% 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_272__5230246_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:24:07.676

% Could-be-implicit typings (14)
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__List__Olist_It__Nat__Onat_J, type,
    list_nat : $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 (56)
thf(sy_c_Event_Obad, type,
    bad : set_agent).
thf(sy_c_Event_Oevent_OGets, type,
    gets : agent > msg > event).
thf(sy_c_Event_Oevent_ONotes, type,
    notes : agent > msg > event).
thf(sy_c_Event_Oevent_OSays, type,
    says : agent > agent > msg > event).
thf(sy_c_Event_OinitState, type,
    initState : agent > set_msg).
thf(sy_c_Event_Oknows, type,
    knows : agent > list_event > set_msg).
thf(sy_c_Event_Oused, type,
    used : list_event > set_msg).
thf(sy_c_List_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_OCons_001t__Nat__Onat, type,
    cons_nat : nat > list_nat > list_nat).
thf(sy_c_List_Olist_Oset_001t__Event__Oevent, type,
    set_event2 : list_event > set_event).
thf(sy_c_List_Olist_Oset_001t__List__Olist_It__Event__Oevent_J, type,
    set_list_event2 : list_list_event > set_list_event).
thf(sy_c_List_Olist_Oset_001t__Message__Oagent, type,
    set_agent2 : list_agent > set_agent).
thf(sy_c_List_Olist_Oset_001t__Message__Omsg, type,
    set_msg2 : list_msg > set_msg).
thf(sy_c_List_Olist_Oset_001t__Nat__Onat, type,
    set_nat2 : list_nat > set_nat).
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_OkeysFor, type,
    keysFor : set_msg > set_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_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_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_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_A_H, type,
    a2 : agent).
thf(sy_v_Aa, type,
    aa : agent).
thf(sy_v_B, type,
    b : agent).
thf(sy_v_Ba, type,
    ba : agent).
thf(sy_v_K, type,
    k : nat).
thf(sy_v_KAB, type,
    kab : nat).
thf(sy_v_NA, type,
    na : msg).
thf(sy_v_NAa, type,
    nAa : nat).
thf(sy_v_evs2, type,
    evs2 : list_event).

% Relevant facts (185)
thf(fact_0_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_1_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_2_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_3_shrK__in__used, axiom,
    ((![A : agent, Evs : list_event]: (member_msg @ (key @ (shrK @ A)) @ (used @ Evs))))). % shrK_in_used
thf(fact_4_shrK__in__knows, axiom,
    ((![A : agent, Evs : list_event]: (member_msg @ (key @ (shrK @ A)) @ (knows @ A @ Evs))))). % shrK_in_knows
thf(fact_5_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_6_Spy__in__bad, axiom,
    ((member_agent @ spy @ bad))). % Spy_in_bad
thf(fact_7_sym__shrK, axiom,
    ((![X : agent]: (member_nat @ (shrK @ X) @ symKeys)))). % sym_shrK
thf(fact_8_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_9_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_10_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_11_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_12_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_13_ns__shared_ONS2, axiom,
    ((![Evs2 : list_event, KAB : nat, A2 : agent, A : agent, B : agent, NA : nat]: ((member_list_event @ Evs2 @ nS_Sha1061662329shared) => ((~ ((member_msg @ (key @ KAB) @ (used @ Evs2)))) => ((member_nat @ KAB @ symKeys) => ((member_event @ (says @ A2 @ server @ (mPair @ (agent2 @ A) @ (mPair @ (agent2 @ B) @ (nonce @ NA)))) @ (set_event2 @ Evs2)) => (member_list_event @ (cons_event @ (says @ server @ A @ (crypt @ (shrK @ A) @ (mPair @ (nonce @ NA) @ (mPair @ (agent2 @ B) @ (mPair @ (key @ KAB) @ (crypt @ (shrK @ B) @ (mPair @ (key @ KAB) @ (agent2 @ A)))))))) @ Evs2) @ nS_Sha1061662329shared)))))))). % ns_shared.NS2
thf(fact_14_shrK__injective, axiom,
    ((![X3 : agent, Y : agent]: (((shrK @ X3) = (shrK @ Y)) = (X3 = Y))))). % shrK_injective
thf(fact_15_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_16_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_17_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_18_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_19_symKeys__neq__imp__neq, axiom,
    ((![K : nat, K2 : nat]: ((~ (((member_nat @ K @ symKeys) = (member_nat @ K2 @ symKeys)))) => (~ ((K = K2))))))). % symKeys_neq_imp_neq
thf(fact_20_MPair__used__D, axiom,
    ((![X : msg, Y2 : msg, H : list_event]: ((member_msg @ (mPair @ X @ Y2) @ (used @ H)) => ((member_msg @ X @ (used @ H)) & (member_msg @ Y2 @ (used @ H))))))). % MPair_used_D
thf(fact_21_MPair__used, axiom,
    ((![X : msg, Y2 : msg, H : list_event]: ((member_msg @ (mPair @ X @ Y2) @ (used @ H)) => (~ (((member_msg @ X @ (used @ H)) => (~ ((member_msg @ Y2 @ (used @ H))))))))))). % MPair_used
thf(fact_22_Nonce__supply1, axiom,
    ((![Evs : list_event]: (?[N : nat]: (~ ((member_msg @ (nonce @ N) @ (used @ Evs)))))))). % Nonce_supply1
thf(fact_23_ns__shared_ONS1, axiom,
    ((![Evs1 : list_event, NA : nat, A : agent, B : agent]: ((member_list_event @ Evs1 @ nS_Sha1061662329shared) => ((~ ((member_msg @ (nonce @ NA) @ (used @ Evs1)))) => (member_list_event @ (cons_event @ (says @ A @ server @ (mPair @ (agent2 @ A) @ (mPair @ (agent2 @ B) @ (nonce @ NA)))) @ Evs1) @ nS_Sha1061662329shared)))))). % ns_shared.NS1
thf(fact_24_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_25_Server__not__bad, axiom,
    ((~ ((member_agent @ server @ bad))))). % Server_not_bad
thf(fact_26_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_27_ns__shared_ONS5, axiom,
    ((![Evs5 : list_event, K : nat, B2 : agent, A : agent, NB : 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 @ NB))) @ (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 @ NB) @ (nonce @ NB)))) @ Evs5) @ nS_Sha1061662329shared)))))))). % ns_shared.NS5
thf(fact_28_analz__impI, axiom,
    ((![Y2 : msg, Evs : list_event, Q : $o]: (((~ ((member_msg @ Y2 @ (analz @ (knows @ spy @ Evs))))) => Q) => ((~ ((member_msg @ Y2 @ (analz @ (knows @ spy @ Evs))))) => Q))))). % analz_impI
thf(fact_29_shrK__neq, axiom,
    ((![K : nat, Evs : list_event, B : agent]: ((~ ((member_msg @ (key @ K) @ (used @ Evs)))) => (~ (((shrK @ B) = K))))))). % shrK_neq
thf(fact_30_neq__shrK, axiom,
    ((![S2 : nat, Evs : list_event, B : agent]: ((~ ((member_msg @ (key @ S2) @ (used @ Evs)))) => (~ ((S2 = (shrK @ B)))))))). % neq_shrK
thf(fact_31_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_32_Says__imp__used, axiom,
    ((![A : agent, B : agent, X : msg, Evs : list_event]: ((member_event @ (says @ A @ B @ X) @ (set_event2 @ Evs)) => (member_msg @ X @ (used @ Evs)))))). % Says_imp_used
thf(fact_33_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_34_ns__shared_ONS4, axiom,
    ((![Evs4 : list_event, NB : nat, K : nat, A2 : agent, B : agent, A : agent]: ((member_list_event @ Evs4 @ nS_Sha1061662329shared) => ((~ ((member_msg @ (nonce @ NB) @ (used @ Evs4)))) => ((member_nat @ K @ symKeys) => ((member_event @ (says @ A2 @ B @ (crypt @ (shrK @ B) @ (mPair @ (key @ K) @ (agent2 @ A)))) @ (set_event2 @ Evs4)) => (member_list_event @ (cons_event @ (says @ B @ A @ (crypt @ K @ (nonce @ NB))) @ Evs4) @ nS_Sha1061662329shared)))))))). % ns_shared.NS4
thf(fact_35_Notes__imp__used, axiom,
    ((![A : agent, X : msg, Evs : list_event]: ((member_event @ (notes @ A @ X) @ (set_event2 @ Evs)) => (member_msg @ X @ (used @ Evs)))))). % Notes_imp_used
thf(fact_36_ns__shared_OOops, axiom,
    ((![Evso : list_event, B : agent, A : agent, K : nat, NB : nat, NA : nat, X : msg]: ((member_list_event @ Evso @ nS_Sha1061662329shared) => ((member_event @ (says @ B @ A @ (crypt @ K @ (nonce @ NB))) @ (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 @ NB) @ (key @ K)))) @ Evso) @ nS_Sha1061662329shared))))))). % ns_shared.Oops
thf(fact_37_ns__sharedp_ONS2, axiom,
    ((![Evs2 : list_event, KAB : nat, A2 : agent, A : agent, B : agent, NA : nat]: ((nS_Sha1092415543haredp @ Evs2) => ((~ ((member_msg @ (key @ KAB) @ (used @ Evs2)))) => ((member_nat @ KAB @ symKeys) => ((member_event @ (says @ A2 @ server @ (mPair @ (agent2 @ A) @ (mPair @ (agent2 @ B) @ (nonce @ NA)))) @ (set_event2 @ Evs2)) => (nS_Sha1092415543haredp @ (cons_event @ (says @ server @ A @ (crypt @ (shrK @ A) @ (mPair @ (nonce @ NA) @ (mPair @ (agent2 @ B) @ (mPair @ (key @ KAB) @ (crypt @ (shrK @ B) @ (mPair @ (key @ KAB) @ (agent2 @ A)))))))) @ Evs2))))))))). % ns_sharedp.NS2
thf(fact_38_ns__sharedp_OOops, axiom,
    ((![Evso : list_event, B : agent, A : agent, K : nat, NB : nat, NA : nat, X : msg]: ((nS_Sha1092415543haredp @ Evso) => ((member_event @ (says @ B @ A @ (crypt @ K @ (nonce @ NB))) @ (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 @ NB) @ (key @ K)))) @ Evso)))))))). % ns_sharedp.Oops
thf(fact_39_ns__sharedp_ONS4, axiom,
    ((![Evs4 : list_event, NB : nat, K : nat, A2 : agent, B : agent, A : agent]: ((nS_Sha1092415543haredp @ Evs4) => ((~ ((member_msg @ (nonce @ NB) @ (used @ Evs4)))) => ((member_nat @ K @ symKeys) => ((member_event @ (says @ A2 @ B @ (crypt @ (shrK @ B) @ (mPair @ (key @ K) @ (agent2 @ A)))) @ (set_event2 @ Evs4)) => (nS_Sha1092415543haredp @ (cons_event @ (says @ B @ A @ (crypt @ K @ (nonce @ NB))) @ Evs4))))))))). % ns_sharedp.NS4
thf(fact_40_ns__sharedp_ONS5, axiom,
    ((![Evs5 : list_event, K : nat, B2 : agent, A : agent, NB : nat, S : agent, NA : nat, B : agent, X : msg]: ((nS_Sha1092415543haredp @ Evs5) => ((member_nat @ K @ symKeys) => ((member_event @ (says @ B2 @ A @ (crypt @ K @ (nonce @ NB))) @ (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 @ NB) @ (nonce @ NB)))) @ Evs5))))))))). % ns_sharedp.NS5
thf(fact_41_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_42_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_43_ns__sharedp_ONS1, axiom,
    ((![Evs1 : list_event, NA : nat, A : agent, B : agent]: ((nS_Sha1092415543haredp @ Evs1) => ((~ ((member_msg @ (nonce @ NA) @ (used @ Evs1)))) => (nS_Sha1092415543haredp @ (cons_event @ (says @ A @ server @ (mPair @ (agent2 @ A) @ (mPair @ (agent2 @ B) @ (nonce @ NA)))) @ Evs1))))))). % ns_sharedp.NS1
thf(fact_44_analz__trivial, axiom,
    ((![H : set_msg]: ((![X4 : msg, Y3 : msg]: (~ ((member_msg @ (mPair @ X4 @ Y3) @ H)))) => ((![X4 : msg, K3 : nat]: (~ ((member_msg @ (crypt @ K3 @ X4) @ H)))) => ((analz @ H) = H)))))). % analz_trivial
thf(fact_45_mem__Collect__eq, axiom,
    ((![A3 : agent, P : agent > $o]: ((member_agent @ A3 @ (collect_agent @ P)) = (P @ A3))))). % mem_Collect_eq
thf(fact_46_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_47_mem__Collect__eq, axiom,
    ((![A3 : event, P : event > $o]: ((member_event @ A3 @ (collect_event @ P)) = (P @ A3))))). % mem_Collect_eq
thf(fact_48_mem__Collect__eq, axiom,
    ((![A3 : msg, P : msg > $o]: ((member_msg @ A3 @ (collect_msg @ 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_agent]: ((collect_agent @ (^[X5 : agent]: (member_agent @ X5 @ A))) = A)))). % Collect_mem_eq
thf(fact_51_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_52_Collect__mem__eq, axiom,
    ((![A : set_event]: ((collect_event @ (^[X5 : event]: (member_event @ X5 @ A))) = A)))). % Collect_mem_eq
thf(fact_53_Collect__mem__eq, axiom,
    ((![A : set_msg]: ((collect_msg @ (^[X5 : msg]: (member_msg @ X5 @ A))) = A)))). % Collect_mem_eq
thf(fact_54_Collect__mem__eq, axiom,
    ((![A : set_nat]: ((collect_nat @ (^[X5 : nat]: (member_nat @ X5 @ A))) = A)))). % Collect_mem_eq
thf(fact_55_msg_Oinject_I1_J, axiom,
    ((![X1 : agent, Y1 : agent]: (((agent2 @ X1) = (agent2 @ Y1)) = (X1 = Y1))))). % msg.inject(1)
thf(fact_56_msg_Oinject_I3_J, axiom,
    ((![X33 : nat, Y33 : nat]: (((nonce @ X33) = (nonce @ Y33)) = (X33 = Y33))))). % msg.inject(3)
thf(fact_57_analz__idem, axiom,
    ((![H : set_msg]: ((analz @ (analz @ H)) = (analz @ H))))). % analz_idem
thf(fact_58_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_59_parts__idem, axiom,
    ((![H : set_msg]: ((parts @ (parts @ H)) = (parts @ H))))). % parts_idem
thf(fact_60_msg_Oinject_I4_J, axiom,
    ((![X42 : nat, Y4 : nat]: (((key @ X42) = (key @ Y4)) = (X42 = Y4))))). % msg.inject(4)
thf(fact_61_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_62_analz__parts, axiom,
    ((![H : set_msg]: ((analz @ (parts @ H)) = (parts @ H))))). % analz_parts
thf(fact_63_parts__analz, axiom,
    ((![H : set_msg]: ((parts @ (analz @ H)) = (parts @ H))))). % parts_analz
thf(fact_64_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_65_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_66_usedI, axiom,
    ((![C : msg, Evs : list_event]: ((member_msg @ C @ (parts @ (knows @ spy @ Evs))) => (member_msg @ C @ (used @ Evs)))))). % usedI
thf(fact_67_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_68_parts__partsD, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ (parts @ (parts @ H))) => (member_msg @ X @ (parts @ H)))))). % parts_partsD
thf(fact_69_parts_OInj, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ H) => (member_msg @ X @ (parts @ H)))))). % parts.Inj
thf(fact_70_analz__into__parts, axiom,
    ((![C : msg, H : set_msg]: ((member_msg @ C @ (analz @ H)) => (member_msg @ C @ (parts @ H)))))). % analz_into_parts
thf(fact_71_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_72_parts_OFst, axiom,
    ((![X : msg, Y2 : msg, H : set_msg]: ((member_msg @ (mPair @ X @ Y2) @ (parts @ H)) => (member_msg @ X @ (parts @ H)))))). % parts.Fst
thf(fact_73_parts_OSnd, axiom,
    ((![X : msg, Y2 : msg, H : set_msg]: ((member_msg @ (mPair @ X @ Y2) @ (parts @ H)) => (member_msg @ Y2 @ (parts @ H)))))). % parts.Snd
thf(fact_74_MPair__parts, axiom,
    ((![X : msg, Y2 : msg, H : set_msg]: ((member_msg @ (mPair @ X @ Y2) @ (parts @ H)) => (~ (((member_msg @ X @ (parts @ H)) => (~ ((member_msg @ Y2 @ (parts @ H))))))))))). % MPair_parts
thf(fact_75_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_76_parts_Ocases, axiom,
    ((![A3 : msg, H : set_msg]: ((member_msg @ A3 @ (parts @ H)) => ((~ ((member_msg @ A3 @ H))) => ((![Y3 : msg]: (~ ((member_msg @ (mPair @ A3 @ Y3) @ (parts @ H))))) => ((![X4 : msg]: (~ ((member_msg @ (mPair @ X4 @ A3) @ (parts @ H))))) => (~ ((![K3 : nat]: (~ ((member_msg @ (crypt @ K3 @ A3) @ (parts @ H)))))))))))))). % parts.cases
thf(fact_77_parts_Osimps, axiom,
    ((![A3 : msg, H : set_msg]: ((member_msg @ A3 @ (parts @ H)) = (((?[X6 : msg]: (((A3 = X6)) & ((member_msg @ X6 @ H))))) | ((((?[X6 : msg]: (?[Y5 : msg]: (((A3 = X6)) & ((member_msg @ (mPair @ X6 @ Y5) @ (parts @ H))))))) | ((((?[X6 : msg]: (?[Y5 : msg]: (((A3 = Y5)) & ((member_msg @ (mPair @ X6 @ Y5) @ (parts @ H))))))) | ((?[K4 : nat]: (?[X6 : msg]: (((A3 = X6)) & ((member_msg @ (crypt @ K4 @ X6) @ (parts @ H)))))))))))))))). % parts.simps
thf(fact_78_parts_Oinducts, axiom,
    ((![X3 : msg, H : set_msg, P : msg > $o]: ((member_msg @ X3 @ (parts @ H)) => ((![X4 : msg]: ((member_msg @ X4 @ H) => (P @ X4))) => ((![X4 : msg, Y3 : msg]: ((member_msg @ (mPair @ X4 @ Y3) @ (parts @ H)) => ((P @ (mPair @ X4 @ Y3)) => (P @ X4)))) => ((![X4 : msg, Y3 : msg]: ((member_msg @ (mPair @ X4 @ Y3) @ (parts @ H)) => ((P @ (mPair @ X4 @ Y3)) => (P @ Y3)))) => ((![K3 : nat, X4 : msg]: ((member_msg @ (crypt @ K3 @ X4) @ (parts @ H)) => ((P @ (crypt @ K3 @ X4)) => (P @ X4)))) => (P @ X3))))))))). % parts.inducts
thf(fact_79_ns__sharedp__ns__shared__eq, axiom,
    ((nS_Sha1092415543haredp = (^[X5 : list_event]: (member_list_event @ X5 @ nS_Sha1061662329shared))))). % ns_sharedp_ns_shared_eq
thf(fact_80_analz_OInj, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ H) => (member_msg @ X @ (analz @ H)))))). % analz.Inj
thf(fact_81_analz__analzD, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ (analz @ (analz @ H))) => (member_msg @ X @ (analz @ H)))))). % analz_analzD
thf(fact_82_NS3__msg__in__parts__spies, axiom,
    ((![S : agent, A : agent, KA : nat, N2 : msg, B : msg, K : msg, X : msg, Evs : list_event]: ((member_event @ (says @ S @ A @ (crypt @ KA @ (mPair @ N2 @ (mPair @ B @ (mPair @ K @ X))))) @ (set_event2 @ Evs)) => (member_msg @ X @ (parts @ (knows @ spy @ Evs))))))). % NS3_msg_in_parts_spies
thf(fact_83_analz_OFst, axiom,
    ((![X : msg, Y2 : msg, H : set_msg]: ((member_msg @ (mPair @ X @ Y2) @ (analz @ H)) => (member_msg @ X @ (analz @ H)))))). % analz.Fst
thf(fact_84_analz_OSnd, axiom,
    ((![X : msg, Y2 : msg, H : set_msg]: ((member_msg @ (mPair @ X @ Y2) @ (analz @ H)) => (member_msg @ Y2 @ (analz @ H)))))). % analz.Snd
thf(fact_85_MPair__analz, axiom,
    ((![X : msg, Y2 : msg, H : set_msg]: ((member_msg @ (mPair @ X @ Y2) @ (analz @ H)) => (~ (((member_msg @ X @ (analz @ H)) => (~ ((member_msg @ Y2 @ (analz @ H))))))))))). % MPair_analz
thf(fact_86_msg_Odistinct_I33_J, axiom,
    ((![X42 : nat, X61 : msg, X62 : msg]: (~ (((key @ X42) = (mPair @ X61 @ X62))))))). % msg.distinct(33)
thf(fact_87_msg_Odistinct_I41_J, axiom,
    ((![X61 : msg, X62 : msg, X71 : nat, X72 : msg]: (~ (((mPair @ X61 @ X62) = (crypt @ X71 @ X72))))))). % msg.distinct(41)
thf(fact_88_msg_Odistinct_I35_J, axiom,
    ((![X42 : nat, X71 : nat, X72 : msg]: (~ (((key @ X42) = (crypt @ X71 @ X72))))))). % msg.distinct(35)
thf(fact_89_msg_Odistinct_I27_J, axiom,
    ((![X33 : nat, X61 : msg, X62 : msg]: (~ (((nonce @ X33) = (mPair @ X61 @ X62))))))). % msg.distinct(27)
thf(fact_90_msg_Odistinct_I9_J, axiom,
    ((![X1 : agent, X61 : msg, X62 : msg]: (~ (((agent2 @ X1) = (mPair @ X61 @ X62))))))). % msg.distinct(9)
thf(fact_91_msg_Odistinct_I23_J, axiom,
    ((![X33 : nat, X42 : nat]: (~ (((nonce @ X33) = (key @ X42))))))). % msg.distinct(23)
thf(fact_92_msg_Odistinct_I5_J, axiom,
    ((![X1 : agent, X42 : nat]: (~ (((agent2 @ X1) = (key @ X42))))))). % msg.distinct(5)
thf(fact_93_msg_Odistinct_I29_J, axiom,
    ((![X33 : nat, X71 : nat, X72 : msg]: (~ (((nonce @ X33) = (crypt @ X71 @ X72))))))). % msg.distinct(29)
thf(fact_94_msg_Odistinct_I11_J, axiom,
    ((![X1 : agent, X71 : nat, X72 : msg]: (~ (((agent2 @ X1) = (crypt @ X71 @ X72))))))). % msg.distinct(11)
thf(fact_95_msg_Odistinct_I3_J, axiom,
    ((![X1 : agent, X33 : nat]: (~ (((agent2 @ X1) = (nonce @ X33))))))). % msg.distinct(3)
thf(fact_96_agent_Odistinct_I3_J, axiom,
    ((~ ((server = spy))))). % agent.distinct(3)
thf(fact_97_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_98_new__keys__not__used, axiom,
    ((![K : nat, Evs : list_event]: ((~ ((member_msg @ (key @ K) @ (used @ Evs)))) => ((member_nat @ K @ symKeys) => ((member_list_event @ Evs @ nS_Sha1061662329shared) => (~ ((member_nat @ K @ (keysFor @ (parts @ (knows @ spy @ Evs)))))))))))). % new_keys_not_used
thf(fact_99_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_100_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_101_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_102_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_103_list_Oset__intros_I2_J, axiom,
    ((![Y : agent, X22 : list_agent, X21 : agent]: ((member_agent @ Y @ (set_agent2 @ X22)) => (member_agent @ Y @ (set_agent2 @ (cons_agent @ X21 @ X22))))))). % list.set_intros(2)
thf(fact_104_list_Oset__intros_I2_J, axiom,
    ((![Y : list_event, X22 : list_list_event, X21 : list_event]: ((member_list_event @ Y @ (set_list_event2 @ X22)) => (member_list_event @ Y @ (set_list_event2 @ (cons_list_event @ X21 @ X22))))))). % list.set_intros(2)
thf(fact_105_list_Oset__intros_I2_J, axiom,
    ((![Y : msg, X22 : list_msg, X21 : msg]: ((member_msg @ Y @ (set_msg2 @ X22)) => (member_msg @ Y @ (set_msg2 @ (cons_msg @ X21 @ X22))))))). % list.set_intros(2)
thf(fact_106_list_Oset__intros_I2_J, axiom,
    ((![Y : nat, X22 : list_nat, X21 : nat]: ((member_nat @ Y @ (set_nat2 @ X22)) => (member_nat @ Y @ (set_nat2 @ (cons_nat @ X21 @ X22))))))). % list.set_intros(2)
thf(fact_107_list_Oset__intros_I2_J, axiom,
    ((![Y : event, X22 : list_event, X21 : event]: ((member_event @ Y @ (set_event2 @ X22)) => (member_event @ Y @ (set_event2 @ (cons_event @ X21 @ X22))))))). % list.set_intros(2)
thf(fact_108_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_109_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_110_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_111_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_112_analz__insert__MPair, axiom,
    ((![X : msg, Y2 : msg, H : set_msg]: ((analz @ (insert_msg @ (mPair @ X @ Y2) @ H)) = (insert_msg @ (mPair @ X @ Y2) @ (analz @ (insert_msg @ X @ (insert_msg @ Y2 @ H)))))))). % analz_insert_MPair
thf(fact_113_parts__insert__MPair, axiom,
    ((![X : msg, Y2 : msg, H : set_msg]: ((parts @ (insert_msg @ (mPair @ X @ Y2) @ H)) = (insert_msg @ (mPair @ X @ Y2) @ (parts @ (insert_msg @ X @ (insert_msg @ Y2 @ H)))))))). % parts_insert_MPair
thf(fact_114_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_115_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_116_analz__insert__Nonce, axiom,
    ((![N2 : nat, H : set_msg]: ((analz @ (insert_msg @ (nonce @ N2) @ H)) = (insert_msg @ (nonce @ N2) @ (analz @ H)))))). % analz_insert_Nonce
thf(fact_117_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_118_parts__insert__Nonce, axiom,
    ((![N2 : nat, H : set_msg]: ((parts @ (insert_msg @ (nonce @ N2) @ H)) = (insert_msg @ (nonce @ N2) @ (parts @ H)))))). % parts_insert_Nonce
thf(fact_119_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_120_keysFor__insert__MPair, axiom,
    ((![X : msg, Y2 : msg, H : set_msg]: ((keysFor @ (insert_msg @ (mPair @ X @ Y2) @ H)) = (keysFor @ H))))). % keysFor_insert_MPair
thf(fact_121_keysFor__insert__Key, axiom,
    ((![K : nat, H : set_msg]: ((keysFor @ (insert_msg @ (key @ K) @ H)) = (keysFor @ H))))). % keysFor_insert_Key
thf(fact_122_keysFor__insert__Nonce, axiom,
    ((![N2 : nat, H : set_msg]: ((keysFor @ (insert_msg @ (nonce @ N2) @ H)) = (keysFor @ H))))). % keysFor_insert_Nonce
thf(fact_123_keysFor__insert__Agent, axiom,
    ((![A : agent, H : set_msg]: ((keysFor @ (insert_msg @ (agent2 @ A) @ H)) = (keysFor @ H))))). % keysFor_insert_Agent
thf(fact_124_shrK__in__initState, axiom,
    ((![A : agent]: (member_msg @ (key @ (shrK @ A)) @ (initState @ A))))). % shrK_in_initState
thf(fact_125_used__Gets, axiom,
    ((![A : agent, X : msg, Evs : list_event]: ((used @ (cons_event @ (gets @ A @ X) @ Evs)) = (used @ Evs))))). % used_Gets
thf(fact_126_analz__insert__Key, axiom,
    ((![K : nat, H : set_msg]: ((~ ((member_nat @ K @ (keysFor @ (analz @ H))))) => ((analz @ (insert_msg @ (key @ K) @ H)) = (insert_msg @ (key @ K) @ (analz @ H))))))). % analz_insert_Key
thf(fact_127_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_128_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_129_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_130_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_131_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_132_analz__cut, axiom,
    ((![Y2 : msg, X : msg, H : set_msg]: ((member_msg @ Y2 @ (analz @ (insert_msg @ X @ H))) => ((member_msg @ X @ (analz @ H)) => (member_msg @ Y2 @ (analz @ H))))))). % analz_cut
thf(fact_133_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_134_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_135_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_136_event_Odistinct_I5_J, axiom,
    ((![X21 : agent, X22 : msg, X31 : agent, X32 : msg]: (~ (((gets @ X21 @ X22) = (notes @ X31 @ X32))))))). % event.distinct(5)
thf(fact_137_pushKeys_I5_J, axiom,
    ((![K : nat, X : msg, Y2 : msg, A : set_msg]: ((insert_msg @ (key @ K) @ (insert_msg @ (mPair @ X @ Y2) @ A)) = (insert_msg @ (mPair @ X @ Y2) @ (insert_msg @ (key @ K) @ A)))))). % pushKeys(5)
thf(fact_138_pushCrypts_I6_J, axiom,
    ((![X : nat, K : msg, X2 : msg, Y2 : msg, A : set_msg]: ((insert_msg @ (crypt @ X @ K) @ (insert_msg @ (mPair @ X2 @ Y2) @ A)) = (insert_msg @ (mPair @ X2 @ Y2) @ (insert_msg @ (crypt @ X @ K) @ A)))))). % pushCrypts(6)
thf(fact_139_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_140_pushKeys_I2_J, axiom,
    ((![K : nat, N2 : nat, A : set_msg]: ((insert_msg @ (key @ K) @ (insert_msg @ (nonce @ N2) @ A)) = (insert_msg @ (nonce @ N2) @ (insert_msg @ (key @ K) @ A)))))). % pushKeys(2)
thf(fact_141_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_142_pushCrypts_I3_J, axiom,
    ((![X : nat, K : msg, N2 : nat, A : set_msg]: ((insert_msg @ (crypt @ X @ K) @ (insert_msg @ (nonce @ N2) @ A)) = (insert_msg @ (nonce @ N2) @ (insert_msg @ (crypt @ X @ K) @ A)))))). % pushCrypts(3)
thf(fact_143_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_144_Crypt__imp__keysFor, axiom,
    ((![K : nat, X : msg, H : set_msg]: ((member_msg @ (crypt @ K @ X) @ H) => ((member_nat @ K @ symKeys) => (member_nat @ K @ (keysFor @ H))))))). % Crypt_imp_keysFor
thf(fact_145_not__Cons__self2, axiom,
    ((![X3 : event, Xs : list_event]: (~ (((cons_event @ X3 @ Xs) = Xs)))))). % not_Cons_self2
thf(fact_146_Crypt__notin__initState, axiom,
    ((![K : nat, X : msg, B : agent]: (~ ((member_msg @ (crypt @ K @ X) @ (parts @ (initState @ B)))))))). % Crypt_notin_initState
thf(fact_147_Nonce__notin__initState, axiom,
    ((![N2 : nat, B : agent]: (~ ((member_msg @ (nonce @ N2) @ (parts @ (initState @ B)))))))). % Nonce_notin_initState
thf(fact_148_initState__into__used, axiom,
    ((![X : msg, B : agent, Evs : list_event]: ((member_msg @ X @ (parts @ (initState @ B))) => (member_msg @ X @ (used @ Evs)))))). % initState_into_used
thf(fact_149_event_Oexhaust, axiom,
    ((![Y : event]: ((![X112 : agent, X122 : agent, X132 : msg]: (~ ((Y = (says @ X112 @ X122 @ X132))))) => ((![X212 : agent, X222 : msg]: (~ ((Y = (gets @ X212 @ X222))))) => (~ ((![X312 : agent, X322 : msg]: (~ ((Y = (notes @ X312 @ X322)))))))))))). % event.exhaust
thf(fact_150_event_Oinduct, axiom,
    ((![P : event > $o, Event : event]: ((![X14 : agent, X23 : agent, X34 : msg]: (P @ (says @ X14 @ X23 @ X34))) => ((![X14 : agent, X23 : msg]: (P @ (gets @ X14 @ X23))) => ((![X14 : agent, X23 : msg]: (P @ (notes @ X14 @ X23))) => (P @ Event))))))). % event.induct
thf(fact_151_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_152_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_153_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_154_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_155_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_156_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_157_list_Oset__cases, axiom,
    ((![E : nat, A3 : list_nat]: ((member_nat @ E @ (set_nat2 @ A3)) => ((![Z2 : list_nat]: (~ ((A3 = (cons_nat @ E @ Z2))))) => (~ ((![Z1 : nat, Z2 : list_nat]: ((A3 = (cons_nat @ Z1 @ Z2)) => (~ ((member_nat @ E @ (set_nat2 @ Z2))))))))))))). % list.set_cases
thf(fact_158_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_159_set__ConsD, axiom,
    ((![Y : agent, X3 : agent, Xs : list_agent]: ((member_agent @ Y @ (set_agent2 @ (cons_agent @ X3 @ Xs))) => ((Y = X3) | (member_agent @ Y @ (set_agent2 @ Xs))))))). % set_ConsD
thf(fact_160_set__ConsD, axiom,
    ((![Y : list_event, X3 : list_event, Xs : list_list_event]: ((member_list_event @ Y @ (set_list_event2 @ (cons_list_event @ X3 @ Xs))) => ((Y = X3) | (member_list_event @ Y @ (set_list_event2 @ Xs))))))). % set_ConsD
thf(fact_161_set__ConsD, axiom,
    ((![Y : msg, X3 : msg, Xs : list_msg]: ((member_msg @ Y @ (set_msg2 @ (cons_msg @ X3 @ Xs))) => ((Y = X3) | (member_msg @ Y @ (set_msg2 @ Xs))))))). % set_ConsD
thf(fact_162_set__ConsD, axiom,
    ((![Y : nat, X3 : nat, Xs : list_nat]: ((member_nat @ Y @ (set_nat2 @ (cons_nat @ X3 @ Xs))) => ((Y = X3) | (member_nat @ Y @ (set_nat2 @ Xs))))))). % set_ConsD
thf(fact_163_set__ConsD, axiom,
    ((![Y : event, X3 : event, Xs : list_event]: ((member_event @ Y @ (set_event2 @ (cons_event @ X3 @ Xs))) => ((Y = X3) | (member_event @ Y @ (set_event2 @ Xs))))))). % set_ConsD
thf(fact_164_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_165_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_166_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_167_list_Oset__intros_I1_J, axiom,
    ((![X21 : nat, X22 : list_nat]: (member_nat @ X21 @ (set_nat2 @ (cons_nat @ X21 @ X22)))))). % list.set_intros(1)
thf(fact_168_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_169_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_170_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_171_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_172_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_173_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_174_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_175_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_176_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_177_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_178_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_179_insert__absorb2, axiom,
    ((![X3 : msg, A : set_msg]: ((insert_msg @ X3 @ (insert_msg @ X3 @ A)) = (insert_msg @ X3 @ A))))). % insert_absorb2
thf(fact_180_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_181_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_182_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_183_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_184_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

% Conjectures (8)
thf(conj_0, hypothesis,
    ((~ ((member_agent @ a @ bad))))).
thf(conj_1, hypothesis,
    ((~ ((member_agent @ b @ bad))))).
thf(conj_2, hypothesis,
    ((member_list_event @ evs2 @ nS_Sha1061662329shared))).
thf(conj_3, hypothesis,
    (((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 @ evs2)) => ((![NB2 : msg]: (~ ((member_event @ (notes @ spy @ (mPair @ na @ (mPair @ NB2 @ (key @ k)))) @ (set_event2 @ evs2))))) => (~ ((member_msg @ (key @ k) @ (analz @ (knows @ spy @ evs2))))))))).
thf(conj_4, hypothesis,
    ((~ ((member_msg @ (key @ kab) @ (used @ evs2)))))).
thf(conj_5, hypothesis,
    ((member_nat @ kab @ symKeys))).
thf(conj_6, hypothesis,
    ((member_event @ (says @ a2 @ server @ (mPair @ (agent2 @ aa) @ (mPair @ (agent2 @ ba) @ (nonce @ nAa)))) @ (set_event2 @ evs2)))).
thf(conj_7, conjecture,
    (((((~ ((a = aa))) | ((~ ((na = (nonce @ nAa)))) | ((~ ((b = ba))) | ((~ ((k = kab))) | ((~ ((b = ba))) | ((~ ((k = kab))) | (~ ((a = aa))))))))) | ((?[NB3 : msg]: (member_event @ (notes @ spy @ (mPair @ (nonce @ nAa) @ (mPair @ NB3 @ (key @ kab)))) @ (set_event2 @ evs2))) | ((~ ((member_agent @ aa @ bad))) & (~ ((member_msg @ (key @ kab) @ (analz @ (knows @ spy @ evs2)))))))) & ((~ ((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 @ evs2)))) | ((?[NB3 : msg]: (member_event @ (notes @ spy @ (mPair @ na @ (mPair @ NB3 @ (key @ k)))) @ (set_event2 @ evs2))) | (((member_agent @ aa @ bad) & ((((shrK @ ba) = kab) & (~ ((k = kab)))) | (((member_agent @ ba @ bad) & (~ ((k = kab)))) | ((~ (((shrK @ ba) = kab))) & ((~ ((member_agent @ ba @ bad))) & (~ ((k = kab)))))))) | (~ ((member_agent @ aa @ bad))))))))).
