type,
    cons_agent : agent > list_agent > list_agent).
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__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_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_OinvKey, type,
    invKey : nat > nat).
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_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_Public_OpublicKey, type,
    publicKey : keymode > agent > 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_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_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).
thf(sy_v_evs, type,
    evs : list_event).

% Relevant facts (198)
thf(fact_0_Spy__in__bad, axiom,
    ((member_agent @ spy @ bad))). % Spy_in_bad
thf(fact_1_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_2_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_3_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_4_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_5_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_6_msg_Oinject_I3_J, axiom,
    ((![X3 : nat, Y3 : nat]: (((nonce @ X3) = (nonce @ Y3)) = (X3 = Y3))))). % msg.inject(3)
thf(fact_7_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_8_msg_Oinject_I4_J, axiom,
    ((![X4 : nat, Y4 : nat]: (((key @ X4) = (key @ Y4)) = (X4 = Y4))))). % msg.inject(4)
thf(fact_9_analz__idem, axiom,
    ((![H : set_msg]: ((analz @ (analz @ H)) = (analz @ H))))). % analz_idem
thf(fact_10_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_11_msg_Odistinct_I29_J, axiom,
    ((![X3 : nat, X71 : nat, X72 : msg]: (~ (((nonce @ X3) = (crypt @ X71 @ X72))))))). % msg.distinct(29)
thf(fact_12_analz__analzD, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ (analz @ (analz @ H))) => (member_msg @ X @ (analz @ H)))))). % analz_analzD
thf(fact_13_analz_OInj, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ H) => (member_msg @ X @ (analz @ H)))))). % analz.Inj
thf(fact_14_msg_Odistinct_I35_J, axiom,
    ((![X4 : nat, X71 : nat, X72 : msg]: (~ (((key @ X4) = (crypt @ X71 @ X72))))))). % msg.distinct(35)
thf(fact_15_msg_Odistinct_I23_J, axiom,
    ((![X3 : nat, X4 : nat]: (~ (((nonce @ X3) = (key @ X4))))))). % msg.distinct(23)
thf(fact_16_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_17_shrK__in__knows, axiom,
    ((![A : agent, Evs : list_event]: (member_msg @ (key @ (shrK @ A)) @ (knows @ A @ Evs))))). % shrK_in_knows
thf(fact_18_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_19_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_20_shrK__injective, axiom,
    ((![X2 : agent, Y2 : agent]: (((shrK @ X2) = (shrK @ Y2)) = (X2 = Y2))))). % shrK_injective
thf(fact_21_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_22_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_23_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_24_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_25_analz__spies__pubK, axiom,
    ((![B2 : keymode, A : agent, Evs : list_event]: (member_msg @ (key @ (publicKey @ B2 @ A)) @ (analz @ (knows @ spy @ Evs)))))). % analz_spies_pubK
thf(fact_26_parts__idem, axiom,
    ((![H : set_msg]: ((parts @ (parts @ H)) = (parts @ H))))). % parts_idem
thf(fact_27_publicKey__inject, axiom,
    ((![B2 : keymode, A : agent, C : keymode, A2 : agent]: (((publicKey @ B2 @ A) = (publicKey @ C @ A2)) = (((B2 = C)) & ((A = A2))))))). % publicKey_inject
thf(fact_28_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_29_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_30_analz__parts, axiom,
    ((![H : set_msg]: ((analz @ (parts @ H)) = (parts @ H))))). % analz_parts
thf(fact_31_parts__analz, axiom,
    ((![H : set_msg]: ((parts @ (analz @ H)) = (parts @ H))))). % parts_analz
thf(fact_32_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_33_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_34_spies__pubK, axiom,
    ((![B2 : keymode, A : agent, Evs : list_event]: (member_msg @ (key @ (publicKey @ B2 @ A)) @ (knows @ spy @ Evs))))). % spies_pubK
thf(fact_35_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_36_event_Odistinct_I5_J, axiom,
    ((![X21 : agent, X22 : msg, X31 : agent, X32 : msg]: (~ (((gets @ X21 @ X22) = (notes @ X31 @ X32))))))). % event.distinct(5)
thf(fact_37_parts_OInj, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ H) => (member_msg @ X @ (parts @ H)))))). % parts.Inj
thf(fact_38_parts__partsD, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ (parts @ (parts @ H))) => (member_msg @ X @ (parts @ H)))))). % parts_partsD
thf(fact_39_injective__publicKey, axiom,
    ((![B2 : keymode, A : agent, C : keymode, A2 : agent]: (((publicKey @ B2 @ A) = (publicKey @ C @ A2)) => ((B2 = C) & (A = A2)))))). % injective_publicKey
thf(fact_40_shrK__neq__pubK, axiom,
    ((![B2 : keymode, C2 : agent, A : agent]: (~ (((publicKey @ B2 @ C2) = (shrK @ A))))))). % shrK_neq_pubK
thf(fact_41_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_42_event_Oexhaust, axiom,
    ((![Y2 : event]: ((![X112 : agent, X122 : agent, X132 : msg]: (~ ((Y2 = (says @ X112 @ X122 @ X132))))) => ((![X212 : agent, X222 : msg]: (~ ((Y2 = (gets @ X212 @ X222))))) => (~ ((![X312 : agent, X322 : msg]: (~ ((Y2 = (notes @ X312 @ X322)))))))))))). % event.exhaust
thf(fact_43_analz__into__parts, axiom,
    ((![C : msg, H : set_msg]: ((member_msg @ C @ (analz @ H)) => (member_msg @ C @ (parts @ H)))))). % analz_into_parts
thf(fact_44_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_45_mem__Collect__eq, axiom,
    ((![A3 : event, P : event > $o]: ((member_event @ A3 @ (collect_event @ P)) = (P @ A3))))). % mem_Collect_eq
thf(fact_46_mem__Collect__eq, axiom,
    ((![A3 : msg, P : msg > $o]: ((member_msg @ A3 @ (collect_msg @ P)) = (P @ A3))))). % mem_Collect_eq
thf(fact_47_mem__Collect__eq, axiom,
    ((![A3 : agent, P : agent > $o]: ((member_agent @ A3 @ (collect_agent @ P)) = (P @ A3))))). % mem_Collect_eq
thf(fact_48_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_49_Collect__mem__eq, axiom,
    ((![A : set_event]: ((collect_event @ (^[X5 : event]: (member_event @ X5 @ A))) = A)))). % Collect_mem_eq
thf(fact_50_Collect__mem__eq, axiom,
    ((![A : set_msg]: ((collect_msg @ (^[X5 : msg]: (member_msg @ X5 @ A))) = A)))). % Collect_mem_eq
thf(fact_51_Collect__mem__eq, axiom,
    ((![A : set_agent]: ((collect_agent @ (^[X5 : agent]: (member_agent @ X5 @ A))) = A)))). % Collect_mem_eq
thf(fact_52_Collect__mem__eq, axiom,
    ((![A : set_list_event]: ((collect_list_event @ (^[X5 : list_event]: (member_list_event @ X5 @ A))) = A)))). % Collect_mem_eq
thf(fact_53_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_54_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_55_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_56_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_57_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_58_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_59_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_60_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_61_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_62_Spy__spies__bad__privateKey, axiom,
    ((![A : agent, B2 : keymode, Evs : list_event]: ((member_agent @ A @ bad) => (member_msg @ (key @ (invKey @ (publicKey @ B2 @ A))) @ (knows @ spy @ Evs)))))). % Spy_spies_bad_privateKey
thf(fact_63_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_64_list_Oset__intros_I2_J, axiom,
    ((![Y2 : msg, X22 : list_msg, X21 : msg]: ((member_msg @ Y2 @ (set_msg2 @ X22)) => (member_msg @ Y2 @ (set_msg2 @ (cons_msg @ X21 @ X22))))))). % list.set_intros(2)
thf(fact_65_list_Oset__intros_I2_J, axiom,
    ((![Y2 : agent, X22 : list_agent, X21 : agent]: ((member_agent @ Y2 @ (set_agent2 @ X22)) => (member_agent @ Y2 @ (set_agent2 @ (cons_agent @ X21 @ X22))))))). % list.set_intros(2)
thf(fact_66_list_Oset__intros_I2_J, axiom,
    ((![Y2 : list_event, X22 : list_list_event, X21 : list_event]: ((member_list_event @ Y2 @ (set_list_event2 @ X22)) => (member_list_event @ Y2 @ (set_list_event2 @ (cons_list_event @ X21 @ X22))))))). % list.set_intros(2)
thf(fact_67_list_Oset__intros_I2_J, axiom,
    ((![Y2 : event, X22 : list_event, X21 : event]: ((member_event @ Y2 @ (set_event2 @ X22)) => (member_event @ Y2 @ (set_event2 @ (cons_event @ X21 @ X22))))))). % list.set_intros(2)
thf(fact_68_list_Oset__intros_I1_J, axiom,
    ((![X21 : msg, X22 : list_msg]: (member_msg @ X21 @ (set_msg2 @ (cons_msg @ X21 @ X22)))))). % list.set_intros(1)
thf(fact_69_list_Oset__intros_I1_J, axiom,
    ((![X21 : agent, X22 : list_agent]: (member_agent @ X21 @ (set_agent2 @ (cons_agent @ X21 @ X22)))))). % list.set_intros(1)
thf(fact_70_list_Oset__intros_I1_J, axiom,
    ((![X21 : list_event, X22 : list_list_event]: (member_list_event @ X21 @ (set_list_event2 @ (cons_list_event @ X21 @ X22)))))). % list.set_intros(1)
thf(fact_71_list_Oset__intros_I1_J, axiom,
    ((![X21 : event, X22 : list_event]: (member_event @ X21 @ (set_event2 @ (cons_event @ X21 @ X22)))))). % list.set_intros(1)
thf(fact_72_set__ConsD, axiom,
    ((![Y2 : msg, X2 : msg, Xs : list_msg]: ((member_msg @ Y2 @ (set_msg2 @ (cons_msg @ X2 @ Xs))) => ((Y2 = X2) | (member_msg @ Y2 @ (set_msg2 @ Xs))))))). % set_ConsD
thf(fact_73_set__ConsD, axiom,
    ((![Y2 : agent, X2 : agent, Xs : list_agent]: ((member_agent @ Y2 @ (set_agent2 @ (cons_agent @ X2 @ Xs))) => ((Y2 = X2) | (member_agent @ Y2 @ (set_agent2 @ Xs))))))). % set_ConsD
thf(fact_74_set__ConsD, axiom,
    ((![Y2 : list_event, X2 : list_event, Xs : list_list_event]: ((member_list_event @ Y2 @ (set_list_event2 @ (cons_list_event @ X2 @ Xs))) => ((Y2 = X2) | (member_list_event @ Y2 @ (set_list_event2 @ Xs))))))). % set_ConsD
thf(fact_75_set__ConsD, axiom,
    ((![Y2 : event, X2 : event, Xs : list_event]: ((member_event @ Y2 @ (set_event2 @ (cons_event @ X2 @ Xs))) => ((Y2 = X2) | (member_event @ Y2 @ (set_event2 @ Xs))))))). % set_ConsD
thf(fact_76_invKey__eq, axiom,
    ((![K : nat, K2 : nat]: (((invKey @ K) = (invKey @ K2)) = (K = K2))))). % invKey_eq
thf(fact_77_invKey, axiom,
    ((![K : nat]: ((invKey @ (invKey @ K)) = K)))). % invKey
thf(fact_78_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_79_invKey__shrK, axiom,
    ((![A : agent]: ((invKey @ (shrK @ A)) = (shrK @ A))))). % invKey_shrK
thf(fact_80_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_81_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_82_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_83_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_84_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_85_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_86_shrK__in__initState, axiom,
    ((![A : agent]: (member_msg @ (key @ (shrK @ A)) @ (initState @ A))))). % shrK_in_initState
thf(fact_87_publicKey__in__initState, axiom,
    ((![B2 : keymode, A : agent, B : agent]: (member_msg @ (key @ (publicKey @ B2 @ A)) @ (initState @ B))))). % publicKey_in_initState
thf(fact_88_priK__in__initState, axiom,
    ((![B2 : keymode, A : agent]: (member_msg @ (key @ (invKey @ (publicKey @ B2 @ A))) @ (initState @ A))))). % priK_in_initState
thf(fact_89_analz__Crypt__if, axiom,
    ((![K : nat, H : set_msg, X : msg]: (((member_msg @ (key @ (invKey @ K)) @ (analz @ H)) => ((analz @ (insert_msg @ (crypt @ K @ X) @ H)) = (insert_msg @ (crypt @ K @ X) @ (analz @ (insert_msg @ X @ H))))) & ((~ ((member_msg @ (key @ (invKey @ K)) @ (analz @ H)))) => ((analz @ (insert_msg @ (crypt @ K @ X) @ H)) = (insert_msg @ (crypt @ K @ X) @ (analz @ H)))))))). % analz_Crypt_if
thf(fact_90_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_91_analz__insert__eq__I, axiom,
    ((![X : msg, H : set_msg]: ((![X6 : msg]: ((member_msg @ X6 @ (analz @ (insert_msg @ X @ H))) => (member_msg @ X6 @ (insert_msg @ X @ (analz @ H))))) => ((analz @ (insert_msg @ X @ H)) = (insert_msg @ X @ (analz @ H))))))). % analz_insert_eq_I
thf(fact_92_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_93_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_94_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_95_analz__cut, axiom,
    ((![Y : msg, X : msg, H : set_msg]: ((member_msg @ Y @ (analz @ (insert_msg @ X @ H))) => ((member_msg @ X @ (analz @ H)) => (member_msg @ Y @ (analz @ H))))))). % analz_cut
thf(fact_96_parts__insert__eq__I, axiom,
    ((![X : msg, H : set_msg]: ((![X6 : msg]: ((member_msg @ X6 @ (parts @ (insert_msg @ X @ H))) => (member_msg @ X6 @ (insert_msg @ X @ (parts @ H))))) => ((parts @ (insert_msg @ X @ H)) = (insert_msg @ X @ (parts @ H))))))). % parts_insert_eq_I
thf(fact_97_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_98_publicKey__neq__privateKey, axiom,
    ((![C : keymode, A2 : agent, B2 : keymode, A : agent]: (~ (((publicKey @ C @ A2) = (invKey @ (publicKey @ B2 @ A)))))))). % publicKey_neq_privateKey
thf(fact_99_analz__insert__Decrypt, axiom,
    ((![K : nat, H : set_msg, X : msg]: ((member_msg @ (key @ (invKey @ K)) @ (analz @ H)) => ((analz @ (insert_msg @ (crypt @ K @ X) @ H)) = (insert_msg @ (crypt @ K @ X) @ (analz @ (insert_msg @ X @ H)))))))). % analz_insert_Decrypt
thf(fact_100_analz__insert__Crypt, axiom,
    ((![K : nat, H : set_msg, X : msg]: ((~ ((member_msg @ (key @ (invKey @ K)) @ (analz @ H)))) => ((analz @ (insert_msg @ (crypt @ K @ X) @ H)) = (insert_msg @ (crypt @ K @ X) @ (analz @ H))))))). % analz_insert_Crypt
thf(fact_101_pushKeys_I6_J, axiom,
    ((![K : nat, X : nat, K2 : msg, A : set_msg]: ((insert_msg @ (key @ K) @ (insert_msg @ (crypt @ X @ K2) @ A)) = (insert_msg @ (crypt @ X @ K2) @ (insert_msg @ (key @ K) @ A)))))). % pushKeys(6)
thf(fact_102_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_103_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_104_shrK__neq__priK, axiom,
    ((![B2 : keymode, C2 : agent, A : agent]: (~ (((invKey @ (publicKey @ B2 @ C2)) = (shrK @ A))))))). % shrK_neq_priK
thf(fact_105_not__Cons__self2, axiom,
    ((![X2 : event, Xs : list_event]: (~ (((cons_event @ X2 @ Xs) = Xs)))))). % not_Cons_self2
thf(fact_106_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_107_Crypt__notin__initState, axiom,
    ((![K : nat, X : msg, B : agent]: (~ ((member_msg @ (crypt @ K @ X) @ (parts @ (initState @ B)))))))). % Crypt_notin_initState
thf(fact_108_Nonce__notin__initState, axiom,
    ((![N : nat, B : agent]: (~ ((member_msg @ (nonce @ N) @ (parts @ (initState @ B)))))))). % Nonce_notin_initState
thf(fact_109_list_Oset__cases, axiom,
    ((![E : msg, A3 : list_msg]: ((member_msg @ E @ (set_msg2 @ A3)) => ((![Z2 : list_msg]: (~ ((A3 = (cons_msg @ E @ Z2))))) => (~ ((![Z1 : msg, Z2 : list_msg]: ((A3 = (cons_msg @ Z1 @ Z2)) => (~ ((member_msg @ E @ (set_msg2 @ Z2))))))))))))). % list.set_cases
thf(fact_110_list_Oset__cases, axiom,
    ((![E : agent, A3 : list_agent]: ((member_agent @ E @ (set_agent2 @ A3)) => ((![Z2 : list_agent]: (~ ((A3 = (cons_agent @ E @ Z2))))) => (~ ((![Z1 : agent, Z2 : list_agent]: ((A3 = (cons_agent @ Z1 @ Z2)) => (~ ((member_agent @ E @ (set_agent2 @ Z2))))))))))))). % list.set_cases
thf(fact_111_list_Oset__cases, axiom,
    ((![E : list_event, A3 : list_list_event]: ((member_list_event @ E @ (set_list_event2 @ A3)) => ((![Z2 : list_list_event]: (~ ((A3 = (cons_list_event @ E @ Z2))))) => (~ ((![Z1 : list_event, Z2 : list_list_event]: ((A3 = (cons_list_event @ Z1 @ Z2)) => (~ ((member_list_event @ E @ (set_list_event2 @ Z2))))))))))))). % list.set_cases
thf(fact_112_list_Oset__cases, axiom,
    ((![E : event, A3 : list_event]: ((member_event @ E @ (set_event2 @ A3)) => ((![Z2 : list_event]: (~ ((A3 = (cons_event @ E @ Z2))))) => (~ ((![Z1 : event, Z2 : list_event]: ((A3 = (cons_event @ Z1 @ Z2)) => (~ ((member_event @ E @ (set_event2 @ Z2))))))))))))). % list.set_cases
thf(fact_113_insertCI, axiom,
    ((![A3 : event, B : set_event, B2 : event]: (((~ ((member_event @ A3 @ B))) => (A3 = B2)) => (member_event @ A3 @ (insert_event @ B2 @ B)))))). % insertCI
thf(fact_114_insertCI, axiom,
    ((![A3 : msg, B : set_msg, B2 : msg]: (((~ ((member_msg @ A3 @ B))) => (A3 = B2)) => (member_msg @ A3 @ (insert_msg @ B2 @ B)))))). % insertCI
thf(fact_115_insertCI, axiom,
    ((![A3 : agent, B : set_agent, B2 : agent]: (((~ ((member_agent @ A3 @ B))) => (A3 = B2)) => (member_agent @ A3 @ (insert_agent @ B2 @ B)))))). % insertCI
thf(fact_116_insertCI, axiom,
    ((![A3 : list_event, B : set_list_event, B2 : list_event]: (((~ ((member_list_event @ A3 @ B))) => (A3 = B2)) => (member_list_event @ A3 @ (insert_list_event @ B2 @ B)))))). % insertCI
thf(fact_117_insert__iff, axiom,
    ((![A3 : event, B2 : event, A : set_event]: ((member_event @ A3 @ (insert_event @ B2 @ A)) = (((A3 = B2)) | ((member_event @ A3 @ A))))))). % insert_iff
thf(fact_118_insert__iff, axiom,
    ((![A3 : msg, B2 : msg, A : set_msg]: ((member_msg @ A3 @ (insert_msg @ B2 @ A)) = (((A3 = B2)) | ((member_msg @ A3 @ A))))))). % insert_iff
thf(fact_119_insert__iff, axiom,
    ((![A3 : agent, B2 : agent, A : set_agent]: ((member_agent @ A3 @ (insert_agent @ B2 @ A)) = (((A3 = B2)) | ((member_agent @ A3 @ A))))))). % insert_iff
thf(fact_120_insert__iff, axiom,
    ((![A3 : list_event, B2 : list_event, A : set_list_event]: ((member_list_event @ A3 @ (insert_list_event @ B2 @ A)) = (((A3 = B2)) | ((member_list_event @ A3 @ A))))))). % insert_iff
thf(fact_121_insert__absorb2, axiom,
    ((![X2 : msg, A : set_msg]: ((insert_msg @ X2 @ (insert_msg @ X2 @ A)) = (insert_msg @ X2 @ A))))). % insert_absorb2
thf(fact_122_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_123_B__trusts__NS5, axiom,
    ((![K : nat, NB : nat, Evs : list_event, B : agent, A : agent]: ((member_msg @ (crypt @ K @ (mPair @ (nonce @ NB) @ (nonce @ NB))) @ (parts @ (knows @ spy @ Evs))) => ((member_msg @ (crypt @ (shrK @ B) @ (mPair @ (key @ K) @ (agent2 @ A))) @ (parts @ (knows @ spy @ Evs))) => ((![NA : msg, NB2 : msg]: (~ ((member_event @ (notes @ spy @ (mPair @ NA @ (mPair @ NB2 @ (key @ K)))) @ (set_event2 @ Evs))))) => ((~ ((member_agent @ A @ bad))) => ((~ ((member_agent @ B @ bad))) => ((member_list_event @ Evs @ nS_Sha1061662329shared) => (member_event @ (says @ A @ B @ (crypt @ K @ (mPair @ (nonce @ NB) @ (nonce @ NB)))) @ (set_event2 @ Evs))))))))))). % B_trusts_NS5
thf(fact_124_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_125_msg_Oinject_I1_J, axiom,
    ((![X14 : agent, Y1 : agent]: (((agent2 @ X14) = (agent2 @ Y1)) = (X14 = Y1))))). % msg.inject(1)
thf(fact_126_analz__insert__MPair, axiom,
    ((![X : msg, Y : msg, H : set_msg]: ((analz @ (insert_msg @ (mPair @ X @ Y) @ H)) = (insert_msg @ (mPair @ X @ Y) @ (analz @ (insert_msg @ X @ (insert_msg @ Y @ H)))))))). % analz_insert_MPair
thf(fact_127_parts__insert__MPair, axiom,
    ((![X : msg, Y : msg, H : set_msg]: ((parts @ (insert_msg @ (mPair @ X @ Y) @ H)) = (insert_msg @ (mPair @ X @ Y) @ (parts @ (insert_msg @ X @ (insert_msg @ Y @ H)))))))). % parts_insert_MPair
thf(fact_128_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_129_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_130_msg_Odistinct_I5_J, axiom,
    ((![X14 : agent, X4 : nat]: (~ (((agent2 @ X14) = (key @ X4))))))). % msg.distinct(5)
thf(fact_131_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_132_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_133_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_134_msg_Odistinct_I11_J, axiom,
    ((![X14 : agent, X71 : nat, X72 : msg]: (~ (((agent2 @ X14) = (crypt @ X71 @ X72))))))). % msg.distinct(11)
thf(fact_135_msg_Odistinct_I33_J, axiom,
    ((![X4 : nat, X61 : msg, X62 : msg]: (~ (((key @ X4) = (mPair @ X61 @ X62))))))). % msg.distinct(33)
thf(fact_136_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_137_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_138_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_139_msg_Odistinct_I41_J, axiom,
    ((![X61 : msg, X62 : msg, X71 : nat, X72 : msg]: (~ (((mPair @ X61 @ X62) = (crypt @ X71 @ X72))))))). % msg.distinct(41)
thf(fact_140_msg_Odistinct_I3_J, axiom,
    ((![X14 : agent, X3 : nat]: (~ (((agent2 @ X14) = (nonce @ X3))))))). % msg.distinct(3)
thf(fact_141_msg_Odistinct_I9_J, axiom,
    ((![X14 : agent, X61 : msg, X62 : msg]: (~ (((agent2 @ X14) = (mPair @ X61 @ X62))))))). % msg.distinct(9)
thf(fact_142_msg_Odistinct_I27_J, axiom,
    ((![X3 : nat, X61 : msg, X62 : msg]: (~ (((nonce @ X3) = (mPair @ X61 @ X62))))))). % msg.distinct(27)
thf(fact_143_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_144_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_145_analz__trivial, axiom,
    ((![H : set_msg]: ((![X7 : msg, Y5 : msg]: (~ ((member_msg @ (mPair @ X7 @ Y5) @ H)))) => ((![X7 : msg, K3 : nat]: (~ ((member_msg @ (crypt @ K3 @ X7) @ H)))) => ((analz @ H) = H)))))). % analz_trivial
thf(fact_146_pushKeys_I5_J, axiom,
    ((![K : nat, X : msg, Y : msg, A : set_msg]: ((insert_msg @ (key @ K) @ (insert_msg @ (mPair @ X @ Y) @ A)) = (insert_msg @ (mPair @ X @ Y) @ (insert_msg @ (key @ K) @ A)))))). % pushKeys(5)
thf(fact_147_pushCrypts_I6_J, axiom,
    ((![X : nat, K : msg, X8 : msg, Y : msg, A : set_msg]: ((insert_msg @ (crypt @ X @ K) @ (insert_msg @ (mPair @ X8 @ Y) @ A)) = (insert_msg @ (mPair @ X8 @ Y) @ (insert_msg @ (crypt @ X @ K) @ A)))))). % pushCrypts(6)
thf(fact_148_parts_Ocases, axiom,
    ((![A3 : msg, H : set_msg]: ((member_msg @ A3 @ (parts @ H)) => ((~ ((member_msg @ A3 @ H))) => ((![Y5 : msg]: (~ ((member_msg @ (mPair @ A3 @ Y5) @ (parts @ H))))) => ((![X7 : msg]: (~ ((member_msg @ (mPair @ X7 @ A3) @ (parts @ H))))) => (~ ((![K3 : nat]: (~ ((member_msg @ (crypt @ K3 @ A3) @ (parts @ H)))))))))))))). % parts.cases
thf(fact_149_parts_Osimps, axiom,
    ((![A3 : msg, H : set_msg]: ((member_msg @ A3 @ (parts @ H)) = (((?[X9 : msg]: (((A3 = X9)) & ((member_msg @ X9 @ H))))) | ((((?[X9 : msg]: (?[Y6 : msg]: (((A3 = X9)) & ((member_msg @ (mPair @ X9 @ Y6) @ (parts @ H))))))) | ((((?[X9 : msg]: (?[Y6 : msg]: (((A3 = Y6)) & ((member_msg @ (mPair @ X9 @ Y6) @ (parts @ H))))))) | ((?[K4 : nat]: (?[X9 : msg]: (((A3 = X9)) & ((member_msg @ (crypt @ K4 @ X9) @ (parts @ H)))))))))))))))). % parts.simps
thf(fact_150_parts_Oinducts, axiom,
    ((![X2 : msg, H : set_msg, P : msg > $o]: ((member_msg @ X2 @ (parts @ H)) => ((![X7 : msg]: ((member_msg @ X7 @ H) => (P @ X7))) => ((![X7 : msg, Y5 : msg]: ((member_msg @ (mPair @ X7 @ Y5) @ (parts @ H)) => ((P @ (mPair @ X7 @ Y5)) => (P @ X7)))) => ((![X7 : msg, Y5 : msg]: ((member_msg @ (mPair @ X7 @ Y5) @ (parts @ H)) => ((P @ (mPair @ X7 @ Y5)) => (P @ Y5)))) => ((![K3 : nat, X7 : msg]: ((member_msg @ (crypt @ K3 @ X7) @ (parts @ H)) => ((P @ (crypt @ K3 @ X7)) => (P @ X7)))) => (P @ X2))))))))). % parts.inducts
thf(fact_151_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_152_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_153_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_154_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_155_insert__commute, axiom,
    ((![X2 : msg, Y2 : msg, A : set_msg]: ((insert_msg @ X2 @ (insert_msg @ Y2 @ A)) = (insert_msg @ Y2 @ (insert_msg @ X2 @ A)))))). % insert_commute
thf(fact_156_insert__eq__iff, axiom,
    ((![A3 : event, A : set_event, B2 : event, B : set_event]: ((~ ((member_event @ A3 @ A))) => ((~ ((member_event @ B2 @ B))) => (((insert_event @ A3 @ A) = (insert_event @ B2 @ B)) = (((((A3 = B2)) => ((A = B)))) & ((((~ ((A3 = B2)))) => ((?[C3 : set_event]: (((A = (insert_event @ B2 @ C3))) & ((((~ ((member_event @ B2 @ C3)))) & ((((B = (insert_event @ A3 @ C3))) & ((~ ((member_event @ A3 @ C3)))))))))))))))))))). % insert_eq_iff
thf(fact_157_insert__eq__iff, axiom,
    ((![A3 : msg, A : set_msg, B2 : msg, B : set_msg]: ((~ ((member_msg @ A3 @ A))) => ((~ ((member_msg @ B2 @ B))) => (((insert_msg @ A3 @ A) = (insert_msg @ B2 @ B)) = (((((A3 = B2)) => ((A = B)))) & ((((~ ((A3 = B2)))) => ((?[C3 : set_msg]: (((A = (insert_msg @ B2 @ C3))) & ((((~ ((member_msg @ B2 @ C3)))) & ((((B = (insert_msg @ A3 @ C3))) & ((~ ((member_msg @ A3 @ C3)))))))))))))))))))). % insert_eq_iff
thf(fact_158_insert__eq__iff, axiom,
    ((![A3 : agent, A : set_agent, B2 : agent, B : set_agent]: ((~ ((member_agent @ A3 @ A))) => ((~ ((member_agent @ B2 @ B))) => (((insert_agent @ A3 @ A) = (insert_agent @ B2 @ B)) = (((((A3 = B2)) => ((A = B)))) & ((((~ ((A3 = B2)))) => ((?[C3 : set_agent]: (((A = (insert_agent @ B2 @ C3))) & ((((~ ((member_agent @ B2 @ C3)))) & ((((B = (insert_agent @ A3 @ C3))) & ((~ ((member_agent @ A3 @ C3)))))))))))))))))))). % insert_eq_iff
thf(fact_159_insert__eq__iff, axiom,
    ((![A3 : list_event, A : set_list_event, B2 : list_event, B : set_list_event]: ((~ ((member_list_event @ A3 @ A))) => ((~ ((member_list_event @ B2 @ B))) => (((insert_list_event @ A3 @ A) = (insert_list_event @ B2 @ B)) = (((((A3 = B2)) => ((A = B)))) & ((((~ ((A3 = B2)))) => ((?[C3 : set_list_event]: (((A = (insert_list_event @ B2 @ C3))) & ((((~ ((member_list_event @ B2 @ C3)))) & ((((B = (insert_list_event @ A3 @ C3))) & ((~ ((member_list_event @ A3 @ C3)))))))))))))))))))). % insert_eq_iff
thf(fact_160_insert__absorb, axiom,
    ((![A3 : event, A : set_event]: ((member_event @ A3 @ A) => ((insert_event @ A3 @ A) = A))))). % insert_absorb
thf(fact_161_insert__absorb, axiom,
    ((![A3 : msg, A : set_msg]: ((member_msg @ A3 @ A) => ((insert_msg @ A3 @ A) = A))))). % insert_absorb
thf(fact_162_insert__absorb, axiom,
    ((![A3 : agent, A : set_agent]: ((member_agent @ A3 @ A) => ((insert_agent @ A3 @ A) = A))))). % insert_absorb
thf(fact_163_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_164_insert__ident, axiom,
    ((![X2 : event, A : set_event, B : set_event]: ((~ ((member_event @ X2 @ A))) => ((~ ((member_event @ X2 @ B))) => (((insert_event @ X2 @ A) = (insert_event @ X2 @ B)) = (A = B))))))). % insert_ident
thf(fact_165_insert__ident, axiom,
    ((![X2 : msg, A : set_msg, B : set_msg]: ((~ ((member_msg @ X2 @ A))) => ((~ ((member_msg @ X2 @ B))) => (((insert_msg @ X2 @ A) = (insert_msg @ X2 @ B)) = (A = B))))))). % insert_ident
thf(fact_166_insert__ident, axiom,
    ((![X2 : agent, A : set_agent, B : set_agent]: ((~ ((member_agent @ X2 @ A))) => ((~ ((member_agent @ X2 @ B))) => (((insert_agent @ X2 @ A) = (insert_agent @ X2 @ B)) = (A = B))))))). % insert_ident
thf(fact_167_insert__ident, axiom,
    ((![X2 : list_event, A : set_list_event, B : set_list_event]: ((~ ((member_list_event @ X2 @ A))) => ((~ ((member_list_event @ X2 @ B))) => (((insert_list_event @ X2 @ A) = (insert_list_event @ X2 @ B)) = (A = B))))))). % insert_ident
thf(fact_168_Set_Oset__insert, axiom,
    ((![X2 : event, A : set_event]: ((member_event @ X2 @ A) => (~ ((![B3 : set_event]: ((A = (insert_event @ X2 @ B3)) => (member_event @ X2 @ B3))))))))). % Set.set_insert
thf(fact_169_Set_Oset__insert, axiom,
    ((![X2 : msg, A : set_msg]: ((member_msg @ X2 @ A) => (~ ((![B3 : set_msg]: ((A = (insert_msg @ X2 @ B3)) => (member_msg @ X2 @ B3))))))))). % Set.set_insert
thf(fact_170_Set_Oset__insert, axiom,
    ((![X2 : agent, A : set_agent]: ((member_agent @ X2 @ A) => (~ ((![B3 : set_agent]: ((A = (insert_agent @ X2 @ B3)) => (member_agent @ X2 @ B3))))))))). % Set.set_insert
thf(fact_171_Set_Oset__insert, axiom,
    ((![X2 : list_event, A : set_list_event]: ((member_list_event @ X2 @ A) => (~ ((![B3 : set_list_event]: ((A = (insert_list_event @ X2 @ B3)) => (member_list_event @ X2 @ B3))))))))). % Set.set_insert
thf(fact_172_insertI2, axiom,
    ((![A3 : event, B : set_event, B2 : event]: ((member_event @ A3 @ B) => (member_event @ A3 @ (insert_event @ B2 @ B)))))). % insertI2
thf(fact_173_insertI2, axiom,
    ((![A3 : msg, B : set_msg, B2 : msg]: ((member_msg @ A3 @ B) => (member_msg @ A3 @ (insert_msg @ B2 @ B)))))). % insertI2
thf(fact_174_insertI2, axiom,
    ((![A3 : agent, B : set_agent, B2 : agent]: ((member_agent @ A3 @ B) => (member_agent @ A3 @ (insert_agent @ B2 @ B)))))). % insertI2
thf(fact_175_insertI2, axiom,
    ((![A3 : list_event, B : set_list_event, B2 : list_event]: ((member_list_event @ A3 @ B) => (member_list_event @ A3 @ (insert_list_event @ B2 @ B)))))). % insertI2
thf(fact_176_insertI1, axiom,
    ((![A3 : event, B : set_event]: (member_event @ A3 @ (insert_event @ A3 @ B))))). % insertI1
thf(fact_177_insertI1, axiom,
    ((![A3 : msg, B : set_msg]: (member_msg @ A3 @ (insert_msg @ A3 @ B))))). % insertI1
thf(fact_178_insertI1, axiom,
    ((![A3 : agent, B : set_agent]: (member_agent @ A3 @ (insert_agent @ A3 @ B))))). % insertI1
thf(fact_179_insertI1, axiom,
    ((![A3 : list_event, B : set_list_event]: (member_list_event @ A3 @ (insert_list_event @ A3 @ B))))). % insertI1
thf(fact_180_insertE, axiom,
    ((![A3 : event, B2 : event, A : set_event]: ((member_event @ A3 @ (insert_event @ B2 @ A)) => ((~ ((A3 = B2))) => (member_event @ A3 @ A)))))). % insertE
thf(fact_181_insertE, axiom,
    ((![A3 : msg, B2 : msg, A : set_msg]: ((member_msg @ A3 @ (insert_msg @ B2 @ A)) => ((~ ((A3 = B2))) => (member_msg @ A3 @ A)))))). % insertE
thf(fact_182_insertE, axiom,
    ((![A3 : agent, B2 : agent, A : set_agent]: ((member_agent @ A3 @ (insert_agent @ B2 @ A)) => ((~ ((A3 = B2))) => (member_agent @ A3 @ A)))))). % insertE
thf(fact_183_insertE, axiom,
    ((![A3 : list_event, B2 : list_event, A : set_list_event]: ((member_list_event @ A3 @ (insert_list_event @ B2 @ A)) => ((~ ((A3 = B2))) => (member_list_event @ A3 @ A)))))). % insertE
thf(fact_184_analz_Ocases, axiom,
    ((![A3 : msg, H : set_msg]: ((member_msg @ A3 @ (analz @ H)) => ((~ ((member_msg @ A3 @ H))) => ((![Y5 : msg]: (~ ((member_msg @ (mPair @ A3 @ Y5) @ (analz @ H))))) => ((![X7 : msg]: (~ ((member_msg @ (mPair @ X7 @ A3) @ (analz @ H))))) => (~ ((![K3 : nat]: ((member_msg @ (crypt @ K3 @ A3) @ (analz @ H)) => (~ ((member_msg @ (key @ (invKey @ K3)) @ (analz @ H))))))))))))))). % analz.cases
thf(fact_185_analz_Osimps, axiom,
    ((![A3 : msg, H : set_msg]: ((member_msg @ A3 @ (analz @ H)) = (((?[X9 : msg]: (((A3 = X9)) & ((member_msg @ X9 @ H))))) | ((((?[X9 : msg]: (?[Y6 : msg]: (((A3 = X9)) & ((member_msg @ (mPair @ X9 @ Y6) @ (analz @ H))))))) | ((((?[X9 : msg]: (?[Y6 : msg]: (((A3 = Y6)) & ((member_msg @ (mPair @ X9 @ Y6) @ (analz @ H))))))) | ((?[K4 : nat]: (?[X9 : msg]: (((A3 = X9)) & ((((member_msg @ (crypt @ K4 @ X9) @ (analz @ H))) & ((member_msg @ (key @ (invKey @ K4)) @ (analz @ H)))))))))))))))))). % analz.simps
thf(fact_186_analz_Oinducts, axiom,
    ((![X2 : msg, H : set_msg, P : msg > $o]: ((member_msg @ X2 @ (analz @ H)) => ((![X7 : msg]: ((member_msg @ X7 @ H) => (P @ X7))) => ((![X7 : msg, Y5 : msg]: ((member_msg @ (mPair @ X7 @ Y5) @ (analz @ H)) => ((P @ (mPair @ X7 @ Y5)) => (P @ X7)))) => ((![X7 : msg, Y5 : msg]: ((member_msg @ (mPair @ X7 @ Y5) @ (analz @ H)) => ((P @ (mPair @ X7 @ Y5)) => (P @ Y5)))) => ((![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 @ X2))))))))). % analz.inducts
thf(fact_187_A__trusts__NS4, axiom,
    ((![K : nat, NB : nat, Evs : list_event, A : agent, NA2 : msg, B : agent, X : msg]: ((member_msg @ (crypt @ K @ (nonce @ NB)) @ (parts @ (knows @ spy @ Evs))) => ((member_msg @ (crypt @ (shrK @ A) @ (mPair @ NA2 @ (mPair @ (agent2 @ B) @ (mPair @ (key @ K) @ X)))) @ (parts @ (knows @ spy @ Evs))) => ((![NB2 : msg]: (~ ((member_event @ (notes @ spy @ (mPair @ NA2 @ (mPair @ NB2 @ (key @ K)))) @ (set_event2 @ Evs))))) => ((~ ((member_agent @ A @ bad))) => ((~ ((member_agent @ B @ bad))) => ((member_list_event @ Evs @ nS_Sha1061662329shared) => (member_event @ (says @ B @ A @ (crypt @ K @ (nonce @ NB))) @ (set_event2 @ Evs))))))))))). % A_trusts_NS4
thf(fact_188_B__trusts__NS5__lemma, axiom,
    ((![B : agent, Evs : list_event, K : nat, A : agent, NA2 : msg, NB : nat]: ((~ ((member_agent @ B @ bad))) => ((member_list_event @ Evs @ nS_Sha1061662329shared) => ((~ ((member_msg @ (key @ K) @ (analz @ (knows @ spy @ Evs))))) => ((member_event @ (says @ server @ A @ (crypt @ (shrK @ A) @ (mPair @ NA2 @ (mPair @ (agent2 @ B) @ (mPair @ (key @ K) @ (crypt @ (shrK @ B) @ (mPair @ (key @ K) @ (agent2 @ A)))))))) @ (set_event2 @ Evs)) => ((member_msg @ (crypt @ K @ (mPair @ (nonce @ NB) @ (nonce @ NB))) @ (parts @ (knows @ spy @ Evs))) => (member_event @ (says @ A @ B @ (crypt @ K @ (mPair @ (nonce @ NB) @ (nonce @ NB)))) @ (set_event2 @ Evs)))))))))). % B_trusts_NS5_lemma
thf(fact_189_secrecy__lemma, axiom,
    ((![A : agent, NA2 : msg, B : agent, K : nat, Evs : list_event]: ((member_event @ (says @ server @ A @ (crypt @ (shrK @ A) @ (mPair @ NA2 @ (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) => ((![NB2 : msg]: (~ ((member_event @ (notes @ spy @ (mPair @ NA2 @ (mPair @ NB2 @ (key @ K)))) @ (set_event2 @ Evs))))) => (~ ((member_msg @ (key @ K) @ (analz @ (knows @ spy @ Evs))))))))))))). % secrecy_lemma
thf(fact_190_NS4__implies__NS3, axiom,
    ((![Evs : list_event, K : nat, A : agent, NA2 : msg, B : agent, X : msg, NB : nat]: ((member_list_event @ Evs @ nS_Sha1061662329shared) => ((~ ((member_msg @ (key @ K) @ (analz @ (knows @ spy @ Evs))))) => ((member_event @ (says @ server @ A @ (crypt @ (shrK @ A) @ (mPair @ NA2 @ (mPair @ (agent2 @ B) @ (mPair @ (key @ K) @ X))))) @ (set_event2 @ Evs)) => ((member_msg @ (crypt @ K @ (nonce @ NB)) @ (parts @ (knows @ spy @ Evs))) => (?[A5 : agent]: (member_event @ (says @ A5 @ B @ X) @ (set_event2 @ Evs)))))))))). % NS4_implies_NS3
thf(fact_191_agent_Odistinct_I3_J, axiom,
    ((~ ((server = spy))))). % agent.distinct(3)
thf(fact_192_Server__not__bad, axiom,
    ((~ ((member_agent @ server @ bad))))). % Server_not_bad
thf(fact_193_Oops__parts__spies, axiom,
    ((![A : agent, NA2 : msg, B : msg, K : msg, X : msg, Evs : list_event]: ((member_event @ (says @ server @ A @ (crypt @ (shrK @ A) @ (mPair @ NA2 @ (mPair @ B @ (mPair @ K @ X))))) @ (set_event2 @ Evs)) => (member_msg @ K @ (parts @ (knows @ spy @ Evs))))))). % Oops_parts_spies
thf(fact_194_unique__session__keys, axiom,
    ((![A : agent, NA2 : msg, B : agent, K : nat, X : msg, Evs : list_event, A2 : agent, NA3 : msg, B4 : agent, X8 : msg]: ((member_event @ (says @ server @ A @ (crypt @ (shrK @ A) @ (mPair @ NA2 @ (mPair @ (agent2 @ B) @ (mPair @ (key @ K) @ X))))) @ (set_event2 @ Evs)) => ((member_event @ (says @ server @ A2 @ (crypt @ (shrK @ A2) @ (mPair @ NA3 @ (mPair @ (agent2 @ B4) @ (mPair @ (key @ K) @ X8))))) @ (set_event2 @ Evs)) => ((member_list_event @ Evs @ nS_Sha1061662329shared) => ((A = A2) & ((NA2 = NA3) & ((B = B4) & (X = X8)))))))))). % unique_session_keys
thf(fact_195_ns__shared_ONS3, axiom,
    ((![Evs3 : list_event, A : agent, S : agent, NA2 : 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 @ NA2) @ (mPair @ (agent2 @ B) @ (mPair @ (key @ K) @ X))))) @ (set_event2 @ Evs3)) => ((member_event @ (says @ A @ server @ (mPair @ (agent2 @ A) @ (mPair @ (agent2 @ B) @ (nonce @ NA2)))) @ (set_event2 @ Evs3)) => (member_list_event @ (cons_event @ (says @ A @ B @ X) @ Evs3) @ nS_Sha1061662329shared)))))))). % ns_shared.NS3
thf(fact_196_B__trusts__NS3, axiom,
    ((![B : agent, K : nat, A : agent, Evs : list_event]: ((member_msg @ (crypt @ (shrK @ B) @ (mPair @ (key @ K) @ (agent2 @ A))) @ (parts @ (knows @ spy @ Evs))) => ((~ ((member_agent @ B @ bad))) => ((member_list_event @ Evs @ nS_Sha1061662329shared) => (?[NA : msg]: (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))))))))). % B_trusts_NS3
thf(fact_197_A__trusts__NS2, axiom,
    ((![A : agent, NA2 : msg, B : agent, K : nat, X : msg, Evs : list_event]: ((member_msg @ (crypt @ (shrK @ A) @ (mPair @ NA2 @ (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 @ NA2 @ (mPair @ (agent2 @ B) @ (mPair @ (key @ K) @ X))))) @ (set_event2 @ Evs)))))))). % A_trusts_NS2

% Conjectures (6)
thf(conj_0, hypothesis,
    ((member_event @ (says @ b @ a @ (crypt @ k @ (nonce @ nb))) @ (set_event2 @ evs)))).
thf(conj_1, hypothesis,
    ((~ ((member_msg @ (key @ k) @ (analz @ (knows @ spy @ evs))))))).
thf(conj_2, hypothesis,
    ((~ ((member_agent @ a @ bad))))).
thf(conj_3, hypothesis,
    ((~ ((member_agent @ b @ bad))))).
thf(conj_4, hypothesis,
    ((member_list_event @ evs @ nS_Sha1061662329shared))).
thf(conj_5, conjecture,
    ((nS_Sha1425748201Issues @ b @ a @ (crypt @ k @ (nonce @ nb)) @ evs))).
