% 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_134__5229010_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:23:39.837

% 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 (35)
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_Oanalzp, type,
    analzp : (msg > $o) > msg > $o).
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_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_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_evs, type,
    evs : list_event).

% Relevant facts (235)
thf(fact_0_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_1_shrK__in__knows, axiom,
    ((![A : agent, Evs : list_event]: (member_msg @ (key @ (shrK @ A)) @ (knows @ A @ Evs))))). % shrK_in_knows
thf(fact_2_Spy__in__bad, axiom,
    ((member_agent @ spy @ bad))). % Spy_in_bad
thf(fact_3_analz__impI, axiom,
    ((![Y : msg, Evs : list_event, Q : $o]: (((~ ((member_msg @ Y @ (analz @ (knows @ spy @ Evs))))) => Q) => ((~ ((member_msg @ Y @ (analz @ (knows @ spy @ Evs))))) => Q))))). % analz_impI
thf(fact_4_shrK__injective, axiom,
    ((![X : agent, Y2 : agent]: (((shrK @ X) = (shrK @ Y2)) = (X = Y2))))). % shrK_injective
thf(fact_5_msg_Oinject_I4_J, axiom,
    ((![X4 : nat, Y4 : nat]: (((key @ X4) = (key @ Y4)) = (X4 = Y4))))). % msg.inject(4)
thf(fact_6_analz__idem, axiom,
    ((![H : set_msg]: ((analz @ (analz @ H)) = (analz @ H))))). % analz_idem
thf(fact_7_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_8_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_9_Crypt__Spy__analz__bad, axiom,
    ((![A : agent, X2 : msg, Evs : list_event]: ((member_msg @ (crypt @ (shrK @ A) @ X2) @ (analz @ (knows @ spy @ Evs))) => ((member_agent @ A @ bad) => (member_msg @ X2 @ (analz @ (knows @ spy @ Evs)))))))). % Crypt_Spy_analz_bad
thf(fact_10_analz_OInj, axiom,
    ((![X2 : msg, H : set_msg]: ((member_msg @ X2 @ H) => (member_msg @ X2 @ (analz @ H)))))). % analz.Inj
thf(fact_11_analz__analzD, axiom,
    ((![X2 : msg, H : set_msg]: ((member_msg @ X2 @ (analz @ (analz @ H))) => (member_msg @ X2 @ (analz @ H)))))). % analz_analzD
thf(fact_12_parts__idem, axiom,
    ((![H : set_msg]: ((parts @ (parts @ H)) = (parts @ H))))). % parts_idem
thf(fact_13_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_14_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_15_analz__disj__parts, axiom,
    ((![X2 : msg, H : set_msg]: ((((member_msg @ X2 @ (analz @ H))) | ((member_msg @ X2 @ (parts @ H)))) = (member_msg @ X2 @ (parts @ H)))))). % analz_disj_parts
thf(fact_16_analz__conj__parts, axiom,
    ((![X2 : msg, H : set_msg]: ((((member_msg @ X2 @ (analz @ H))) & ((member_msg @ X2 @ (parts @ H)))) = (member_msg @ X2 @ (analz @ H)))))). % analz_conj_parts
thf(fact_17_parts__analz, axiom,
    ((![H : set_msg]: ((parts @ (analz @ H)) = (parts @ H))))). % parts_analz
thf(fact_18_analz__parts, axiom,
    ((![H : set_msg]: ((analz @ (parts @ H)) = (parts @ H))))). % analz_parts
thf(fact_19_spies__pubK, axiom,
    ((![B : keymode, A : agent, Evs : list_event]: (member_msg @ (key @ (publicKey @ B @ A)) @ (knows @ spy @ Evs))))). % spies_pubK
thf(fact_20_parts_OInj, axiom,
    ((![X2 : msg, H : set_msg]: ((member_msg @ X2 @ H) => (member_msg @ X2 @ (parts @ H)))))). % parts.Inj
thf(fact_21_parts_OBody, axiom,
    ((![K : nat, X2 : msg, H : set_msg]: ((member_msg @ (crypt @ K @ X2) @ (parts @ H)) => (member_msg @ X2 @ (parts @ H)))))). % parts.Body
thf(fact_22_parts__partsD, axiom,
    ((![X2 : msg, H : set_msg]: ((member_msg @ X2 @ (parts @ (parts @ H))) => (member_msg @ X2 @ (parts @ H)))))). % parts_partsD
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_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_25_analz__into__parts, axiom,
    ((![C : msg, H : set_msg]: ((member_msg @ C @ (analz @ H)) => (member_msg @ C @ (parts @ H)))))). % analz_into_parts
thf(fact_26_msg_Odistinct_I35_J, axiom,
    ((![X4 : nat, X71 : nat, X72 : msg]: (~ (((key @ X4) = (crypt @ X71 @ X72))))))). % msg.distinct(35)
thf(fact_27_shrK__neq__pubK, axiom,
    ((![B : keymode, C2 : agent, A : agent]: (~ (((publicKey @ B @ C2) = (shrK @ A))))))). % shrK_neq_pubK
thf(fact_28_analz__shrK__Decrypt, axiom,
    ((![A : agent, X2 : msg, H : set_msg]: ((member_msg @ (crypt @ (shrK @ A) @ X2) @ (analz @ H)) => ((member_msg @ (key @ (shrK @ A)) @ (analz @ H)) => (member_msg @ X2 @ (analz @ H))))))). % analz_shrK_Decrypt
thf(fact_29_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_30_analz__symKeys__Decrypt, axiom,
    ((![K : nat, X2 : msg, H : set_msg]: ((member_msg @ (crypt @ K @ X2) @ (analz @ H)) => ((member_nat @ K @ symKeys) => ((member_msg @ (key @ K) @ (analz @ H)) => (member_msg @ X2 @ (analz @ H)))))))). % analz_symKeys_Decrypt
thf(fact_31_shrK__in__initState, axiom,
    ((![A : agent]: (member_msg @ (key @ (shrK @ A)) @ (initState @ A))))). % shrK_in_initState
thf(fact_32_publicKey__in__initState, axiom,
    ((![B : keymode, A : agent, B2 : agent]: (member_msg @ (key @ (publicKey @ B @ A)) @ (initState @ B2))))). % publicKey_in_initState
thf(fact_33_usedI, axiom,
    ((![C : msg, Evs : list_event]: ((member_msg @ C @ (parts @ (knows @ spy @ Evs))) => (member_msg @ C @ (used @ Evs)))))). % usedI
thf(fact_34_Crypt__notin__initState, axiom,
    ((![K : nat, X2 : msg, B2 : agent]: (~ ((member_msg @ (crypt @ K @ X2) @ (parts @ (initState @ B2)))))))). % Crypt_notin_initState
thf(fact_35_analz_ODecrypt, axiom,
    ((![K : nat, X2 : msg, H : set_msg]: ((member_msg @ (crypt @ K @ X2) @ (analz @ H)) => ((member_msg @ (key @ (invKey @ K)) @ (analz @ H)) => (member_msg @ X2 @ (analz @ H))))))). % analz.Decrypt
thf(fact_36_shrK__in__used, axiom,
    ((![A : agent, Evs : list_event]: (member_msg @ (key @ (shrK @ A)) @ (used @ Evs))))). % shrK_in_used
thf(fact_37_publicKey__into__used, axiom,
    ((![B : keymode, A : agent, Evs : list_event]: (member_msg @ (key @ (publicKey @ B @ A)) @ (used @ Evs))))). % publicKey_into_used
thf(fact_38_invKey, axiom,
    ((![K : nat]: ((invKey @ (invKey @ K)) = K)))). % invKey
thf(fact_39_invKey__eq, axiom,
    ((![K : nat, K2 : nat]: (((invKey @ K) = (invKey @ K2)) = (K = K2))))). % invKey_eq
thf(fact_40_invKey__shrK, axiom,
    ((![A : agent]: ((invKey @ (shrK @ A)) = (shrK @ A))))). % invKey_shrK
thf(fact_41_invKey__K, axiom,
    ((![K : nat]: ((member_nat @ K @ symKeys) => ((invKey @ K) = K))))). % invKey_K
thf(fact_42_symKeys__invKey__iff, axiom,
    ((![K : nat]: ((member_nat @ (invKey @ K) @ symKeys) = (member_nat @ K @ symKeys))))). % symKeys_invKey_iff
thf(fact_43_sym__shrK, axiom,
    ((![X2 : agent]: (member_nat @ (shrK @ X2) @ symKeys)))). % sym_shrK
thf(fact_44_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_45_mem__Collect__eq, axiom,
    ((![A3 : msg, P : msg > $o]: ((member_msg @ A3 @ (collect_msg @ P)) = (P @ A3))))). % mem_Collect_eq
thf(fact_46_mem__Collect__eq, axiom,
    ((![A3 : agent, P : agent > $o]: ((member_agent @ A3 @ (collect_agent @ P)) = (P @ A3))))). % mem_Collect_eq
thf(fact_47_mem__Collect__eq, axiom,
    ((![A3 : nat, P : nat > $o]: ((member_nat @ A3 @ (collect_nat @ P)) = (P @ A3))))). % mem_Collect_eq
thf(fact_48_Collect__mem__eq, axiom,
    ((![A : set_list_event]: ((collect_list_event @ (^[X3 : list_event]: (member_list_event @ X3 @ A))) = A)))). % Collect_mem_eq
thf(fact_49_Collect__mem__eq, axiom,
    ((![A : set_msg]: ((collect_msg @ (^[X3 : msg]: (member_msg @ X3 @ A))) = A)))). % Collect_mem_eq
thf(fact_50_Collect__mem__eq, axiom,
    ((![A : set_agent]: ((collect_agent @ (^[X3 : agent]: (member_agent @ X3 @ A))) = A)))). % Collect_mem_eq
thf(fact_51_Collect__mem__eq, axiom,
    ((![A : set_nat]: ((collect_nat @ (^[X3 : nat]: (member_nat @ X3 @ A))) = A)))). % Collect_mem_eq
thf(fact_52_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_53_priK__in__initState, axiom,
    ((![B : keymode, A : agent]: (member_msg @ (key @ (invKey @ (publicKey @ B @ A))) @ (initState @ A))))). % priK_in_initState
thf(fact_54_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_55_initState__into__used, axiom,
    ((![X2 : msg, B2 : agent, Evs : list_event]: ((member_msg @ X2 @ (parts @ (initState @ B2))) => (member_msg @ X2 @ (used @ Evs)))))). % initState_into_used
thf(fact_56_not__symKeys__priK, axiom,
    ((![B : keymode, A : agent]: (~ ((member_nat @ (invKey @ (publicKey @ B @ A)) @ symKeys)))))). % not_symKeys_priK
thf(fact_57_publicKey__neq__privateKey, axiom,
    ((![C : keymode, A2 : agent, B : keymode, A : agent]: (~ (((publicKey @ C @ A2) = (invKey @ (publicKey @ B @ A)))))))). % publicKey_neq_privateKey
thf(fact_58_not__symKeys__pubK, axiom,
    ((![B : keymode, A : agent]: (~ ((member_nat @ (publicKey @ B @ A) @ symKeys)))))). % not_symKeys_pubK
thf(fact_59_shrK__neq__priK, axiom,
    ((![B : keymode, C2 : agent, A : agent]: (~ (((invKey @ (publicKey @ B @ C2)) = (shrK @ A))))))). % shrK_neq_priK
thf(fact_60_neq__shrK, axiom,
    ((![S : nat, Evs : list_event, B2 : agent]: ((~ ((member_msg @ (key @ S) @ (used @ Evs)))) => (~ ((S = (shrK @ B2)))))))). % neq_shrK
thf(fact_61_shrK__neq, axiom,
    ((![K : nat, Evs : list_event, B2 : agent]: ((~ ((member_msg @ (key @ K) @ (used @ Evs)))) => (~ (((shrK @ B2) = K))))))). % shrK_neq
thf(fact_62_symKey__neq__priEK, axiom,
    ((![K : nat, A : agent]: ((member_nat @ K @ symKeys) => (~ ((K = (invKey @ (publicKey @ encryption @ A))))))))). % symKey_neq_priEK
thf(fact_63_priEK__noteq__shrK, axiom,
    ((![A : agent, B2 : agent]: (~ (((invKey @ (publicKey @ encryption @ A)) = (shrK @ B2))))))). % priEK_noteq_shrK
thf(fact_64_analz__Crypt__if, axiom,
    ((![K : nat, H : set_msg, X2 : msg]: (((member_msg @ (key @ (invKey @ K)) @ (analz @ H)) => ((analz @ (insert_msg @ (crypt @ K @ X2) @ H)) = (insert_msg @ (crypt @ K @ X2) @ (analz @ (insert_msg @ X2 @ H))))) & ((~ ((member_msg @ (key @ (invKey @ K)) @ (analz @ H)))) => ((analz @ (insert_msg @ (crypt @ K @ X2) @ H)) = (insert_msg @ (crypt @ K @ X2) @ (analz @ H)))))))). % analz_Crypt_if
thf(fact_65_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_66_analz__insert__Crypt, axiom,
    ((![K : nat, H : set_msg, X2 : msg]: ((~ ((member_msg @ (key @ (invKey @ K)) @ (analz @ H)))) => ((analz @ (insert_msg @ (crypt @ K @ X2) @ H)) = (insert_msg @ (crypt @ K @ X2) @ (analz @ H))))))). % analz_insert_Crypt
thf(fact_67_analz__insert__Decrypt, axiom,
    ((![K : nat, H : set_msg, X2 : msg]: ((member_msg @ (key @ (invKey @ K)) @ (analz @ H)) => ((analz @ (insert_msg @ (crypt @ K @ X2) @ H)) = (insert_msg @ (crypt @ K @ X2) @ (analz @ (insert_msg @ X2 @ H)))))))). % analz_insert_Decrypt
thf(fact_68_analzp_ODecrypt, axiom,
    ((![H : msg > $o, K : nat, X2 : msg]: ((analzp @ H @ (crypt @ K @ X2)) => ((analzp @ H @ (key @ (invKey @ K))) => (analzp @ H @ X2)))))). % analzp.Decrypt
thf(fact_69_parts__cut__eq, axiom,
    ((![X2 : msg, H : set_msg]: ((member_msg @ X2 @ (parts @ H)) => ((parts @ (insert_msg @ X2 @ H)) = (parts @ H)))))). % parts_cut_eq
thf(fact_70_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_71_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_72_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_73_parts__insert__Crypt, axiom,
    ((![K : nat, X2 : msg, H : set_msg]: ((parts @ (insert_msg @ (crypt @ K @ X2) @ H)) = (insert_msg @ (crypt @ K @ X2) @ (parts @ (insert_msg @ X2 @ H))))))). % parts_insert_Crypt
thf(fact_74_gen__analz__insert__eq, axiom,
    ((![X2 : msg, H : set_msg, G : set_msg]: ((member_msg @ X2 @ (analz @ H)) => ((ord_less_eq_set_msg @ H @ G) => ((analz @ (insert_msg @ X2 @ G)) = (analz @ G))))))). % gen_analz_insert_eq
thf(fact_75_analz__insert, axiom,
    ((![X2 : msg, H : set_msg]: (ord_less_eq_set_msg @ (insert_msg @ X2 @ (analz @ H)) @ (analz @ (insert_msg @ X2 @ H)))))). % analz_insert
thf(fact_76_parts__insert__subset, axiom,
    ((![X2 : msg, H : set_msg]: (ord_less_eq_set_msg @ (insert_msg @ X2 @ (parts @ H)) @ (parts @ (insert_msg @ X2 @ H)))))). % parts_insert_subset
thf(fact_77_analzp_OInj, axiom,
    ((![H : msg > $o, X2 : msg]: ((H @ X2) => (analzp @ H @ X2))))). % analzp.Inj
thf(fact_78_analz__insert__Crypt__subset, axiom,
    ((![K : nat, X2 : msg, H : set_msg]: (ord_less_eq_set_msg @ (analz @ (insert_msg @ (crypt @ K @ X2) @ H)) @ (insert_msg @ (crypt @ K @ X2) @ (analz @ (insert_msg @ X2 @ H))))))). % analz_insert_Crypt_subset
thf(fact_79_analz__insert__eq__I, axiom,
    ((![X2 : msg, H : set_msg]: ((![X5 : msg]: ((member_msg @ X5 @ (analz @ (insert_msg @ X2 @ H))) => (member_msg @ X5 @ (insert_msg @ X2 @ (analz @ H))))) => ((analz @ (insert_msg @ X2 @ H)) = (insert_msg @ X2 @ (analz @ H))))))). % analz_insert_eq_I
thf(fact_80_analz__insert__cong, axiom,
    ((![H : set_msg, H2 : set_msg, X2 : msg]: (((analz @ H) = (analz @ H2)) => ((analz @ (insert_msg @ X2 @ H)) = (analz @ (insert_msg @ X2 @ H2))))))). % analz_insert_cong
thf(fact_81_analz__insert__eq, axiom,
    ((![X2 : msg, H : set_msg]: ((member_msg @ X2 @ (analz @ H)) => ((analz @ (insert_msg @ X2 @ H)) = (analz @ H)))))). % analz_insert_eq
thf(fact_82_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_83_analz__cut, axiom,
    ((![Y : msg, X2 : msg, H : set_msg]: ((member_msg @ Y @ (analz @ (insert_msg @ X2 @ H))) => ((member_msg @ X2 @ (analz @ H)) => (member_msg @ Y @ (analz @ H))))))). % analz_cut
thf(fact_84_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_85_parts__insert__eq__I, axiom,
    ((![X2 : msg, H : set_msg]: ((![X5 : msg]: ((member_msg @ X5 @ (parts @ (insert_msg @ X2 @ H))) => (member_msg @ X5 @ (insert_msg @ X2 @ (parts @ H))))) => ((parts @ (insert_msg @ X2 @ H)) = (insert_msg @ X2 @ (parts @ H))))))). % parts_insert_eq_I
thf(fact_86_analz__increasing, axiom,
    ((![H : set_msg]: (ord_less_eq_set_msg @ H @ (analz @ H))))). % analz_increasing
thf(fact_87_analz__trans, axiom,
    ((![X2 : msg, G : set_msg, H : set_msg]: ((member_msg @ X2 @ (analz @ G)) => ((ord_less_eq_set_msg @ G @ (analz @ H)) => (member_msg @ X2 @ (analz @ H))))))). % analz_trans
thf(fact_88_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_89_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_90_parts__trans, axiom,
    ((![X2 : msg, G : set_msg, H : set_msg]: ((member_msg @ X2 @ (parts @ G)) => ((ord_less_eq_set_msg @ G @ (parts @ H)) => (member_msg @ X2 @ (parts @ H))))))). % parts_trans
thf(fact_91_parts__increasing, axiom,
    ((![H : set_msg]: (ord_less_eq_set_msg @ H @ (parts @ H))))). % parts_increasing
thf(fact_92_lemma1, axiom,
    ((![K : nat, H : set_msg, X2 : msg]: ((member_msg @ (key @ (invKey @ K)) @ (analz @ H)) => (ord_less_eq_set_msg @ (analz @ (insert_msg @ (crypt @ K @ X2) @ H)) @ (insert_msg @ (crypt @ K @ X2) @ (analz @ (insert_msg @ X2 @ H)))))))). % lemma1
thf(fact_93_lemma2, axiom,
    ((![K : nat, H : set_msg, X2 : msg]: ((member_msg @ (key @ (invKey @ K)) @ (analz @ H)) => (ord_less_eq_set_msg @ (insert_msg @ (crypt @ K @ X2) @ (analz @ (insert_msg @ X2 @ H))) @ (analz @ (insert_msg @ (crypt @ K @ X2) @ H))))))). % lemma2
thf(fact_94_pushKeys_I6_J, axiom,
    ((![K : nat, X2 : nat, K2 : msg, A : set_msg]: ((insert_msg @ (key @ K) @ (insert_msg @ (crypt @ X2 @ K2) @ A)) = (insert_msg @ (crypt @ X2 @ K2) @ (insert_msg @ (key @ K) @ A)))))). % pushKeys(6)
thf(fact_95_analz__subset__parts, axiom,
    ((![H : set_msg]: (ord_less_eq_set_msg @ (analz @ H) @ (parts @ H))))). % analz_subset_parts
thf(fact_96_initState__subset__knows, axiom,
    ((![A : agent, Evs : list_event]: (ord_less_eq_set_msg @ (initState @ A) @ (knows @ A @ Evs))))). % initState_subset_knows
thf(fact_97_insert__subset, axiom,
    ((![X : list_event, A : set_list_event, B2 : set_list_event]: ((ord_le119303592_event @ (insert_list_event @ X @ A) @ B2) = (((member_list_event @ X @ B2)) & ((ord_le119303592_event @ A @ B2))))))). % insert_subset
thf(fact_98_insert__subset, axiom,
    ((![X : agent, A : set_agent, B2 : set_agent]: ((ord_le722097072_agent @ (insert_agent @ X @ A) @ B2) = (((member_agent @ X @ B2)) & ((ord_le722097072_agent @ A @ B2))))))). % insert_subset
thf(fact_99_insert__subset, axiom,
    ((![X : msg, A : set_msg, B2 : set_msg]: ((ord_less_eq_set_msg @ (insert_msg @ X @ A) @ B2) = (((member_msg @ X @ B2)) & ((ord_less_eq_set_msg @ A @ B2))))))). % insert_subset
thf(fact_100_insert__subset, axiom,
    ((![X : nat, A : set_nat, B2 : set_nat]: ((ord_less_eq_set_nat @ (insert_nat @ X @ A) @ B2) = (((member_nat @ X @ B2)) & ((ord_less_eq_set_nat @ A @ B2))))))). % insert_subset
thf(fact_101_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_102_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_103_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_104_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_105_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_106_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_107_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_108_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_109_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_110_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_111_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_112_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_113_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_114_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_115_insert__absorb2, axiom,
    ((![X : msg, A : set_msg]: ((insert_msg @ X @ (insert_msg @ X @ A)) = (insert_msg @ X @ A))))). % insert_absorb2
thf(fact_116_insert__absorb2, axiom,
    ((![X : nat, A : set_nat]: ((insert_nat @ X @ (insert_nat @ X @ A)) = (insert_nat @ X @ A))))). % insert_absorb2
thf(fact_117_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_118_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_119_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_120_mk__disjoint__insert, axiom,
    ((![A3 : nat, A : set_nat]: ((member_nat @ A3 @ A) => (?[B3 : set_nat]: ((A = (insert_nat @ A3 @ B3)) & (~ ((member_nat @ A3 @ B3))))))))). % mk_disjoint_insert
thf(fact_121_insert__commute, axiom,
    ((![X : msg, Y2 : msg, A : set_msg]: ((insert_msg @ X @ (insert_msg @ Y2 @ A)) = (insert_msg @ Y2 @ (insert_msg @ X @ A)))))). % insert_commute
thf(fact_122_insert__commute, axiom,
    ((![X : nat, Y2 : nat, A : set_nat]: ((insert_nat @ X @ (insert_nat @ Y2 @ A)) = (insert_nat @ Y2 @ (insert_nat @ X @ A)))))). % insert_commute
thf(fact_123_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_124_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_125_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_126_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_127_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_128_insert__absorb, axiom,
    ((![A3 : msg, A : set_msg]: ((member_msg @ A3 @ A) => ((insert_msg @ A3 @ A) = A))))). % insert_absorb
thf(fact_129_insert__absorb, axiom,
    ((![A3 : agent, A : set_agent]: ((member_agent @ A3 @ A) => ((insert_agent @ A3 @ A) = A))))). % insert_absorb
thf(fact_130_insert__absorb, axiom,
    ((![A3 : nat, A : set_nat]: ((member_nat @ A3 @ A) => ((insert_nat @ A3 @ A) = A))))). % insert_absorb
thf(fact_131_insert__ident, axiom,
    ((![X : list_event, A : set_list_event, B2 : set_list_event]: ((~ ((member_list_event @ X @ A))) => ((~ ((member_list_event @ X @ B2))) => (((insert_list_event @ X @ A) = (insert_list_event @ X @ B2)) = (A = B2))))))). % insert_ident
thf(fact_132_insert__ident, axiom,
    ((![X : msg, A : set_msg, B2 : set_msg]: ((~ ((member_msg @ X @ A))) => ((~ ((member_msg @ X @ B2))) => (((insert_msg @ X @ A) = (insert_msg @ X @ B2)) = (A = B2))))))). % insert_ident
thf(fact_133_insert__ident, axiom,
    ((![X : agent, A : set_agent, B2 : set_agent]: ((~ ((member_agent @ X @ A))) => ((~ ((member_agent @ X @ B2))) => (((insert_agent @ X @ A) = (insert_agent @ X @ B2)) = (A = B2))))))). % insert_ident
thf(fact_134_insert__ident, axiom,
    ((![X : nat, A : set_nat, B2 : set_nat]: ((~ ((member_nat @ X @ A))) => ((~ ((member_nat @ X @ B2))) => (((insert_nat @ X @ A) = (insert_nat @ X @ B2)) = (A = B2))))))). % insert_ident
thf(fact_135_Set_Oset__insert, axiom,
    ((![X : list_event, A : set_list_event]: ((member_list_event @ X @ A) => (~ ((![B3 : set_list_event]: ((A = (insert_list_event @ X @ B3)) => (member_list_event @ X @ B3))))))))). % Set.set_insert
thf(fact_136_Set_Oset__insert, axiom,
    ((![X : msg, A : set_msg]: ((member_msg @ X @ A) => (~ ((![B3 : set_msg]: ((A = (insert_msg @ X @ B3)) => (member_msg @ X @ B3))))))))). % Set.set_insert
thf(fact_137_Set_Oset__insert, axiom,
    ((![X : agent, A : set_agent]: ((member_agent @ X @ A) => (~ ((![B3 : set_agent]: ((A = (insert_agent @ X @ B3)) => (member_agent @ X @ B3))))))))). % Set.set_insert
thf(fact_138_Set_Oset__insert, axiom,
    ((![X : nat, A : set_nat]: ((member_nat @ X @ A) => (~ ((![B3 : set_nat]: ((A = (insert_nat @ X @ B3)) => (member_nat @ X @ B3))))))))). % Set.set_insert
thf(fact_139_insertI2, axiom,
    ((![A3 : list_event, B2 : set_list_event, B : list_event]: ((member_list_event @ A3 @ B2) => (member_list_event @ A3 @ (insert_list_event @ B @ B2)))))). % insertI2
thf(fact_140_insertI2, axiom,
    ((![A3 : msg, B2 : set_msg, B : msg]: ((member_msg @ A3 @ B2) => (member_msg @ A3 @ (insert_msg @ B @ B2)))))). % insertI2
thf(fact_141_insertI2, axiom,
    ((![A3 : agent, B2 : set_agent, B : agent]: ((member_agent @ A3 @ B2) => (member_agent @ A3 @ (insert_agent @ B @ B2)))))). % insertI2
thf(fact_142_insertI2, axiom,
    ((![A3 : nat, B2 : set_nat, B : nat]: ((member_nat @ A3 @ B2) => (member_nat @ A3 @ (insert_nat @ B @ B2)))))). % insertI2
thf(fact_143_insertI1, axiom,
    ((![A3 : list_event, B2 : set_list_event]: (member_list_event @ A3 @ (insert_list_event @ A3 @ B2))))). % insertI1
thf(fact_144_insertI1, axiom,
    ((![A3 : msg, B2 : set_msg]: (member_msg @ A3 @ (insert_msg @ A3 @ B2))))). % insertI1
thf(fact_145_insertI1, axiom,
    ((![A3 : agent, B2 : set_agent]: (member_agent @ A3 @ (insert_agent @ A3 @ B2))))). % insertI1
thf(fact_146_insertI1, axiom,
    ((![A3 : nat, B2 : set_nat]: (member_nat @ A3 @ (insert_nat @ A3 @ B2))))). % insertI1
thf(fact_147_insertE, 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)))))). % insertE
thf(fact_148_insertE, axiom,
    ((![A3 : msg, B : msg, A : set_msg]: ((member_msg @ A3 @ (insert_msg @ B @ A)) => ((~ ((A3 = B))) => (member_msg @ A3 @ A)))))). % insertE
thf(fact_149_insertE, axiom,
    ((![A3 : agent, B : agent, A : set_agent]: ((member_agent @ A3 @ (insert_agent @ B @ A)) => ((~ ((A3 = B))) => (member_agent @ A3 @ A)))))). % insertE
thf(fact_150_insertE, axiom,
    ((![A3 : nat, B : nat, A : set_nat]: ((member_nat @ A3 @ (insert_nat @ B @ A)) => ((~ ((A3 = B))) => (member_nat @ A3 @ A)))))). % insertE
thf(fact_151_Collect__mono__iff, axiom,
    ((![P : msg > $o, Q : msg > $o]: ((ord_less_eq_set_msg @ (collect_msg @ P) @ (collect_msg @ Q)) = (![X3 : msg]: (((P @ X3)) => ((Q @ X3)))))))). % Collect_mono_iff
thf(fact_152_Collect__mono__iff, axiom,
    ((![P : nat > $o, Q : nat > $o]: ((ord_less_eq_set_nat @ (collect_nat @ P) @ (collect_nat @ Q)) = (![X3 : nat]: (((P @ X3)) => ((Q @ X3)))))))). % Collect_mono_iff
thf(fact_153_set__eq__subset, axiom,
    (((^[Y3 : set_msg]: (^[Z : set_msg]: (Y3 = Z))) = (^[A4 : set_msg]: (^[B4 : set_msg]: (((ord_less_eq_set_msg @ A4 @ B4)) & ((ord_less_eq_set_msg @ B4 @ A4)))))))). % set_eq_subset
thf(fact_154_set__eq__subset, axiom,
    (((^[Y3 : set_nat]: (^[Z : set_nat]: (Y3 = Z))) = (^[A4 : set_nat]: (^[B4 : set_nat]: (((ord_less_eq_set_nat @ A4 @ B4)) & ((ord_less_eq_set_nat @ B4 @ A4)))))))). % set_eq_subset
thf(fact_155_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_156_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_157_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_158_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_159_subset__refl, axiom,
    ((![A : set_msg]: (ord_less_eq_set_msg @ A @ A)))). % subset_refl
thf(fact_160_subset__refl, axiom,
    ((![A : set_nat]: (ord_less_eq_set_nat @ A @ A)))). % subset_refl
thf(fact_161_subset__iff, axiom,
    ((ord_le119303592_event = (^[A4 : set_list_event]: (^[B4 : set_list_event]: (![T : list_event]: (((member_list_event @ T @ A4)) => ((member_list_event @ T @ B4))))))))). % subset_iff
thf(fact_162_subset__iff, axiom,
    ((ord_le722097072_agent = (^[A4 : set_agent]: (^[B4 : set_agent]: (![T : agent]: (((member_agent @ T @ A4)) => ((member_agent @ T @ B4))))))))). % subset_iff
thf(fact_163_subset__iff, axiom,
    ((ord_less_eq_set_msg = (^[A4 : set_msg]: (^[B4 : set_msg]: (![T : msg]: (((member_msg @ T @ A4)) => ((member_msg @ T @ B4))))))))). % subset_iff
thf(fact_164_subset__iff, axiom,
    ((ord_less_eq_set_nat = (^[A4 : set_nat]: (^[B4 : set_nat]: (![T : nat]: (((member_nat @ T @ A4)) => ((member_nat @ T @ B4))))))))). % subset_iff
thf(fact_165_equalityD2, axiom,
    ((![A : set_msg, B2 : set_msg]: ((A = B2) => (ord_less_eq_set_msg @ B2 @ A))))). % equalityD2
thf(fact_166_equalityD2, axiom,
    ((![A : set_nat, B2 : set_nat]: ((A = B2) => (ord_less_eq_set_nat @ B2 @ A))))). % equalityD2
thf(fact_167_equalityD1, axiom,
    ((![A : set_msg, B2 : set_msg]: ((A = B2) => (ord_less_eq_set_msg @ A @ B2))))). % equalityD1
thf(fact_168_equalityD1, axiom,
    ((![A : set_nat, B2 : set_nat]: ((A = B2) => (ord_less_eq_set_nat @ A @ B2))))). % equalityD1
thf(fact_169_subset__eq, axiom,
    ((ord_le119303592_event = (^[A4 : set_list_event]: (^[B4 : set_list_event]: (![X3 : list_event]: (((member_list_event @ X3 @ A4)) => ((member_list_event @ X3 @ B4))))))))). % subset_eq
thf(fact_170_subset__eq, axiom,
    ((ord_le722097072_agent = (^[A4 : set_agent]: (^[B4 : set_agent]: (![X3 : agent]: (((member_agent @ X3 @ A4)) => ((member_agent @ X3 @ B4))))))))). % subset_eq
thf(fact_171_subset__eq, axiom,
    ((ord_less_eq_set_msg = (^[A4 : set_msg]: (^[B4 : set_msg]: (![X3 : msg]: (((member_msg @ X3 @ A4)) => ((member_msg @ X3 @ B4))))))))). % subset_eq
thf(fact_172_subset__eq, axiom,
    ((ord_less_eq_set_nat = (^[A4 : set_nat]: (^[B4 : set_nat]: (![X3 : nat]: (((member_nat @ X3 @ A4)) => ((member_nat @ X3 @ B4))))))))). % subset_eq
thf(fact_173_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_174_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_175_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_176_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_177_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_178_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_179_in__mono, axiom,
    ((![A : set_list_event, B2 : set_list_event, X : list_event]: ((ord_le119303592_event @ A @ B2) => ((member_list_event @ X @ A) => (member_list_event @ X @ B2)))))). % in_mono
thf(fact_180_in__mono, axiom,
    ((![A : set_agent, B2 : set_agent, X : agent]: ((ord_le722097072_agent @ A @ B2) => ((member_agent @ X @ A) => (member_agent @ X @ B2)))))). % in_mono
thf(fact_181_in__mono, axiom,
    ((![A : set_msg, B2 : set_msg, X : msg]: ((ord_less_eq_set_msg @ A @ B2) => ((member_msg @ X @ A) => (member_msg @ X @ B2)))))). % in_mono
thf(fact_182_in__mono, axiom,
    ((![A : set_nat, B2 : set_nat, X : nat]: ((ord_less_eq_set_nat @ A @ B2) => ((member_nat @ X @ A) => (member_nat @ X @ B2)))))). % in_mono
thf(fact_183_subset__insertI2, axiom,
    ((![A : set_msg, B2 : set_msg, B : msg]: ((ord_less_eq_set_msg @ A @ B2) => (ord_less_eq_set_msg @ A @ (insert_msg @ B @ B2)))))). % subset_insertI2
thf(fact_184_subset__insertI2, axiom,
    ((![A : set_nat, B2 : set_nat, B : nat]: ((ord_less_eq_set_nat @ A @ B2) => (ord_less_eq_set_nat @ A @ (insert_nat @ B @ B2)))))). % subset_insertI2
thf(fact_185_subset__insertI, axiom,
    ((![B2 : set_msg, A3 : msg]: (ord_less_eq_set_msg @ B2 @ (insert_msg @ A3 @ B2))))). % subset_insertI
thf(fact_186_subset__insertI, axiom,
    ((![B2 : set_nat, A3 : nat]: (ord_less_eq_set_nat @ B2 @ (insert_nat @ A3 @ B2))))). % subset_insertI
thf(fact_187_subset__insert, axiom,
    ((![X : list_event, A : set_list_event, B2 : set_list_event]: ((~ ((member_list_event @ X @ A))) => ((ord_le119303592_event @ A @ (insert_list_event @ X @ B2)) = (ord_le119303592_event @ A @ B2)))))). % subset_insert
thf(fact_188_subset__insert, axiom,
    ((![X : agent, A : set_agent, B2 : set_agent]: ((~ ((member_agent @ X @ A))) => ((ord_le722097072_agent @ A @ (insert_agent @ X @ B2)) = (ord_le722097072_agent @ A @ B2)))))). % subset_insert
thf(fact_189_subset__insert, axiom,
    ((![X : msg, A : set_msg, B2 : set_msg]: ((~ ((member_msg @ X @ A))) => ((ord_less_eq_set_msg @ A @ (insert_msg @ X @ B2)) = (ord_less_eq_set_msg @ A @ B2)))))). % subset_insert
thf(fact_190_subset__insert, axiom,
    ((![X : nat, A : set_nat, B2 : set_nat]: ((~ ((member_nat @ X @ A))) => ((ord_less_eq_set_nat @ A @ (insert_nat @ X @ B2)) = (ord_less_eq_set_nat @ A @ B2)))))). % subset_insert
thf(fact_191_insert__mono, axiom,
    ((![C2 : set_msg, D : set_msg, A3 : msg]: ((ord_less_eq_set_msg @ C2 @ D) => (ord_less_eq_set_msg @ (insert_msg @ A3 @ C2) @ (insert_msg @ A3 @ D)))))). % insert_mono
thf(fact_192_insert__mono, axiom,
    ((![C2 : set_nat, D : set_nat, A3 : nat]: ((ord_less_eq_set_nat @ C2 @ D) => (ord_less_eq_set_nat @ (insert_nat @ A3 @ C2) @ (insert_nat @ A3 @ D)))))). % insert_mono
thf(fact_193_order__refl, axiom,
    ((![X : set_msg]: (ord_less_eq_set_msg @ X @ X)))). % order_refl
thf(fact_194_order__refl, axiom,
    ((![X : set_nat]: (ord_less_eq_set_nat @ X @ X)))). % order_refl
thf(fact_195_insert__subsetI, axiom,
    ((![X : list_event, A : set_list_event, X2 : set_list_event]: ((member_list_event @ X @ A) => ((ord_le119303592_event @ X2 @ A) => (ord_le119303592_event @ (insert_list_event @ X @ X2) @ A)))))). % insert_subsetI
thf(fact_196_insert__subsetI, axiom,
    ((![X : agent, A : set_agent, X2 : set_agent]: ((member_agent @ X @ A) => ((ord_le722097072_agent @ X2 @ A) => (ord_le722097072_agent @ (insert_agent @ X @ X2) @ A)))))). % insert_subsetI
thf(fact_197_insert__subsetI, axiom,
    ((![X : msg, A : set_msg, X2 : set_msg]: ((member_msg @ X @ A) => ((ord_less_eq_set_msg @ X2 @ A) => (ord_less_eq_set_msg @ (insert_msg @ X @ X2) @ A)))))). % insert_subsetI
thf(fact_198_insert__subsetI, axiom,
    ((![X : nat, A : set_nat, X2 : set_nat]: ((member_nat @ X @ A) => ((ord_less_eq_set_nat @ X2 @ A) => (ord_less_eq_set_nat @ (insert_nat @ X @ X2) @ A)))))). % insert_subsetI
thf(fact_199_keysFor__insert__Crypt, axiom,
    ((![K : nat, X2 : msg, H : set_msg]: ((keysFor @ (insert_msg @ (crypt @ K @ X2) @ H)) = (insert_nat @ (invKey @ K) @ (keysFor @ H)))))). % keysFor_insert_Crypt
thf(fact_200_keysFor__insert__Key, axiom,
    ((![K : nat, H : set_msg]: ((keysFor @ (insert_msg @ (key @ K) @ H)) = (keysFor @ H))))). % keysFor_insert_Key
thf(fact_201_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_202_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_203_Crypt__imp__invKey__keysFor, axiom,
    ((![K : nat, X2 : msg, H : set_msg]: ((member_msg @ (crypt @ K @ X2) @ H) => (member_nat @ (invKey @ K) @ (keysFor @ H)))))). % Crypt_imp_invKey_keysFor
thf(fact_204_Crypt__imp__keysFor, axiom,
    ((![K : nat, X2 : msg, H : set_msg]: ((member_msg @ (crypt @ K @ X2) @ H) => ((member_nat @ K @ symKeys) => (member_nat @ K @ (keysFor @ H))))))). % Crypt_imp_keysFor
thf(fact_205_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, Y5 : set_msg]: ((ord_less_eq_set_msg @ X5 @ Y5) => (ord_less_eq_set_msg @ (F @ X5) @ (F @ Y5)))) => (ord_less_eq_set_msg @ A3 @ (F @ C)))))))). % order_subst1
thf(fact_206_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, Y5 : set_nat]: ((ord_less_eq_set_nat @ X5 @ Y5) => (ord_less_eq_set_msg @ (F @ X5) @ (F @ Y5)))) => (ord_less_eq_set_msg @ A3 @ (F @ C)))))))). % order_subst1
thf(fact_207_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, Y5 : set_msg]: ((ord_less_eq_set_msg @ X5 @ Y5) => (ord_less_eq_set_nat @ (F @ X5) @ (F @ Y5)))) => (ord_less_eq_set_nat @ A3 @ (F @ C)))))))). % order_subst1
thf(fact_208_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, Y5 : set_nat]: ((ord_less_eq_set_nat @ X5 @ Y5) => (ord_less_eq_set_nat @ (F @ X5) @ (F @ Y5)))) => (ord_less_eq_set_nat @ A3 @ (F @ C)))))))). % order_subst1
thf(fact_209_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, Y5 : set_msg]: ((ord_less_eq_set_msg @ X5 @ Y5) => (ord_less_eq_set_msg @ (F @ X5) @ (F @ Y5)))) => (ord_less_eq_set_msg @ (F @ A3) @ C))))))). % order_subst2
thf(fact_210_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, Y5 : set_msg]: ((ord_less_eq_set_msg @ X5 @ Y5) => (ord_less_eq_set_nat @ (F @ X5) @ (F @ Y5)))) => (ord_less_eq_set_nat @ (F @ A3) @ C))))))). % order_subst2
thf(fact_211_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, Y5 : set_nat]: ((ord_less_eq_set_nat @ X5 @ Y5) => (ord_less_eq_set_msg @ (F @ X5) @ (F @ Y5)))) => (ord_less_eq_set_msg @ (F @ A3) @ C))))))). % order_subst2
thf(fact_212_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, Y5 : set_nat]: ((ord_less_eq_set_nat @ X5 @ Y5) => (ord_less_eq_set_nat @ (F @ X5) @ (F @ Y5)))) => (ord_less_eq_set_nat @ (F @ A3) @ C))))))). % order_subst2
thf(fact_213_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, Y5 : set_msg]: ((ord_less_eq_set_msg @ X5 @ Y5) => (ord_less_eq_set_msg @ (F @ X5) @ (F @ Y5)))) => (ord_less_eq_set_msg @ A3 @ (F @ C)))))))). % ord_eq_le_subst
thf(fact_214_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, Y5 : set_msg]: ((ord_less_eq_set_msg @ X5 @ Y5) => (ord_less_eq_set_nat @ (F @ X5) @ (F @ Y5)))) => (ord_less_eq_set_nat @ A3 @ (F @ C)))))))). % ord_eq_le_subst
thf(fact_215_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, Y5 : set_nat]: ((ord_less_eq_set_nat @ X5 @ Y5) => (ord_less_eq_set_msg @ (F @ X5) @ (F @ Y5)))) => (ord_less_eq_set_msg @ A3 @ (F @ C)))))))). % ord_eq_le_subst
thf(fact_216_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, Y5 : set_nat]: ((ord_less_eq_set_nat @ X5 @ Y5) => (ord_less_eq_set_nat @ (F @ X5) @ (F @ Y5)))) => (ord_less_eq_set_nat @ A3 @ (F @ C)))))))). % ord_eq_le_subst
thf(fact_217_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, Y5 : set_msg]: ((ord_less_eq_set_msg @ X5 @ Y5) => (ord_less_eq_set_msg @ (F @ X5) @ (F @ Y5)))) => (ord_less_eq_set_msg @ (F @ A3) @ C))))))). % ord_le_eq_subst
thf(fact_218_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, Y5 : set_msg]: ((ord_less_eq_set_msg @ X5 @ Y5) => (ord_less_eq_set_nat @ (F @ X5) @ (F @ Y5)))) => (ord_less_eq_set_nat @ (F @ A3) @ C))))))). % ord_le_eq_subst
thf(fact_219_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, Y5 : set_nat]: ((ord_less_eq_set_nat @ X5 @ Y5) => (ord_less_eq_set_msg @ (F @ X5) @ (F @ Y5)))) => (ord_less_eq_set_msg @ (F @ A3) @ C))))))). % ord_le_eq_subst
thf(fact_220_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, Y5 : set_nat]: ((ord_less_eq_set_nat @ X5 @ Y5) => (ord_less_eq_set_nat @ (F @ X5) @ (F @ Y5)))) => (ord_less_eq_set_nat @ (F @ A3) @ C))))))). % ord_le_eq_subst
thf(fact_221_eq__iff, axiom,
    (((^[Y3 : set_msg]: (^[Z : set_msg]: (Y3 = Z))) = (^[X3 : set_msg]: (^[Y6 : set_msg]: (((ord_less_eq_set_msg @ X3 @ Y6)) & ((ord_less_eq_set_msg @ Y6 @ X3)))))))). % eq_iff
thf(fact_222_eq__iff, axiom,
    (((^[Y3 : set_nat]: (^[Z : set_nat]: (Y3 = Z))) = (^[X3 : set_nat]: (^[Y6 : set_nat]: (((ord_less_eq_set_nat @ X3 @ Y6)) & ((ord_less_eq_set_nat @ Y6 @ X3)))))))). % eq_iff
thf(fact_223_antisym, axiom,
    ((![X : set_msg, Y2 : set_msg]: ((ord_less_eq_set_msg @ X @ Y2) => ((ord_less_eq_set_msg @ Y2 @ X) => (X = Y2)))))). % antisym
thf(fact_224_antisym, axiom,
    ((![X : set_nat, Y2 : set_nat]: ((ord_less_eq_set_nat @ X @ Y2) => ((ord_less_eq_set_nat @ Y2 @ X) => (X = Y2)))))). % antisym
thf(fact_225_eq__refl, axiom,
    ((![X : set_msg, Y2 : set_msg]: ((X = Y2) => (ord_less_eq_set_msg @ X @ Y2))))). % eq_refl
thf(fact_226_eq__refl, axiom,
    ((![X : set_nat, Y2 : set_nat]: ((X = Y2) => (ord_less_eq_set_nat @ X @ Y2))))). % eq_refl
thf(fact_227_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_228_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_229_antisym__conv, axiom,
    ((![Y2 : set_msg, X : set_msg]: ((ord_less_eq_set_msg @ Y2 @ X) => ((ord_less_eq_set_msg @ X @ Y2) = (X = Y2)))))). % antisym_conv
thf(fact_230_antisym__conv, axiom,
    ((![Y2 : set_nat, X : set_nat]: ((ord_less_eq_set_nat @ Y2 @ X) => ((ord_less_eq_set_nat @ X @ Y2) = (X = Y2)))))). % antisym_conv
thf(fact_231_order__class_Oorder_Oeq__iff, axiom,
    (((^[Y3 : set_msg]: (^[Z : set_msg]: (Y3 = Z))) = (^[A5 : set_msg]: (^[B5 : set_msg]: (((ord_less_eq_set_msg @ A5 @ B5)) & ((ord_less_eq_set_msg @ B5 @ A5)))))))). % order_class.order.eq_iff
thf(fact_232_order__class_Oorder_Oeq__iff, axiom,
    (((^[Y3 : set_nat]: (^[Z : set_nat]: (Y3 = Z))) = (^[A5 : set_nat]: (^[B5 : set_nat]: (((ord_less_eq_set_nat @ A5 @ B5)) & ((ord_less_eq_set_nat @ B5 @ A5)))))))). % order_class.order.eq_iff
thf(fact_233_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_234_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

% Conjectures (2)
thf(conj_0, hypothesis,
    ((member_list_event @ evs @ nS_Sha1061662329shared))).
thf(conj_1, conjecture,
    (((member_msg @ (key @ (shrK @ a)) @ (analz @ (knows @ spy @ evs))) = (member_agent @ a @ bad)))).
