% 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_141__5229056_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:23:41.430

% Could-be-implicit typings (9)
thf(ty_n_t__Set__Oset_It__List__Olist_It__Event__Oevent_J_J, type,
    set_list_event : $tType).
thf(ty_n_t__Set__Oset_It__Message__Oagent_J, type,
    set_agent : $tType).
thf(ty_n_t__List__Olist_It__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__Nat__Onat_J, type,
    set_nat : $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__Nat__Onat, type,
    nat : $tType).

% Explicit typings (41)
thf(sy_c_Event_Obad, type,
    bad : set_agent).
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_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_OkeysFor, type,
    keysFor : set_msg > set_nat).
thf(sy_c_Message_Omsg_OCrypt, type,
    crypt : nat > msg > msg).
thf(sy_c_Message_Omsg_OKey, type,
    key : nat > msg).
thf(sy_c_Message_Oparts, type,
    parts : set_msg > set_msg).
thf(sy_c_Message_OsymKeys, type,
    symKeys : set_nat).
thf(sy_c_NS__Shared__Mirabelle__xwdrtqxrux_Ons__shared, type,
    nS_Sha1061662329shared : set_list_event).
thf(sy_c_NS__Shared__Mirabelle__xwdrtqxrux_Ons__sharedp, type,
    nS_Sha1092415543haredp : list_event > $o).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__List__Olist_It__Event__Oevent_J_J, type,
    bot_bo1693714908_event : set_list_event).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Message__Oagent_J, type,
    bot_bot_set_agent : set_agent).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Message__Omsg_J, type,
    bot_bot_set_msg : set_msg).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Nat__Onat_J, type,
    bot_bot_set_nat : set_nat).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__List__Olist_It__Event__Oevent_J_J, type,
    ord_le119303592_event : set_list_event > set_list_event > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Message__Oagent_J, type,
    ord_le722097072_agent : set_agent > set_agent > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Message__Omsg_J, type,
    ord_less_eq_set_msg : set_msg > set_msg > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Nat__Onat_J, type,
    ord_less_eq_set_nat : set_nat > set_nat > $o).
thf(sy_c_Public_Okeymode_OEncryption, type,
    encryption : keymode).
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__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__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_Set_Ois__empty_001t__Message__Omsg, type,
    is_empty_msg : set_msg > $o).
thf(sy_c_Set_Ois__empty_001t__Nat__Onat, type,
    is_empty_nat : set_nat > $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_K, type,
    k : nat).
thf(sy_v_evs, type,
    evs : list_event).

% Relevant facts (249)
thf(fact_0_usedI, axiom,
    ((![C : msg, Evs : list_event]: ((member_msg @ C @ (parts @ (knows @ spy @ Evs))) => (member_msg @ C @ (used @ Evs)))))). % usedI
thf(fact_1_msg_Oinject_I4_J, axiom,
    ((![X4 : nat, Y4 : nat]: (((key @ X4) = (key @ Y4)) = (X4 = Y4))))). % msg.inject(4)
thf(fact_2_parts__idem, axiom,
    ((![H : set_msg]: ((parts @ (parts @ H)) = (parts @ H))))). % parts_idem
thf(fact_3_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_4_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_5_parts_OInj, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ H) => (member_msg @ X @ (parts @ H)))))). % parts.Inj
thf(fact_6_parts__partsD, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ (parts @ (parts @ H))) => (member_msg @ X @ (parts @ H)))))). % parts_partsD
thf(fact_7_parts__knows__Spy__subset__used, axiom,
    ((![Evs : list_event]: (ord_less_eq_set_msg @ (parts @ (knows @ spy @ Evs)) @ (used @ Evs))))). % parts_knows_Spy_subset_used
thf(fact_8_spies__pubK, axiom,
    ((![B : keymode, A : agent, Evs : list_event]: (member_msg @ (key @ (publicKey @ B @ A)) @ (knows @ spy @ Evs))))). % spies_pubK
thf(fact_9_ns__sharedp__ns__shared__eq, axiom,
    ((nS_Sha1092415543haredp = (^[X2 : list_event]: (member_list_event @ X2 @ nS_Sha1061662329shared))))). % ns_sharedp_ns_shared_eq
thf(fact_10_initState__into__used, axiom,
    ((![X : msg, B2 : agent, Evs : list_event]: ((member_msg @ X @ (parts @ (initState @ B2))) => (member_msg @ X @ (used @ Evs)))))). % initState_into_used
thf(fact_11_shrK__in__used, axiom,
    ((![A : agent, Evs : list_event]: (member_msg @ (key @ (shrK @ A)) @ (used @ Evs))))). % shrK_in_used
thf(fact_12_shrK__injective, axiom,
    ((![X3 : agent, Y : agent]: (((shrK @ X3) = (shrK @ Y)) = (X3 = Y))))). % shrK_injective
thf(fact_13_publicKey__inject, axiom,
    ((![B : keymode, A : agent, C : keymode, A2 : agent]: (((publicKey @ B @ A) = (publicKey @ C @ A2)) = (((B = C)) & ((A = A2))))))). % publicKey_inject
thf(fact_14_parts__subset__iff, axiom,
    ((![G : set_msg, H : set_msg]: ((ord_less_eq_set_msg @ (parts @ G) @ (parts @ H)) = (ord_less_eq_set_msg @ G @ (parts @ H)))))). % parts_subset_iff
thf(fact_15_sym__shrK, axiom,
    ((![X : agent]: (member_nat @ (shrK @ X) @ symKeys)))). % sym_shrK
thf(fact_16_Spy__in__bad, axiom,
    ((member_agent @ spy @ bad))). % Spy_in_bad
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_publicKey__into__used, axiom,
    ((![B : keymode, A : agent, Evs : list_event]: (member_msg @ (key @ (publicKey @ B @ A)) @ (used @ Evs))))). % publicKey_into_used
thf(fact_19_publicKey__in__initState, axiom,
    ((![B : keymode, A : agent, B2 : agent]: (member_msg @ (key @ (publicKey @ B @ A)) @ (initState @ B2))))). % publicKey_in_initState
thf(fact_20_shrK__in__initState, axiom,
    ((![A : agent]: (member_msg @ (key @ (shrK @ A)) @ (initState @ A))))). % shrK_in_initState
thf(fact_21_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_22_shrK__neq__pubK, axiom,
    ((![B : keymode, C2 : agent, A : agent]: (~ (((publicKey @ B @ C2) = (shrK @ A))))))). % shrK_neq_pubK
thf(fact_23_injective__publicKey, axiom,
    ((![B : keymode, A : agent, C : keymode, A2 : agent]: (((publicKey @ B @ A) = (publicKey @ C @ A2)) => ((B = C) & (A = A2)))))). % injective_publicKey
thf(fact_24_initState__subset__knows, axiom,
    ((![A : agent, Evs : list_event]: (ord_less_eq_set_msg @ (initState @ A) @ (knows @ A @ Evs))))). % initState_subset_knows
thf(fact_25_parts__increasing, axiom,
    ((![H : set_msg]: (ord_less_eq_set_msg @ H @ (parts @ H))))). % parts_increasing
thf(fact_26_parts__trans, axiom,
    ((![X : msg, G : set_msg, H : set_msg]: ((member_msg @ X @ (parts @ G)) => ((ord_less_eq_set_msg @ G @ (parts @ H)) => (member_msg @ X @ (parts @ H))))))). % parts_trans
thf(fact_27_parts__mono, axiom,
    ((![G : set_msg, H : set_msg]: ((ord_less_eq_set_msg @ G @ H) => (ord_less_eq_set_msg @ (parts @ G) @ (parts @ H)))))). % parts_mono
thf(fact_28_not__symKeys__pubK, axiom,
    ((![B : keymode, A : agent]: (~ ((member_nat @ (publicKey @ B @ A) @ symKeys)))))). % not_symKeys_pubK
thf(fact_29_shrK__neq, axiom,
    ((![K : nat, Evs : list_event, B2 : agent]: ((~ ((member_msg @ (key @ K) @ (used @ Evs)))) => (~ (((shrK @ B2) = K))))))). % shrK_neq
thf(fact_30_neq__shrK, axiom,
    ((![S : nat, Evs : list_event, B2 : agent]: ((~ ((member_msg @ (key @ S) @ (used @ Evs)))) => (~ ((S = (shrK @ B2)))))))). % neq_shrK
thf(fact_31_subsetI, axiom,
    ((![A : set_list_event, B2 : set_list_event]: ((![X5 : list_event]: ((member_list_event @ X5 @ A) => (member_list_event @ X5 @ B2))) => (ord_le119303592_event @ A @ B2))))). % subsetI
thf(fact_32_subsetI, axiom,
    ((![A : set_agent, B2 : set_agent]: ((![X5 : agent]: ((member_agent @ X5 @ A) => (member_agent @ X5 @ B2))) => (ord_le722097072_agent @ A @ B2))))). % subsetI
thf(fact_33_subsetI, axiom,
    ((![A : set_msg, B2 : set_msg]: ((![X5 : msg]: ((member_msg @ X5 @ A) => (member_msg @ X5 @ B2))) => (ord_less_eq_set_msg @ A @ B2))))). % subsetI
thf(fact_34_subsetI, axiom,
    ((![A : set_nat, B2 : set_nat]: ((![X5 : nat]: ((member_nat @ X5 @ A) => (member_nat @ X5 @ B2))) => (ord_less_eq_set_nat @ A @ B2))))). % subsetI
thf(fact_35_subset__antisym, axiom,
    ((![A : set_msg, B2 : set_msg]: ((ord_less_eq_set_msg @ A @ B2) => ((ord_less_eq_set_msg @ B2 @ A) => (A = B2)))))). % subset_antisym
thf(fact_36_subset__antisym, axiom,
    ((![A : set_nat, B2 : set_nat]: ((ord_less_eq_set_nat @ A @ B2) => ((ord_less_eq_set_nat @ B2 @ A) => (A = B2)))))). % subset_antisym
thf(fact_37_order__refl, axiom,
    ((![X3 : set_msg]: (ord_less_eq_set_msg @ X3 @ X3)))). % order_refl
thf(fact_38_order__refl, axiom,
    ((![X3 : set_nat]: (ord_less_eq_set_nat @ X3 @ X3)))). % order_refl
thf(fact_39_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_40_Spy__spies__bad__privateKey, axiom,
    ((![A : agent, B : keymode, Evs : list_event]: ((member_agent @ A @ bad) => (member_msg @ (key @ (invKey @ (publicKey @ B @ A))) @ (knows @ spy @ Evs)))))). % Spy_spies_bad_privateKey
thf(fact_41_analz__spies__pubK, axiom,
    ((![B : keymode, A : agent, Evs : list_event]: (member_msg @ (key @ (publicKey @ B @ A)) @ (analz @ (knows @ spy @ Evs)))))). % analz_spies_pubK
thf(fact_42_keysFor__parts__initState, axiom,
    ((![C2 : agent]: ((keysFor @ (parts @ (initState @ C2))) = bot_bot_set_nat)))). % keysFor_parts_initState
thf(fact_43_priK__in__initState, axiom,
    ((![B : keymode, A : agent]: (member_msg @ (key @ (invKey @ (publicKey @ B @ A))) @ (initState @ A))))). % priK_in_initState
thf(fact_44_privateKey__into__used, axiom,
    ((![B : keymode, A : agent, Evs : list_event]: (member_msg @ (key @ (invKey @ (publicKey @ B @ A))) @ (used @ Evs))))). % privateKey_into_used
thf(fact_45_in__mono, axiom,
    ((![A : set_list_event, B2 : set_list_event, X3 : list_event]: ((ord_le119303592_event @ A @ B2) => ((member_list_event @ X3 @ A) => (member_list_event @ X3 @ B2)))))). % in_mono
thf(fact_46_in__mono, axiom,
    ((![A : set_agent, B2 : set_agent, X3 : agent]: ((ord_le722097072_agent @ A @ B2) => ((member_agent @ X3 @ A) => (member_agent @ X3 @ B2)))))). % in_mono
thf(fact_47_in__mono, axiom,
    ((![A : set_msg, B2 : set_msg, X3 : msg]: ((ord_less_eq_set_msg @ A @ B2) => ((member_msg @ X3 @ A) => (member_msg @ X3 @ B2)))))). % in_mono
thf(fact_48_in__mono, axiom,
    ((![A : set_nat, B2 : set_nat, X3 : nat]: ((ord_less_eq_set_nat @ A @ B2) => ((member_nat @ X3 @ A) => (member_nat @ X3 @ B2)))))). % in_mono
thf(fact_49_empty__Collect__eq, axiom,
    ((![P : nat > $o]: ((bot_bot_set_nat = (collect_nat @ P)) = (![X2 : nat]: (~ ((P @ X2)))))))). % empty_Collect_eq
thf(fact_50_empty__Collect__eq, axiom,
    ((![P : msg > $o]: ((bot_bot_set_msg = (collect_msg @ P)) = (![X2 : msg]: (~ ((P @ X2)))))))). % empty_Collect_eq
thf(fact_51_Collect__empty__eq, axiom,
    ((![P : nat > $o]: (((collect_nat @ P) = bot_bot_set_nat) = (![X2 : nat]: (~ ((P @ X2)))))))). % Collect_empty_eq
thf(fact_52_Collect__empty__eq, axiom,
    ((![P : msg > $o]: (((collect_msg @ P) = bot_bot_set_msg) = (![X2 : msg]: (~ ((P @ X2)))))))). % Collect_empty_eq
thf(fact_53_all__not__in__conv, axiom,
    ((![A : set_list_event]: ((![X2 : list_event]: (~ ((member_list_event @ X2 @ A)))) = (A = bot_bo1693714908_event))))). % all_not_in_conv
thf(fact_54_all__not__in__conv, axiom,
    ((![A : set_agent]: ((![X2 : agent]: (~ ((member_agent @ X2 @ A)))) = (A = bot_bot_set_agent))))). % all_not_in_conv
thf(fact_55_all__not__in__conv, axiom,
    ((![A : set_nat]: ((![X2 : nat]: (~ ((member_nat @ X2 @ A)))) = (A = bot_bot_set_nat))))). % all_not_in_conv
thf(fact_56_all__not__in__conv, axiom,
    ((![A : set_msg]: ((![X2 : msg]: (~ ((member_msg @ X2 @ A)))) = (A = bot_bot_set_msg))))). % all_not_in_conv
thf(fact_57_mem__Collect__eq, axiom,
    ((![A3 : msg, P : msg > $o]: ((member_msg @ A3 @ (collect_msg @ P)) = (P @ A3))))). % mem_Collect_eq
thf(fact_58_mem__Collect__eq, axiom,
    ((![A3 : nat, P : nat > $o]: ((member_nat @ A3 @ (collect_nat @ P)) = (P @ A3))))). % mem_Collect_eq
thf(fact_59_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_60_mem__Collect__eq, axiom,
    ((![A3 : agent, P : agent > $o]: ((member_agent @ A3 @ (collect_agent @ P)) = (P @ A3))))). % mem_Collect_eq
thf(fact_61_Collect__mem__eq, axiom,
    ((![A : set_msg]: ((collect_msg @ (^[X2 : msg]: (member_msg @ X2 @ A))) = A)))). % Collect_mem_eq
thf(fact_62_Collect__mem__eq, axiom,
    ((![A : set_nat]: ((collect_nat @ (^[X2 : nat]: (member_nat @ X2 @ A))) = A)))). % Collect_mem_eq
thf(fact_63_Collect__mem__eq, axiom,
    ((![A : set_list_event]: ((collect_list_event @ (^[X2 : list_event]: (member_list_event @ X2 @ A))) = A)))). % Collect_mem_eq
thf(fact_64_Collect__mem__eq, axiom,
    ((![A : set_agent]: ((collect_agent @ (^[X2 : agent]: (member_agent @ X2 @ A))) = A)))). % Collect_mem_eq
thf(fact_65_empty__iff, axiom,
    ((![C : list_event]: (~ ((member_list_event @ C @ bot_bo1693714908_event)))))). % empty_iff
thf(fact_66_empty__iff, axiom,
    ((![C : agent]: (~ ((member_agent @ C @ bot_bot_set_agent)))))). % empty_iff
thf(fact_67_empty__iff, axiom,
    ((![C : nat]: (~ ((member_nat @ C @ bot_bot_set_nat)))))). % empty_iff
thf(fact_68_empty__iff, axiom,
    ((![C : msg]: (~ ((member_msg @ C @ bot_bot_set_msg)))))). % empty_iff
thf(fact_69_analz__idem, axiom,
    ((![H : set_msg]: ((analz @ (analz @ H)) = (analz @ H))))). % analz_idem
thf(fact_70_invKey, axiom,
    ((![K : nat]: ((invKey @ (invKey @ K)) = K)))). % invKey
thf(fact_71_invKey__eq, axiom,
    ((![K : nat, K2 : nat]: (((invKey @ K) = (invKey @ K2)) = (K = K2))))). % invKey_eq
thf(fact_72_empty__subsetI, axiom,
    ((![A : set_msg]: (ord_less_eq_set_msg @ bot_bot_set_msg @ A)))). % empty_subsetI
thf(fact_73_empty__subsetI, axiom,
    ((![A : set_nat]: (ord_less_eq_set_nat @ bot_bot_set_nat @ A)))). % empty_subsetI
thf(fact_74_subset__empty, axiom,
    ((![A : set_msg]: ((ord_less_eq_set_msg @ A @ bot_bot_set_msg) = (A = bot_bot_set_msg))))). % subset_empty
thf(fact_75_subset__empty, axiom,
    ((![A : set_nat]: ((ord_less_eq_set_nat @ A @ bot_bot_set_nat) = (A = bot_bot_set_nat))))). % subset_empty
thf(fact_76_analz__parts, axiom,
    ((![H : set_msg]: ((analz @ (parts @ H)) = (parts @ H))))). % analz_parts
thf(fact_77_parts__analz, axiom,
    ((![H : set_msg]: ((parts @ (analz @ H)) = (parts @ H))))). % parts_analz
thf(fact_78_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_79_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_80_analz__subset__iff, axiom,
    ((![G : set_msg, H : set_msg]: ((ord_less_eq_set_msg @ (analz @ G) @ (analz @ H)) = (ord_less_eq_set_msg @ G @ (analz @ H)))))). % analz_subset_iff
thf(fact_81_invKey__shrK, axiom,
    ((![A : agent]: ((invKey @ (shrK @ A)) = (shrK @ A))))). % invKey_shrK
thf(fact_82_invKey__K, axiom,
    ((![K : nat]: ((member_nat @ K @ symKeys) => ((invKey @ K) = K))))). % invKey_K
thf(fact_83_symKeys__invKey__iff, axiom,
    ((![K : nat]: ((member_nat @ (invKey @ K) @ symKeys) = (member_nat @ K @ symKeys))))). % symKeys_invKey_iff
thf(fact_84_analz_OInj, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ H) => (member_msg @ X @ (analz @ H)))))). % analz.Inj
thf(fact_85_analz__analzD, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ (analz @ (analz @ H))) => (member_msg @ X @ (analz @ H)))))). % analz_analzD
thf(fact_86_ex__in__conv, axiom,
    ((![A : set_list_event]: ((?[X2 : list_event]: (member_list_event @ X2 @ A)) = (~ ((A = bot_bo1693714908_event))))))). % ex_in_conv
thf(fact_87_ex__in__conv, axiom,
    ((![A : set_agent]: ((?[X2 : agent]: (member_agent @ X2 @ A)) = (~ ((A = bot_bot_set_agent))))))). % ex_in_conv
thf(fact_88_ex__in__conv, axiom,
    ((![A : set_nat]: ((?[X2 : nat]: (member_nat @ X2 @ A)) = (~ ((A = bot_bot_set_nat))))))). % ex_in_conv
thf(fact_89_ex__in__conv, axiom,
    ((![A : set_msg]: ((?[X2 : msg]: (member_msg @ X2 @ A)) = (~ ((A = bot_bot_set_msg))))))). % ex_in_conv
thf(fact_90_equals0I, axiom,
    ((![A : set_list_event]: ((![Y2 : list_event]: (~ ((member_list_event @ Y2 @ A)))) => (A = bot_bo1693714908_event))))). % equals0I
thf(fact_91_equals0I, axiom,
    ((![A : set_agent]: ((![Y2 : agent]: (~ ((member_agent @ Y2 @ A)))) => (A = bot_bot_set_agent))))). % equals0I
thf(fact_92_equals0I, axiom,
    ((![A : set_nat]: ((![Y2 : nat]: (~ ((member_nat @ Y2 @ A)))) => (A = bot_bot_set_nat))))). % equals0I
thf(fact_93_equals0I, axiom,
    ((![A : set_msg]: ((![Y2 : msg]: (~ ((member_msg @ Y2 @ A)))) => (A = bot_bot_set_msg))))). % equals0I
thf(fact_94_equals0D, axiom,
    ((![A : set_list_event, A3 : list_event]: ((A = bot_bo1693714908_event) => (~ ((member_list_event @ A3 @ A))))))). % equals0D
thf(fact_95_equals0D, axiom,
    ((![A : set_agent, A3 : agent]: ((A = bot_bot_set_agent) => (~ ((member_agent @ A3 @ A))))))). % equals0D
thf(fact_96_equals0D, axiom,
    ((![A : set_nat, A3 : nat]: ((A = bot_bot_set_nat) => (~ ((member_nat @ A3 @ A))))))). % equals0D
thf(fact_97_equals0D, axiom,
    ((![A : set_msg, A3 : msg]: ((A = bot_bot_set_msg) => (~ ((member_msg @ A3 @ A))))))). % equals0D
thf(fact_98_emptyE, axiom,
    ((![A3 : list_event]: (~ ((member_list_event @ A3 @ bot_bo1693714908_event)))))). % emptyE
thf(fact_99_emptyE, axiom,
    ((![A3 : agent]: (~ ((member_agent @ A3 @ bot_bot_set_agent)))))). % emptyE
thf(fact_100_emptyE, axiom,
    ((![A3 : nat]: (~ ((member_nat @ A3 @ bot_bot_set_nat)))))). % emptyE
thf(fact_101_emptyE, axiom,
    ((![A3 : msg]: (~ ((member_msg @ A3 @ bot_bot_set_msg)))))). % emptyE
thf(fact_102_bot_Oextremum__uniqueI, axiom,
    ((![A3 : set_msg]: ((ord_less_eq_set_msg @ A3 @ bot_bot_set_msg) => (A3 = bot_bot_set_msg))))). % bot.extremum_uniqueI
thf(fact_103_bot_Oextremum__uniqueI, axiom,
    ((![A3 : set_nat]: ((ord_less_eq_set_nat @ A3 @ bot_bot_set_nat) => (A3 = bot_bot_set_nat))))). % bot.extremum_uniqueI
thf(fact_104_bot_Oextremum__unique, axiom,
    ((![A3 : set_msg]: ((ord_less_eq_set_msg @ A3 @ bot_bot_set_msg) = (A3 = bot_bot_set_msg))))). % bot.extremum_unique
thf(fact_105_bot_Oextremum__unique, axiom,
    ((![A3 : set_nat]: ((ord_less_eq_set_nat @ A3 @ bot_bot_set_nat) = (A3 = bot_bot_set_nat))))). % bot.extremum_unique
thf(fact_106_bot_Oextremum, axiom,
    ((![A3 : set_msg]: (ord_less_eq_set_msg @ bot_bot_set_msg @ A3)))). % bot.extremum
thf(fact_107_bot_Oextremum, axiom,
    ((![A3 : set_nat]: (ord_less_eq_set_nat @ bot_bot_set_nat @ A3)))). % bot.extremum
thf(fact_108_analz__into__parts, axiom,
    ((![C : msg, H : set_msg]: ((member_msg @ C @ (analz @ H)) => (member_msg @ C @ (parts @ H)))))). % analz_into_parts
thf(fact_109_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_110_analz__increasing, axiom,
    ((![H : set_msg]: (ord_less_eq_set_msg @ H @ (analz @ H))))). % analz_increasing
thf(fact_111_analz__trans, axiom,
    ((![X : msg, G : set_msg, H : set_msg]: ((member_msg @ X @ (analz @ G)) => ((ord_less_eq_set_msg @ G @ (analz @ H)) => (member_msg @ X @ (analz @ H))))))). % analz_trans
thf(fact_112_analz__mono, axiom,
    ((![G : set_msg, H : set_msg]: ((ord_less_eq_set_msg @ G @ H) => (ord_less_eq_set_msg @ (analz @ G) @ (analz @ H)))))). % analz_mono
thf(fact_113_publicKey__neq__privateKey, axiom,
    ((![C : keymode, A2 : agent, B : keymode, A : agent]: (~ (((publicKey @ C @ A2) = (invKey @ (publicKey @ B @ A)))))))). % publicKey_neq_privateKey
thf(fact_114_analz__subset__parts, axiom,
    ((![H : set_msg]: (ord_less_eq_set_msg @ (analz @ H) @ (parts @ H))))). % analz_subset_parts
thf(fact_115_analz__impI, axiom,
    ((![Y3 : msg, Evs : list_event, Q : $o]: (((~ ((member_msg @ Y3 @ (analz @ (knows @ spy @ Evs))))) => Q) => ((~ ((member_msg @ Y3 @ (analz @ (knows @ spy @ Evs))))) => Q))))). % analz_impI
thf(fact_116_keysFor__mono, axiom,
    ((![G : set_msg, H : set_msg]: ((ord_less_eq_set_msg @ G @ H) => (ord_less_eq_set_nat @ (keysFor @ G) @ (keysFor @ H)))))). % keysFor_mono
thf(fact_117_shrK__neq__priK, axiom,
    ((![B : keymode, C2 : agent, A : agent]: (~ (((invKey @ (publicKey @ B @ C2)) = (shrK @ A))))))). % shrK_neq_priK
thf(fact_118_not__symKeys__priK, axiom,
    ((![B : keymode, A : agent]: (~ ((member_nat @ (invKey @ (publicKey @ B @ A)) @ symKeys)))))). % not_symKeys_priK
thf(fact_119_dual__order_Oantisym, axiom,
    ((![B : set_msg, A3 : set_msg]: ((ord_less_eq_set_msg @ B @ A3) => ((ord_less_eq_set_msg @ A3 @ B) => (A3 = B)))))). % dual_order.antisym
thf(fact_120_dual__order_Oantisym, axiom,
    ((![B : set_nat, A3 : set_nat]: ((ord_less_eq_set_nat @ B @ A3) => ((ord_less_eq_set_nat @ A3 @ B) => (A3 = B)))))). % dual_order.antisym
thf(fact_121_dual__order_Oeq__iff, axiom,
    (((^[Y5 : set_msg]: (^[Z : set_msg]: (Y5 = Z))) = (^[A4 : set_msg]: (^[B3 : set_msg]: (((ord_less_eq_set_msg @ B3 @ A4)) & ((ord_less_eq_set_msg @ A4 @ B3)))))))). % dual_order.eq_iff
thf(fact_122_dual__order_Oeq__iff, axiom,
    (((^[Y5 : set_nat]: (^[Z : set_nat]: (Y5 = Z))) = (^[A4 : set_nat]: (^[B3 : set_nat]: (((ord_less_eq_set_nat @ B3 @ A4)) & ((ord_less_eq_set_nat @ A4 @ B3)))))))). % dual_order.eq_iff
thf(fact_123_dual__order_Otrans, axiom,
    ((![B : set_msg, A3 : set_msg, C : set_msg]: ((ord_less_eq_set_msg @ B @ A3) => ((ord_less_eq_set_msg @ C @ B) => (ord_less_eq_set_msg @ C @ A3)))))). % dual_order.trans
thf(fact_124_dual__order_Otrans, axiom,
    ((![B : set_nat, A3 : set_nat, C : set_nat]: ((ord_less_eq_set_nat @ B @ A3) => ((ord_less_eq_set_nat @ C @ B) => (ord_less_eq_set_nat @ C @ A3)))))). % dual_order.trans
thf(fact_125_dual__order_Orefl, axiom,
    ((![A3 : set_msg]: (ord_less_eq_set_msg @ A3 @ A3)))). % dual_order.refl
thf(fact_126_dual__order_Orefl, axiom,
    ((![A3 : set_nat]: (ord_less_eq_set_nat @ A3 @ A3)))). % dual_order.refl
thf(fact_127_order__trans, axiom,
    ((![X3 : set_msg, Y : set_msg, Z2 : set_msg]: ((ord_less_eq_set_msg @ X3 @ Y) => ((ord_less_eq_set_msg @ Y @ Z2) => (ord_less_eq_set_msg @ X3 @ Z2)))))). % order_trans
thf(fact_128_order__trans, axiom,
    ((![X3 : set_nat, Y : set_nat, Z2 : set_nat]: ((ord_less_eq_set_nat @ X3 @ Y) => ((ord_less_eq_set_nat @ Y @ Z2) => (ord_less_eq_set_nat @ X3 @ Z2)))))). % order_trans
thf(fact_129_order__class_Oorder_Oantisym, axiom,
    ((![A3 : set_msg, B : set_msg]: ((ord_less_eq_set_msg @ A3 @ B) => ((ord_less_eq_set_msg @ B @ A3) => (A3 = B)))))). % order_class.order.antisym
thf(fact_130_order__class_Oorder_Oantisym, axiom,
    ((![A3 : set_nat, B : set_nat]: ((ord_less_eq_set_nat @ A3 @ B) => ((ord_less_eq_set_nat @ B @ A3) => (A3 = B)))))). % order_class.order.antisym
thf(fact_131_ord__le__eq__trans, axiom,
    ((![A3 : set_msg, B : set_msg, C : set_msg]: ((ord_less_eq_set_msg @ A3 @ B) => ((B = C) => (ord_less_eq_set_msg @ A3 @ C)))))). % ord_le_eq_trans
thf(fact_132_ord__le__eq__trans, axiom,
    ((![A3 : set_nat, B : set_nat, C : set_nat]: ((ord_less_eq_set_nat @ A3 @ B) => ((B = C) => (ord_less_eq_set_nat @ A3 @ C)))))). % ord_le_eq_trans
thf(fact_133_ord__eq__le__trans, axiom,
    ((![A3 : set_msg, B : set_msg, C : set_msg]: ((A3 = B) => ((ord_less_eq_set_msg @ B @ C) => (ord_less_eq_set_msg @ A3 @ C)))))). % ord_eq_le_trans
thf(fact_134_ord__eq__le__trans, axiom,
    ((![A3 : set_nat, B : set_nat, C : set_nat]: ((A3 = B) => ((ord_less_eq_set_nat @ B @ C) => (ord_less_eq_set_nat @ A3 @ C)))))). % ord_eq_le_trans
thf(fact_135_order__class_Oorder_Oeq__iff, axiom,
    (((^[Y5 : set_msg]: (^[Z : set_msg]: (Y5 = Z))) = (^[A4 : set_msg]: (^[B3 : set_msg]: (((ord_less_eq_set_msg @ A4 @ B3)) & ((ord_less_eq_set_msg @ B3 @ A4)))))))). % order_class.order.eq_iff
thf(fact_136_order__class_Oorder_Oeq__iff, axiom,
    (((^[Y5 : set_nat]: (^[Z : set_nat]: (Y5 = Z))) = (^[A4 : set_nat]: (^[B3 : set_nat]: (((ord_less_eq_set_nat @ A4 @ B3)) & ((ord_less_eq_set_nat @ B3 @ A4)))))))). % order_class.order.eq_iff
thf(fact_137_antisym__conv, axiom,
    ((![Y : set_msg, X3 : set_msg]: ((ord_less_eq_set_msg @ Y @ X3) => ((ord_less_eq_set_msg @ X3 @ Y) = (X3 = Y)))))). % antisym_conv
thf(fact_138_antisym__conv, axiom,
    ((![Y : set_nat, X3 : set_nat]: ((ord_less_eq_set_nat @ Y @ X3) => ((ord_less_eq_set_nat @ X3 @ Y) = (X3 = Y)))))). % antisym_conv
thf(fact_139_order_Otrans, axiom,
    ((![A3 : set_msg, B : set_msg, C : set_msg]: ((ord_less_eq_set_msg @ A3 @ B) => ((ord_less_eq_set_msg @ B @ C) => (ord_less_eq_set_msg @ A3 @ C)))))). % order.trans
thf(fact_140_order_Otrans, axiom,
    ((![A3 : set_nat, B : set_nat, C : set_nat]: ((ord_less_eq_set_nat @ A3 @ B) => ((ord_less_eq_set_nat @ B @ C) => (ord_less_eq_set_nat @ A3 @ C)))))). % order.trans
thf(fact_141_eq__refl, axiom,
    ((![X3 : set_msg, Y : set_msg]: ((X3 = Y) => (ord_less_eq_set_msg @ X3 @ Y))))). % eq_refl
thf(fact_142_eq__refl, axiom,
    ((![X3 : set_nat, Y : set_nat]: ((X3 = Y) => (ord_less_eq_set_nat @ X3 @ Y))))). % eq_refl
thf(fact_143_antisym, axiom,
    ((![X3 : set_msg, Y : set_msg]: ((ord_less_eq_set_msg @ X3 @ Y) => ((ord_less_eq_set_msg @ Y @ X3) => (X3 = Y)))))). % antisym
thf(fact_144_antisym, axiom,
    ((![X3 : set_nat, Y : set_nat]: ((ord_less_eq_set_nat @ X3 @ Y) => ((ord_less_eq_set_nat @ Y @ X3) => (X3 = Y)))))). % antisym
thf(fact_145_eq__iff, axiom,
    (((^[Y5 : set_msg]: (^[Z : set_msg]: (Y5 = Z))) = (^[X2 : set_msg]: (^[Y6 : set_msg]: (((ord_less_eq_set_msg @ X2 @ Y6)) & ((ord_less_eq_set_msg @ Y6 @ X2)))))))). % eq_iff
thf(fact_146_eq__iff, axiom,
    (((^[Y5 : set_nat]: (^[Z : set_nat]: (Y5 = Z))) = (^[X2 : set_nat]: (^[Y6 : set_nat]: (((ord_less_eq_set_nat @ X2 @ Y6)) & ((ord_less_eq_set_nat @ Y6 @ X2)))))))). % eq_iff
thf(fact_147_ord__le__eq__subst, axiom,
    ((![A3 : set_msg, B : set_msg, F : set_msg > set_msg, C : set_msg]: ((ord_less_eq_set_msg @ A3 @ B) => (((F @ B) = C) => ((![X5 : set_msg, Y2 : set_msg]: ((ord_less_eq_set_msg @ X5 @ Y2) => (ord_less_eq_set_msg @ (F @ X5) @ (F @ Y2)))) => (ord_less_eq_set_msg @ (F @ A3) @ C))))))). % ord_le_eq_subst
thf(fact_148_ord__le__eq__subst, axiom,
    ((![A3 : set_msg, B : set_msg, F : set_msg > set_nat, C : set_nat]: ((ord_less_eq_set_msg @ A3 @ B) => (((F @ B) = C) => ((![X5 : set_msg, Y2 : set_msg]: ((ord_less_eq_set_msg @ X5 @ Y2) => (ord_less_eq_set_nat @ (F @ X5) @ (F @ Y2)))) => (ord_less_eq_set_nat @ (F @ A3) @ C))))))). % ord_le_eq_subst
thf(fact_149_ord__le__eq__subst, axiom,
    ((![A3 : set_nat, B : set_nat, F : set_nat > set_msg, C : set_msg]: ((ord_less_eq_set_nat @ A3 @ B) => (((F @ B) = C) => ((![X5 : set_nat, Y2 : set_nat]: ((ord_less_eq_set_nat @ X5 @ Y2) => (ord_less_eq_set_msg @ (F @ X5) @ (F @ Y2)))) => (ord_less_eq_set_msg @ (F @ A3) @ C))))))). % ord_le_eq_subst
thf(fact_150_ord__le__eq__subst, axiom,
    ((![A3 : set_nat, B : set_nat, F : set_nat > set_nat, C : set_nat]: ((ord_less_eq_set_nat @ A3 @ B) => (((F @ B) = C) => ((![X5 : set_nat, Y2 : set_nat]: ((ord_less_eq_set_nat @ X5 @ Y2) => (ord_less_eq_set_nat @ (F @ X5) @ (F @ Y2)))) => (ord_less_eq_set_nat @ (F @ A3) @ C))))))). % ord_le_eq_subst
thf(fact_151_ord__eq__le__subst, axiom,
    ((![A3 : set_msg, F : set_msg > set_msg, B : set_msg, C : set_msg]: ((A3 = (F @ B)) => ((ord_less_eq_set_msg @ B @ C) => ((![X5 : set_msg, Y2 : set_msg]: ((ord_less_eq_set_msg @ X5 @ Y2) => (ord_less_eq_set_msg @ (F @ X5) @ (F @ Y2)))) => (ord_less_eq_set_msg @ A3 @ (F @ C)))))))). % ord_eq_le_subst
thf(fact_152_ord__eq__le__subst, axiom,
    ((![A3 : set_nat, F : set_msg > set_nat, B : set_msg, C : set_msg]: ((A3 = (F @ B)) => ((ord_less_eq_set_msg @ B @ C) => ((![X5 : set_msg, Y2 : set_msg]: ((ord_less_eq_set_msg @ X5 @ Y2) => (ord_less_eq_set_nat @ (F @ X5) @ (F @ Y2)))) => (ord_less_eq_set_nat @ A3 @ (F @ C)))))))). % ord_eq_le_subst
thf(fact_153_ord__eq__le__subst, axiom,
    ((![A3 : set_msg, F : set_nat > set_msg, B : set_nat, C : set_nat]: ((A3 = (F @ B)) => ((ord_less_eq_set_nat @ B @ C) => ((![X5 : set_nat, Y2 : set_nat]: ((ord_less_eq_set_nat @ X5 @ Y2) => (ord_less_eq_set_msg @ (F @ X5) @ (F @ Y2)))) => (ord_less_eq_set_msg @ A3 @ (F @ C)))))))). % ord_eq_le_subst
thf(fact_154_ord__eq__le__subst, axiom,
    ((![A3 : set_nat, F : set_nat > set_nat, B : set_nat, C : set_nat]: ((A3 = (F @ B)) => ((ord_less_eq_set_nat @ B @ C) => ((![X5 : set_nat, Y2 : set_nat]: ((ord_less_eq_set_nat @ X5 @ Y2) => (ord_less_eq_set_nat @ (F @ X5) @ (F @ Y2)))) => (ord_less_eq_set_nat @ A3 @ (F @ C)))))))). % ord_eq_le_subst
thf(fact_155_order__subst2, axiom,
    ((![A3 : set_msg, B : set_msg, F : set_msg > set_msg, C : set_msg]: ((ord_less_eq_set_msg @ A3 @ B) => ((ord_less_eq_set_msg @ (F @ B) @ C) => ((![X5 : set_msg, Y2 : set_msg]: ((ord_less_eq_set_msg @ X5 @ Y2) => (ord_less_eq_set_msg @ (F @ X5) @ (F @ Y2)))) => (ord_less_eq_set_msg @ (F @ A3) @ C))))))). % order_subst2
thf(fact_156_order__subst2, axiom,
    ((![A3 : set_msg, B : set_msg, F : set_msg > set_nat, C : set_nat]: ((ord_less_eq_set_msg @ A3 @ B) => ((ord_less_eq_set_nat @ (F @ B) @ C) => ((![X5 : set_msg, Y2 : set_msg]: ((ord_less_eq_set_msg @ X5 @ Y2) => (ord_less_eq_set_nat @ (F @ X5) @ (F @ Y2)))) => (ord_less_eq_set_nat @ (F @ A3) @ C))))))). % order_subst2
thf(fact_157_order__subst2, axiom,
    ((![A3 : set_nat, B : set_nat, F : set_nat > set_msg, C : set_msg]: ((ord_less_eq_set_nat @ A3 @ B) => ((ord_less_eq_set_msg @ (F @ B) @ C) => ((![X5 : set_nat, Y2 : set_nat]: ((ord_less_eq_set_nat @ X5 @ Y2) => (ord_less_eq_set_msg @ (F @ X5) @ (F @ Y2)))) => (ord_less_eq_set_msg @ (F @ A3) @ C))))))). % order_subst2
thf(fact_158_order__subst2, axiom,
    ((![A3 : set_nat, B : set_nat, F : set_nat > set_nat, C : set_nat]: ((ord_less_eq_set_nat @ A3 @ B) => ((ord_less_eq_set_nat @ (F @ B) @ C) => ((![X5 : set_nat, Y2 : set_nat]: ((ord_less_eq_set_nat @ X5 @ Y2) => (ord_less_eq_set_nat @ (F @ X5) @ (F @ Y2)))) => (ord_less_eq_set_nat @ (F @ A3) @ C))))))). % order_subst2
thf(fact_159_order__subst1, axiom,
    ((![A3 : set_msg, F : set_msg > set_msg, B : set_msg, C : set_msg]: ((ord_less_eq_set_msg @ A3 @ (F @ B)) => ((ord_less_eq_set_msg @ B @ C) => ((![X5 : set_msg, Y2 : set_msg]: ((ord_less_eq_set_msg @ X5 @ Y2) => (ord_less_eq_set_msg @ (F @ X5) @ (F @ Y2)))) => (ord_less_eq_set_msg @ A3 @ (F @ C)))))))). % order_subst1
thf(fact_160_order__subst1, axiom,
    ((![A3 : set_msg, F : set_nat > set_msg, B : set_nat, C : set_nat]: ((ord_less_eq_set_msg @ A3 @ (F @ B)) => ((ord_less_eq_set_nat @ B @ C) => ((![X5 : set_nat, Y2 : set_nat]: ((ord_less_eq_set_nat @ X5 @ Y2) => (ord_less_eq_set_msg @ (F @ X5) @ (F @ Y2)))) => (ord_less_eq_set_msg @ A3 @ (F @ C)))))))). % order_subst1
thf(fact_161_order__subst1, axiom,
    ((![A3 : set_nat, F : set_msg > set_nat, B : set_msg, C : set_msg]: ((ord_less_eq_set_nat @ A3 @ (F @ B)) => ((ord_less_eq_set_msg @ B @ C) => ((![X5 : set_msg, Y2 : set_msg]: ((ord_less_eq_set_msg @ X5 @ Y2) => (ord_less_eq_set_nat @ (F @ X5) @ (F @ Y2)))) => (ord_less_eq_set_nat @ A3 @ (F @ C)))))))). % order_subst1
thf(fact_162_order__subst1, axiom,
    ((![A3 : set_nat, F : set_nat > set_nat, B : set_nat, C : set_nat]: ((ord_less_eq_set_nat @ A3 @ (F @ B)) => ((ord_less_eq_set_nat @ B @ C) => ((![X5 : set_nat, Y2 : set_nat]: ((ord_less_eq_set_nat @ X5 @ Y2) => (ord_less_eq_set_nat @ (F @ X5) @ (F @ Y2)))) => (ord_less_eq_set_nat @ A3 @ (F @ C)))))))). % order_subst1
thf(fact_163_Collect__mono__iff, axiom,
    ((![P : msg > $o, Q : msg > $o]: ((ord_less_eq_set_msg @ (collect_msg @ P) @ (collect_msg @ Q)) = (![X2 : msg]: (((P @ X2)) => ((Q @ X2)))))))). % Collect_mono_iff
thf(fact_164_Collect__mono__iff, axiom,
    ((![P : nat > $o, Q : nat > $o]: ((ord_less_eq_set_nat @ (collect_nat @ P) @ (collect_nat @ Q)) = (![X2 : nat]: (((P @ X2)) => ((Q @ X2)))))))). % Collect_mono_iff
thf(fact_165_set__eq__subset, axiom,
    (((^[Y5 : set_msg]: (^[Z : set_msg]: (Y5 = Z))) = (^[A5 : set_msg]: (^[B4 : set_msg]: (((ord_less_eq_set_msg @ A5 @ B4)) & ((ord_less_eq_set_msg @ B4 @ A5)))))))). % set_eq_subset
thf(fact_166_set__eq__subset, axiom,
    (((^[Y5 : set_nat]: (^[Z : set_nat]: (Y5 = Z))) = (^[A5 : set_nat]: (^[B4 : set_nat]: (((ord_less_eq_set_nat @ A5 @ B4)) & ((ord_less_eq_set_nat @ B4 @ A5)))))))). % set_eq_subset
thf(fact_167_subset__trans, axiom,
    ((![A : set_msg, B2 : set_msg, C2 : set_msg]: ((ord_less_eq_set_msg @ A @ B2) => ((ord_less_eq_set_msg @ B2 @ C2) => (ord_less_eq_set_msg @ A @ C2)))))). % subset_trans
thf(fact_168_subset__trans, axiom,
    ((![A : set_nat, B2 : set_nat, C2 : set_nat]: ((ord_less_eq_set_nat @ A @ B2) => ((ord_less_eq_set_nat @ B2 @ C2) => (ord_less_eq_set_nat @ A @ C2)))))). % subset_trans
thf(fact_169_Collect__mono, axiom,
    ((![P : msg > $o, Q : msg > $o]: ((![X5 : msg]: ((P @ X5) => (Q @ X5))) => (ord_less_eq_set_msg @ (collect_msg @ P) @ (collect_msg @ Q)))))). % Collect_mono
thf(fact_170_Collect__mono, axiom,
    ((![P : nat > $o, Q : nat > $o]: ((![X5 : nat]: ((P @ X5) => (Q @ X5))) => (ord_less_eq_set_nat @ (collect_nat @ P) @ (collect_nat @ Q)))))). % Collect_mono
thf(fact_171_subset__refl, axiom,
    ((![A : set_msg]: (ord_less_eq_set_msg @ A @ A)))). % subset_refl
thf(fact_172_subset__refl, axiom,
    ((![A : set_nat]: (ord_less_eq_set_nat @ A @ A)))). % subset_refl
thf(fact_173_subset__iff, axiom,
    ((ord_le119303592_event = (^[A5 : set_list_event]: (^[B4 : set_list_event]: (![T : list_event]: (((member_list_event @ T @ A5)) => ((member_list_event @ T @ B4))))))))). % subset_iff
thf(fact_174_subset__iff, axiom,
    ((ord_le722097072_agent = (^[A5 : set_agent]: (^[B4 : set_agent]: (![T : agent]: (((member_agent @ T @ A5)) => ((member_agent @ T @ B4))))))))). % subset_iff
thf(fact_175_subset__iff, axiom,
    ((ord_less_eq_set_msg = (^[A5 : set_msg]: (^[B4 : set_msg]: (![T : msg]: (((member_msg @ T @ A5)) => ((member_msg @ T @ B4))))))))). % subset_iff
thf(fact_176_subset__iff, axiom,
    ((ord_less_eq_set_nat = (^[A5 : set_nat]: (^[B4 : set_nat]: (![T : nat]: (((member_nat @ T @ A5)) => ((member_nat @ T @ B4))))))))). % subset_iff
thf(fact_177_equalityD2, axiom,
    ((![A : set_msg, B2 : set_msg]: ((A = B2) => (ord_less_eq_set_msg @ B2 @ A))))). % equalityD2
thf(fact_178_equalityD2, axiom,
    ((![A : set_nat, B2 : set_nat]: ((A = B2) => (ord_less_eq_set_nat @ B2 @ A))))). % equalityD2
thf(fact_179_equalityD1, axiom,
    ((![A : set_msg, B2 : set_msg]: ((A = B2) => (ord_less_eq_set_msg @ A @ B2))))). % equalityD1
thf(fact_180_equalityD1, axiom,
    ((![A : set_nat, B2 : set_nat]: ((A = B2) => (ord_less_eq_set_nat @ A @ B2))))). % equalityD1
thf(fact_181_subset__eq, axiom,
    ((ord_le119303592_event = (^[A5 : set_list_event]: (^[B4 : set_list_event]: (![X2 : list_event]: (((member_list_event @ X2 @ A5)) => ((member_list_event @ X2 @ B4))))))))). % subset_eq
thf(fact_182_subset__eq, axiom,
    ((ord_le722097072_agent = (^[A5 : set_agent]: (^[B4 : set_agent]: (![X2 : agent]: (((member_agent @ X2 @ A5)) => ((member_agent @ X2 @ B4))))))))). % subset_eq
thf(fact_183_subset__eq, axiom,
    ((ord_less_eq_set_msg = (^[A5 : set_msg]: (^[B4 : set_msg]: (![X2 : msg]: (((member_msg @ X2 @ A5)) => ((member_msg @ X2 @ B4))))))))). % subset_eq
thf(fact_184_subset__eq, axiom,
    ((ord_less_eq_set_nat = (^[A5 : set_nat]: (^[B4 : set_nat]: (![X2 : nat]: (((member_nat @ X2 @ A5)) => ((member_nat @ X2 @ B4))))))))). % subset_eq
thf(fact_185_equalityE, axiom,
    ((![A : set_msg, B2 : set_msg]: ((A = B2) => (~ (((ord_less_eq_set_msg @ A @ B2) => (~ ((ord_less_eq_set_msg @ B2 @ A)))))))))). % equalityE
thf(fact_186_equalityE, axiom,
    ((![A : set_nat, B2 : set_nat]: ((A = B2) => (~ (((ord_less_eq_set_nat @ A @ B2) => (~ ((ord_less_eq_set_nat @ B2 @ A)))))))))). % equalityE
thf(fact_187_subsetD, axiom,
    ((![A : set_list_event, B2 : set_list_event, C : list_event]: ((ord_le119303592_event @ A @ B2) => ((member_list_event @ C @ A) => (member_list_event @ C @ B2)))))). % subsetD
thf(fact_188_subsetD, axiom,
    ((![A : set_agent, B2 : set_agent, C : agent]: ((ord_le722097072_agent @ A @ B2) => ((member_agent @ C @ A) => (member_agent @ C @ B2)))))). % subsetD
thf(fact_189_subsetD, axiom,
    ((![A : set_msg, B2 : set_msg, C : msg]: ((ord_less_eq_set_msg @ A @ B2) => ((member_msg @ C @ A) => (member_msg @ C @ B2)))))). % subsetD
thf(fact_190_subsetD, axiom,
    ((![A : set_nat, B2 : set_nat, C : nat]: ((ord_less_eq_set_nat @ A @ B2) => ((member_nat @ C @ A) => (member_nat @ C @ B2)))))). % subsetD
thf(fact_191_subset__emptyI, axiom,
    ((![A : set_list_event]: ((![X5 : list_event]: (~ ((member_list_event @ X5 @ A)))) => (ord_le119303592_event @ A @ bot_bo1693714908_event))))). % subset_emptyI
thf(fact_192_subset__emptyI, axiom,
    ((![A : set_agent]: ((![X5 : agent]: (~ ((member_agent @ X5 @ A)))) => (ord_le722097072_agent @ A @ bot_bot_set_agent))))). % subset_emptyI
thf(fact_193_subset__emptyI, axiom,
    ((![A : set_msg]: ((![X5 : msg]: (~ ((member_msg @ X5 @ A)))) => (ord_less_eq_set_msg @ A @ bot_bot_set_msg))))). % subset_emptyI
thf(fact_194_subset__emptyI, axiom,
    ((![A : set_nat]: ((![X5 : nat]: (~ ((member_nat @ X5 @ A)))) => (ord_less_eq_set_nat @ A @ bot_bot_set_nat))))). % subset_emptyI
thf(fact_195_symKey__neq__priEK, axiom,
    ((![K : nat, A : agent]: ((member_nat @ K @ symKeys) => (~ ((K = (invKey @ (publicKey @ encryption @ A))))))))). % symKey_neq_priEK
thf(fact_196_priEK__noteq__shrK, axiom,
    ((![A : agent, B2 : agent]: (~ (((invKey @ (publicKey @ encryption @ A)) = (shrK @ B2))))))). % priEK_noteq_shrK
thf(fact_197_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_198_Set_Ois__empty__def, axiom,
    ((is_empty_nat = (^[A5 : set_nat]: (A5 = bot_bot_set_nat))))). % Set.is_empty_def
thf(fact_199_Set_Ois__empty__def, axiom,
    ((is_empty_msg = (^[A5 : set_msg]: (A5 = bot_bot_set_msg))))). % Set.is_empty_def
thf(fact_200_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_201_insert__absorb2, axiom,
    ((![X3 : msg, A : set_msg]: ((insert_msg @ X3 @ (insert_msg @ X3 @ A)) = (insert_msg @ X3 @ A))))). % insert_absorb2
thf(fact_202_insert__iff, axiom,
    ((![A3 : msg, B : msg, A : set_msg]: ((member_msg @ A3 @ (insert_msg @ B @ A)) = (((A3 = B)) | ((member_msg @ A3 @ A))))))). % insert_iff
thf(fact_203_insert__iff, axiom,
    ((![A3 : nat, B : nat, A : set_nat]: ((member_nat @ A3 @ (insert_nat @ B @ A)) = (((A3 = B)) | ((member_nat @ A3 @ A))))))). % insert_iff
thf(fact_204_insert__iff, axiom,
    ((![A3 : list_event, B : list_event, A : set_list_event]: ((member_list_event @ A3 @ (insert_list_event @ B @ A)) = (((A3 = B)) | ((member_list_event @ A3 @ A))))))). % insert_iff
thf(fact_205_insert__iff, axiom,
    ((![A3 : agent, B : agent, A : set_agent]: ((member_agent @ A3 @ (insert_agent @ B @ A)) = (((A3 = B)) | ((member_agent @ A3 @ A))))))). % insert_iff
thf(fact_206_insertCI, axiom,
    ((![A3 : msg, B2 : set_msg, B : msg]: (((~ ((member_msg @ A3 @ B2))) => (A3 = B)) => (member_msg @ A3 @ (insert_msg @ B @ B2)))))). % insertCI
thf(fact_207_insertCI, axiom,
    ((![A3 : nat, B2 : set_nat, B : nat]: (((~ ((member_nat @ A3 @ B2))) => (A3 = B)) => (member_nat @ A3 @ (insert_nat @ B @ B2)))))). % insertCI
thf(fact_208_insertCI, axiom,
    ((![A3 : list_event, B2 : set_list_event, B : list_event]: (((~ ((member_list_event @ A3 @ B2))) => (A3 = B)) => (member_list_event @ A3 @ (insert_list_event @ B @ B2)))))). % insertCI
thf(fact_209_insertCI, axiom,
    ((![A3 : agent, B2 : set_agent, B : agent]: (((~ ((member_agent @ A3 @ B2))) => (A3 = B)) => (member_agent @ A3 @ (insert_agent @ B @ B2)))))). % insertCI
thf(fact_210_analz__empty, axiom,
    (((analz @ bot_bot_set_msg) = bot_bot_set_msg))). % analz_empty
thf(fact_211_parts__empty, axiom,
    (((parts @ bot_bot_set_msg) = bot_bot_set_msg))). % parts_empty
thf(fact_212_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_213_singletonI, axiom,
    ((![A3 : list_event]: (member_list_event @ A3 @ (insert_list_event @ A3 @ bot_bo1693714908_event))))). % singletonI
thf(fact_214_singletonI, axiom,
    ((![A3 : agent]: (member_agent @ A3 @ (insert_agent @ A3 @ bot_bot_set_agent))))). % singletonI
thf(fact_215_singletonI, axiom,
    ((![A3 : nat]: (member_nat @ A3 @ (insert_nat @ A3 @ bot_bot_set_nat))))). % singletonI
thf(fact_216_singletonI, axiom,
    ((![A3 : msg]: (member_msg @ A3 @ (insert_msg @ A3 @ bot_bot_set_msg))))). % singletonI
thf(fact_217_insert__subset, axiom,
    ((![X3 : list_event, A : set_list_event, B2 : set_list_event]: ((ord_le119303592_event @ (insert_list_event @ X3 @ A) @ B2) = (((member_list_event @ X3 @ B2)) & ((ord_le119303592_event @ A @ B2))))))). % insert_subset
thf(fact_218_insert__subset, axiom,
    ((![X3 : agent, A : set_agent, B2 : set_agent]: ((ord_le722097072_agent @ (insert_agent @ X3 @ A) @ B2) = (((member_agent @ X3 @ B2)) & ((ord_le722097072_agent @ A @ B2))))))). % insert_subset
thf(fact_219_insert__subset, axiom,
    ((![X3 : msg, A : set_msg, B2 : set_msg]: ((ord_less_eq_set_msg @ (insert_msg @ X3 @ A) @ B2) = (((member_msg @ X3 @ B2)) & ((ord_less_eq_set_msg @ A @ B2))))))). % insert_subset
thf(fact_220_insert__subset, axiom,
    ((![X3 : nat, A : set_nat, B2 : set_nat]: ((ord_less_eq_set_nat @ (insert_nat @ X3 @ A) @ B2) = (((member_nat @ X3 @ B2)) & ((ord_less_eq_set_nat @ A @ B2))))))). % insert_subset
thf(fact_221_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_222_keysFor__empty, axiom,
    (((keysFor @ bot_bot_set_msg) = bot_bot_set_nat))). % keysFor_empty
thf(fact_223_singleton__insert__inj__eq_H, axiom,
    ((![A3 : msg, A : set_msg, B : msg]: (((insert_msg @ A3 @ A) = (insert_msg @ B @ bot_bot_set_msg)) = (((A3 = B)) & ((ord_less_eq_set_msg @ A @ (insert_msg @ B @ bot_bot_set_msg)))))))). % singleton_insert_inj_eq'
thf(fact_224_singleton__insert__inj__eq_H, axiom,
    ((![A3 : nat, A : set_nat, B : nat]: (((insert_nat @ A3 @ A) = (insert_nat @ B @ bot_bot_set_nat)) = (((A3 = B)) & ((ord_less_eq_set_nat @ A @ (insert_nat @ B @ bot_bot_set_nat)))))))). % singleton_insert_inj_eq'
thf(fact_225_singleton__insert__inj__eq, axiom,
    ((![B : msg, A3 : msg, A : set_msg]: (((insert_msg @ B @ bot_bot_set_msg) = (insert_msg @ A3 @ A)) = (((A3 = B)) & ((ord_less_eq_set_msg @ A @ (insert_msg @ B @ bot_bot_set_msg)))))))). % singleton_insert_inj_eq
thf(fact_226_singleton__insert__inj__eq, axiom,
    ((![B : nat, A3 : nat, A : set_nat]: (((insert_nat @ B @ bot_bot_set_nat) = (insert_nat @ A3 @ A)) = (((A3 = B)) & ((ord_less_eq_set_nat @ A @ (insert_nat @ B @ bot_bot_set_nat)))))))). % singleton_insert_inj_eq
thf(fact_227_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_228_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_229_keysFor__insert__Key, axiom,
    ((![K : nat, H : set_msg]: ((keysFor @ (insert_msg @ (key @ K) @ H)) = (keysFor @ H))))). % keysFor_insert_Key
thf(fact_230_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_231_mk__disjoint__insert, axiom,
    ((![A3 : msg, A : set_msg]: ((member_msg @ A3 @ A) => (?[B5 : set_msg]: ((A = (insert_msg @ A3 @ B5)) & (~ ((member_msg @ A3 @ B5))))))))). % mk_disjoint_insert
thf(fact_232_mk__disjoint__insert, axiom,
    ((![A3 : nat, A : set_nat]: ((member_nat @ A3 @ A) => (?[B5 : set_nat]: ((A = (insert_nat @ A3 @ B5)) & (~ ((member_nat @ A3 @ B5))))))))). % mk_disjoint_insert
thf(fact_233_mk__disjoint__insert, axiom,
    ((![A3 : list_event, A : set_list_event]: ((member_list_event @ A3 @ A) => (?[B5 : set_list_event]: ((A = (insert_list_event @ A3 @ B5)) & (~ ((member_list_event @ A3 @ B5))))))))). % mk_disjoint_insert
thf(fact_234_mk__disjoint__insert, axiom,
    ((![A3 : agent, A : set_agent]: ((member_agent @ A3 @ A) => (?[B5 : set_agent]: ((A = (insert_agent @ A3 @ B5)) & (~ ((member_agent @ A3 @ B5))))))))). % mk_disjoint_insert
thf(fact_235_insert__commute, axiom,
    ((![X3 : msg, Y : msg, A : set_msg]: ((insert_msg @ X3 @ (insert_msg @ Y @ A)) = (insert_msg @ Y @ (insert_msg @ X3 @ A)))))). % insert_commute
thf(fact_236_insert__eq__iff, axiom,
    ((![A3 : msg, A : set_msg, B : msg, B2 : set_msg]: ((~ ((member_msg @ A3 @ A))) => ((~ ((member_msg @ B @ B2))) => (((insert_msg @ A3 @ A) = (insert_msg @ B @ B2)) = (((((A3 = B)) => ((A = B2)))) & ((((~ ((A3 = B)))) => ((?[C3 : set_msg]: (((A = (insert_msg @ B @ C3))) & ((((~ ((member_msg @ B @ C3)))) & ((((B2 = (insert_msg @ A3 @ C3))) & ((~ ((member_msg @ A3 @ C3)))))))))))))))))))). % insert_eq_iff
thf(fact_237_insert__eq__iff, axiom,
    ((![A3 : nat, A : set_nat, B : nat, B2 : set_nat]: ((~ ((member_nat @ A3 @ A))) => ((~ ((member_nat @ B @ B2))) => (((insert_nat @ A3 @ A) = (insert_nat @ B @ B2)) = (((((A3 = B)) => ((A = B2)))) & ((((~ ((A3 = B)))) => ((?[C3 : set_nat]: (((A = (insert_nat @ B @ C3))) & ((((~ ((member_nat @ B @ C3)))) & ((((B2 = (insert_nat @ A3 @ C3))) & ((~ ((member_nat @ A3 @ C3)))))))))))))))))))). % insert_eq_iff
thf(fact_238_insert__eq__iff, axiom,
    ((![A3 : list_event, A : set_list_event, B : list_event, B2 : set_list_event]: ((~ ((member_list_event @ A3 @ A))) => ((~ ((member_list_event @ B @ B2))) => (((insert_list_event @ A3 @ A) = (insert_list_event @ B @ B2)) = (((((A3 = B)) => ((A = B2)))) & ((((~ ((A3 = B)))) => ((?[C3 : set_list_event]: (((A = (insert_list_event @ B @ C3))) & ((((~ ((member_list_event @ B @ C3)))) & ((((B2 = (insert_list_event @ A3 @ C3))) & ((~ ((member_list_event @ A3 @ C3)))))))))))))))))))). % insert_eq_iff
thf(fact_239_insert__eq__iff, axiom,
    ((![A3 : agent, A : set_agent, B : agent, B2 : set_agent]: ((~ ((member_agent @ A3 @ A))) => ((~ ((member_agent @ B @ B2))) => (((insert_agent @ A3 @ A) = (insert_agent @ B @ B2)) = (((((A3 = B)) => ((A = B2)))) & ((((~ ((A3 = B)))) => ((?[C3 : set_agent]: (((A = (insert_agent @ B @ C3))) & ((((~ ((member_agent @ B @ C3)))) & ((((B2 = (insert_agent @ A3 @ C3))) & ((~ ((member_agent @ A3 @ C3)))))))))))))))))))). % insert_eq_iff
thf(fact_240_insert__absorb, axiom,
    ((![A3 : msg, A : set_msg]: ((member_msg @ A3 @ A) => ((insert_msg @ A3 @ A) = A))))). % insert_absorb
thf(fact_241_insert__absorb, axiom,
    ((![A3 : nat, A : set_nat]: ((member_nat @ A3 @ A) => ((insert_nat @ A3 @ A) = A))))). % insert_absorb
thf(fact_242_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_243_insert__absorb, axiom,
    ((![A3 : agent, A : set_agent]: ((member_agent @ A3 @ A) => ((insert_agent @ A3 @ A) = A))))). % insert_absorb
thf(fact_244_insert__ident, axiom,
    ((![X3 : msg, A : set_msg, B2 : set_msg]: ((~ ((member_msg @ X3 @ A))) => ((~ ((member_msg @ X3 @ B2))) => (((insert_msg @ X3 @ A) = (insert_msg @ X3 @ B2)) = (A = B2))))))). % insert_ident
thf(fact_245_insert__ident, axiom,
    ((![X3 : nat, A : set_nat, B2 : set_nat]: ((~ ((member_nat @ X3 @ A))) => ((~ ((member_nat @ X3 @ B2))) => (((insert_nat @ X3 @ A) = (insert_nat @ X3 @ B2)) = (A = B2))))))). % insert_ident
thf(fact_246_insert__ident, axiom,
    ((![X3 : list_event, A : set_list_event, B2 : set_list_event]: ((~ ((member_list_event @ X3 @ A))) => ((~ ((member_list_event @ X3 @ B2))) => (((insert_list_event @ X3 @ A) = (insert_list_event @ X3 @ B2)) = (A = B2))))))). % insert_ident
thf(fact_247_insert__ident, axiom,
    ((![X3 : agent, A : set_agent, B2 : set_agent]: ((~ ((member_agent @ X3 @ A))) => ((~ ((member_agent @ X3 @ B2))) => (((insert_agent @ X3 @ A) = (insert_agent @ X3 @ B2)) = (A = B2))))))). % insert_ident
thf(fact_248_Set_Oset__insert, axiom,
    ((![X3 : agent, A : set_agent]: ((member_agent @ X3 @ A) => (~ ((![B5 : set_agent]: ((A = (insert_agent @ X3 @ B5)) => (member_agent @ X3 @ B5))))))))). % Set.set_insert

% Conjectures (4)
thf(conj_0, hypothesis,
    ((~ ((member_msg @ (key @ k) @ (used @ evs)))))).
thf(conj_1, hypothesis,
    ((member_nat @ k @ symKeys))).
thf(conj_2, hypothesis,
    ((member_list_event @ evs @ nS_Sha1061662329shared))).
thf(conj_3, conjecture,
    ((~ ((member_nat @ k @ (keysFor @ (parts @ (knows @ spy @ evs)))))))).
