% 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_215__5229642_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:23:52.226

% 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 (50)
thf(sy_c_Event_Obad, type,
    bad : set_agent).
thf(sy_c_Event_Oknows, type,
    knows : agent > list_event > set_msg).
thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Message__Omsg_J, type,
    sup_sup_set_msg : set_msg > set_msg > 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_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_Osynth, type,
    synth : set_msg > set_msg).
thf(sy_c_NS__Shared__Mirabelle__xwdrtqxrux_Ons__shared, type,
    nS_Sha1061662329shared : set_list_event).
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_Otop__class_Otop_001t__Set__Oset_It__List__Olist_It__Event__Oevent_J_J, type,
    top_to1178833912_event : set_list_event).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Message__Oagent_J, type,
    top_top_set_agent : set_agent).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Message__Omsg_J, type,
    top_top_set_msg : set_msg).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Nat__Onat_J, type,
    top_top_set_nat : set_nat).
thf(sy_c_Public_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_Oimage_001t__List__Olist_It__Event__Oevent_J_001t__Message__Omsg, type,
    image_list_event_msg : (list_event > msg) > set_list_event > set_msg).
thf(sy_c_Set_Oimage_001t__Message__Oagent_001t__List__Olist_It__Event__Oevent_J, type,
    image_832067507_event : (agent > list_event) > set_agent > set_list_event).
thf(sy_c_Set_Oimage_001t__Message__Oagent_001t__Message__Oagent, type,
    image_agent_agent : (agent > agent) > set_agent > set_agent).
thf(sy_c_Set_Oimage_001t__Message__Oagent_001t__Message__Omsg, type,
    image_agent_msg : (agent > msg) > set_agent > set_msg).
thf(sy_c_Set_Oimage_001t__Message__Oagent_001t__Nat__Onat, type,
    image_agent_nat : (agent > nat) > set_agent > set_nat).
thf(sy_c_Set_Oimage_001t__Message__Omsg_001t__Message__Oagent, type,
    image_msg_agent : (msg > agent) > set_msg > set_agent).
thf(sy_c_Set_Oimage_001t__Message__Omsg_001t__Message__Omsg, type,
    image_msg_msg : (msg > msg) > set_msg > set_msg).
thf(sy_c_Set_Oimage_001t__Message__Omsg_001t__Nat__Onat, type,
    image_msg_nat : (msg > nat) > set_msg > set_nat).
thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__List__Olist_It__Event__Oevent_J, type,
    image_nat_list_event : (nat > list_event) > set_nat > set_list_event).
thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Message__Oagent, type,
    image_nat_agent : (nat > agent) > set_nat > set_agent).
thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Message__Omsg, type,
    image_nat_msg : (nat > msg) > set_nat > set_msg).
thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Nat__Onat, type,
    image_nat_nat : (nat > nat) > set_nat > 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_K, type,
    k : nat).
thf(sy_v_KAB, type,
    kab : nat).
thf(sy_v_Kab, type,
    kab2 : nat).
thf(sy_v_X, type,
    x : msg).
thf(sy_v_Xa, type,
    xa : msg).
thf(sy_v_evsf, type,
    evsf : list_event).

% Relevant facts (249)
thf(fact_0_shrK__in__knows, axiom,
    ((![A : agent, Evs : list_event]: (member_msg @ (key @ (shrK @ A)) @ (knows @ A @ Evs))))). % shrK_in_knows
thf(fact_1_synth__simps_I5_J, axiom,
    ((![K : nat, X : msg, H : set_msg]: ((member_msg @ (crypt @ K @ X) @ (synth @ H)) = (((member_msg @ (crypt @ K @ X) @ H)) | ((((member_msg @ X @ (synth @ H))) & ((member_msg @ (key @ K) @ H))))))))). % synth_simps(5)
thf(fact_2_Crypt__synth__eq, axiom,
    ((![K : nat, H : set_msg, X : msg]: ((~ ((member_msg @ (key @ K) @ H))) => ((member_msg @ (crypt @ K @ X) @ (synth @ H)) = (member_msg @ (crypt @ K @ X) @ H)))))). % Crypt_synth_eq
thf(fact_3_Fake__analz__eq, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ (synth @ (analz @ H))) => ((synth @ (analz @ (insert_msg @ X @ H))) = (synth @ (analz @ H))))))). % Fake_analz_eq
thf(fact_4_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_5_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_6_shrK__image__eq, axiom,
    ((![X2 : agent, AA : set_agent]: ((member_nat @ (shrK @ X2) @ (image_agent_nat @ shrK @ AA)) = (member_agent @ X2 @ AA))))). % shrK_image_eq
thf(fact_7_parts__empty, axiom,
    (((parts @ bot_bot_set_msg) = bot_bot_set_msg))). % parts_empty
thf(fact_8_analz__empty, axiom,
    (((analz @ bot_bot_set_msg) = bot_bot_set_msg))). % analz_empty
thf(fact_9_synth__simps_I2_J, axiom,
    ((![K : nat, H : set_msg]: ((member_msg @ (key @ K) @ (synth @ H)) = (member_msg @ (key @ K) @ H))))). % synth_simps(2)
thf(fact_10_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_11_analz__parts, axiom,
    ((![H : set_msg]: ((analz @ (parts @ H)) = (parts @ H))))). % analz_parts
thf(fact_12_analz__idem, axiom,
    ((![H : set_msg]: ((analz @ (analz @ H)) = (analz @ H))))). % analz_idem
thf(fact_13_parts__idem, axiom,
    ((![H : set_msg]: ((parts @ (parts @ H)) = (parts @ H))))). % parts_idem
thf(fact_14_msg_Oinject_I4_J, axiom,
    ((![X4 : nat, Y4 : nat]: (((key @ X4) = (key @ Y4)) = (X4 = Y4))))). % msg.inject(4)
thf(fact_15_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_16_shrK__injective, axiom,
    ((![X2 : agent, Y : agent]: (((shrK @ X2) = (shrK @ Y)) = (X2 = Y))))). % shrK_injective
thf(fact_17_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_18_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_19_parts__analz, axiom,
    ((![H : set_msg]: ((parts @ (analz @ H)) = (parts @ H))))). % parts_analz
thf(fact_20_analz__analzD, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ (analz @ (analz @ H))) => (member_msg @ X @ (analz @ H)))))). % analz_analzD
thf(fact_21_analz_OInj, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ H) => (member_msg @ X @ (analz @ H)))))). % analz.Inj
thf(fact_22_parts__partsD, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ (parts @ (parts @ H))) => (member_msg @ X @ (parts @ H)))))). % parts_partsD
thf(fact_23_parts_OInj, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ H) => (member_msg @ X @ (parts @ H)))))). % parts.Inj
thf(fact_24_synth__synthD, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ (synth @ (synth @ H))) => (member_msg @ X @ (synth @ H)))))). % synth_synthD
thf(fact_25_synth__idem, axiom,
    ((![H : set_msg]: ((synth @ (synth @ H)) = (synth @ H))))). % synth_idem
thf(fact_26_synth_OInj, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ H) => (member_msg @ X @ (synth @ H)))))). % synth.Inj
thf(fact_27_analz__insert__eq__I, axiom,
    ((![X : msg, H : set_msg]: ((![X3 : msg]: ((member_msg @ X3 @ (analz @ (insert_msg @ X @ H))) => (member_msg @ X3 @ (insert_msg @ X @ (analz @ H))))) => ((analz @ (insert_msg @ X @ H)) = (insert_msg @ X @ (analz @ H))))))). % analz_insert_eq_I
thf(fact_28_analz__insert__cong, axiom,
    ((![H : set_msg, H2 : set_msg, X : msg]: (((analz @ H) = (analz @ H2)) => ((analz @ (insert_msg @ X @ H)) = (analz @ (insert_msg @ X @ H2))))))). % analz_insert_cong
thf(fact_29_analz__insert__eq, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ (analz @ H)) => ((analz @ (insert_msg @ X @ H)) = (analz @ H)))))). % analz_insert_eq
thf(fact_30_analz__insertI, axiom,
    ((![C : msg, G : set_msg, A2 : msg]: ((member_msg @ C @ (analz @ G)) => (member_msg @ C @ (analz @ (insert_msg @ A2 @ G))))))). % analz_insertI
thf(fact_31_analz__cut, axiom,
    ((![Y2 : msg, X : msg, H : set_msg]: ((member_msg @ Y2 @ (analz @ (insert_msg @ X @ H))) => ((member_msg @ X @ (analz @ H)) => (member_msg @ Y2 @ (analz @ H))))))). % analz_cut
thf(fact_32_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_33_analz__into__parts, axiom,
    ((![C : msg, H : set_msg]: ((member_msg @ C @ (analz @ H)) => (member_msg @ C @ (parts @ H)))))). % analz_into_parts
thf(fact_34_parts__insert__eq__I, axiom,
    ((![X : msg, H : set_msg]: ((![X3 : msg]: ((member_msg @ X3 @ (parts @ (insert_msg @ X @ H))) => (member_msg @ X3 @ (insert_msg @ X @ (parts @ H))))) => ((parts @ (insert_msg @ X @ H)) = (insert_msg @ X @ (parts @ H))))))). % parts_insert_eq_I
thf(fact_35_parts__insertI, axiom,
    ((![C : msg, G : set_msg, A2 : msg]: ((member_msg @ C @ (parts @ G)) => (member_msg @ C @ (parts @ (insert_msg @ A2 @ G))))))). % parts_insertI
thf(fact_36_parts_OBody, axiom,
    ((![K : nat, X : msg, H : set_msg]: ((member_msg @ (crypt @ K @ X) @ (parts @ H)) => (member_msg @ X @ (parts @ H)))))). % parts.Body
thf(fact_37_msg_Odistinct_I35_J, axiom,
    ((![X4 : nat, X71 : nat, X72 : msg]: (~ (((key @ X4) = (crypt @ X71 @ X72))))))). % msg.distinct(35)
thf(fact_38_synth__cut, axiom,
    ((![Y2 : msg, X : msg, H : set_msg]: ((member_msg @ Y2 @ (synth @ (insert_msg @ X @ H))) => ((member_msg @ X @ (synth @ H)) => (member_msg @ Y2 @ (synth @ H))))))). % synth_cut
thf(fact_39_parts__emptyE, axiom,
    ((![X : msg]: (~ ((member_msg @ X @ (parts @ bot_bot_set_msg))))))). % parts_emptyE
thf(fact_40_pushKeys_I6_J, axiom,
    ((![K : nat, X : nat, K2 : msg, A : set_msg]: ((insert_msg @ (key @ K) @ (insert_msg @ (crypt @ X @ K2) @ A)) = (insert_msg @ (crypt @ X @ K2) @ (insert_msg @ (key @ K) @ A)))))). % pushKeys(6)
thf(fact_41_synth_OCrypt, axiom,
    ((![X : msg, H : set_msg, K : nat]: ((member_msg @ X @ (synth @ H)) => ((member_msg @ (key @ K) @ H) => (member_msg @ (crypt @ K @ X) @ (synth @ H))))))). % synth.Crypt
thf(fact_42_parts__singleton, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ (parts @ H)) => (?[X3 : msg]: ((member_msg @ X3 @ H) & (member_msg @ X @ (parts @ (insert_msg @ X3 @ bot_bot_set_msg))))))))). % parts_singleton
thf(fact_43_analz__shrK__Decrypt, axiom,
    ((![A : agent, X : msg, H : set_msg]: ((member_msg @ (crypt @ (shrK @ A) @ X) @ (analz @ H)) => ((member_msg @ (key @ (shrK @ A)) @ (analz @ H)) => (member_msg @ X @ (analz @ H))))))). % analz_shrK_Decrypt
thf(fact_44_singletonI, axiom,
    ((![A2 : nat]: (member_nat @ A2 @ (insert_nat @ A2 @ bot_bot_set_nat))))). % singletonI
thf(fact_45_singletonI, axiom,
    ((![A2 : list_event]: (member_list_event @ A2 @ (insert_list_event @ A2 @ bot_bo1693714908_event))))). % singletonI
thf(fact_46_singletonI, axiom,
    ((![A2 : agent]: (member_agent @ A2 @ (insert_agent @ A2 @ bot_bot_set_agent))))). % singletonI
thf(fact_47_singletonI, axiom,
    ((![A2 : msg]: (member_msg @ A2 @ (insert_msg @ A2 @ bot_bot_set_msg))))). % singletonI
thf(fact_48_mem__Collect__eq, axiom,
    ((![A2 : nat, P : nat > $o]: ((member_nat @ A2 @ (collect_nat @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_49_mem__Collect__eq, axiom,
    ((![A2 : list_event, P : list_event > $o]: ((member_list_event @ A2 @ (collect_list_event @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_50_mem__Collect__eq, axiom,
    ((![A2 : msg, P : msg > $o]: ((member_msg @ A2 @ (collect_msg @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_51_mem__Collect__eq, axiom,
    ((![A2 : agent, P : agent > $o]: ((member_agent @ A2 @ (collect_agent @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_52_Collect__mem__eq, axiom,
    ((![A : set_nat]: ((collect_nat @ (^[X5 : nat]: (member_nat @ X5 @ A))) = A)))). % Collect_mem_eq
thf(fact_53_Collect__mem__eq, axiom,
    ((![A : set_list_event]: ((collect_list_event @ (^[X5 : list_event]: (member_list_event @ X5 @ A))) = A)))). % Collect_mem_eq
thf(fact_54_Collect__mem__eq, axiom,
    ((![A : set_msg]: ((collect_msg @ (^[X5 : msg]: (member_msg @ X5 @ A))) = A)))). % Collect_mem_eq
thf(fact_55_Collect__mem__eq, axiom,
    ((![A : set_agent]: ((collect_agent @ (^[X5 : agent]: (member_agent @ X5 @ A))) = A)))). % Collect_mem_eq
thf(fact_56_insert__image, axiom,
    ((![X2 : nat, A : set_nat, F : nat > msg]: ((member_nat @ X2 @ A) => ((insert_msg @ (F @ X2) @ (image_nat_msg @ F @ A)) = (image_nat_msg @ F @ A)))))). % insert_image
thf(fact_57_insert__image, axiom,
    ((![X2 : list_event, A : set_list_event, F : list_event > msg]: ((member_list_event @ X2 @ A) => ((insert_msg @ (F @ X2) @ (image_list_event_msg @ F @ A)) = (image_list_event_msg @ F @ A)))))). % insert_image
thf(fact_58_insert__image, axiom,
    ((![X2 : msg, A : set_msg, F : msg > msg]: ((member_msg @ X2 @ A) => ((insert_msg @ (F @ X2) @ (image_msg_msg @ F @ A)) = (image_msg_msg @ F @ A)))))). % insert_image
thf(fact_59_insert__image, axiom,
    ((![X2 : agent, A : set_agent, F : agent > nat]: ((member_agent @ X2 @ A) => ((insert_nat @ (F @ X2) @ (image_agent_nat @ F @ A)) = (image_agent_nat @ F @ A)))))). % insert_image
thf(fact_60_insert__image, axiom,
    ((![X2 : agent, A : set_agent, F : agent > msg]: ((member_agent @ X2 @ A) => ((insert_msg @ (F @ X2) @ (image_agent_msg @ F @ A)) = (image_agent_msg @ F @ A)))))). % insert_image
thf(fact_61_image__insert, axiom,
    ((![F : agent > nat, A2 : agent, B : set_agent]: ((image_agent_nat @ F @ (insert_agent @ A2 @ B)) = (insert_nat @ (F @ A2) @ (image_agent_nat @ F @ B)))))). % image_insert
thf(fact_62_image__insert, axiom,
    ((![F : nat > msg, A2 : nat, B : set_nat]: ((image_nat_msg @ F @ (insert_nat @ A2 @ B)) = (insert_msg @ (F @ A2) @ (image_nat_msg @ F @ B)))))). % image_insert
thf(fact_63_image__insert, axiom,
    ((![F : msg > msg, A2 : msg, B : set_msg]: ((image_msg_msg @ F @ (insert_msg @ A2 @ B)) = (insert_msg @ (F @ A2) @ (image_msg_msg @ F @ B)))))). % image_insert
thf(fact_64_image__is__empty, axiom,
    ((![F : agent > nat, A : set_agent]: (((image_agent_nat @ F @ A) = bot_bot_set_nat) = (A = bot_bot_set_agent))))). % image_is_empty
thf(fact_65_image__is__empty, axiom,
    ((![F : nat > msg, A : set_nat]: (((image_nat_msg @ F @ A) = bot_bot_set_msg) = (A = bot_bot_set_nat))))). % image_is_empty
thf(fact_66_image__is__empty, axiom,
    ((![F : msg > msg, A : set_msg]: (((image_msg_msg @ F @ A) = bot_bot_set_msg) = (A = bot_bot_set_msg))))). % image_is_empty
thf(fact_67_empty__is__image, axiom,
    ((![F : agent > nat, A : set_agent]: ((bot_bot_set_nat = (image_agent_nat @ F @ A)) = (A = bot_bot_set_agent))))). % empty_is_image
thf(fact_68_empty__is__image, axiom,
    ((![F : nat > msg, A : set_nat]: ((bot_bot_set_msg = (image_nat_msg @ F @ A)) = (A = bot_bot_set_nat))))). % empty_is_image
thf(fact_69_empty__is__image, axiom,
    ((![F : msg > msg, A : set_msg]: ((bot_bot_set_msg = (image_msg_msg @ F @ A)) = (A = bot_bot_set_msg))))). % empty_is_image
thf(fact_70_image__empty, axiom,
    ((![F : agent > nat]: ((image_agent_nat @ F @ bot_bot_set_agent) = bot_bot_set_nat)))). % image_empty
thf(fact_71_image__empty, axiom,
    ((![F : nat > msg]: ((image_nat_msg @ F @ bot_bot_set_nat) = bot_bot_set_msg)))). % image_empty
thf(fact_72_image__empty, axiom,
    ((![F : msg > msg]: ((image_msg_msg @ F @ bot_bot_set_msg) = bot_bot_set_msg)))). % image_empty
thf(fact_73_syan__impI, axiom,
    ((![Y2 : msg, Evs : list_event, Q : $o]: (((~ ((member_msg @ Y2 @ (synth @ (analz @ (knows @ spy @ Evs)))))) => Q) => ((~ ((member_msg @ Y2 @ (synth @ (analz @ (knows @ spy @ Evs)))))) => Q))))). % syan_impI
thf(fact_74_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_75_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_76_range__eq__singletonD, axiom,
    ((![F : nat > msg, A2 : msg, X2 : nat]: (((image_nat_msg @ F @ top_top_set_nat) = (insert_msg @ A2 @ bot_bot_set_msg)) => ((F @ X2) = A2))))). % range_eq_singletonD
thf(fact_77_range__eq__singletonD, axiom,
    ((![F : agent > nat, A2 : nat, X2 : agent]: (((image_agent_nat @ F @ top_top_set_agent) = (insert_nat @ A2 @ bot_bot_set_nat)) => ((F @ X2) = A2))))). % range_eq_singletonD
thf(fact_78_range__eq__singletonD, axiom,
    ((![F : agent > msg, A2 : msg, X2 : agent]: (((image_agent_msg @ F @ top_top_set_agent) = (insert_msg @ A2 @ bot_bot_set_msg)) => ((F @ X2) = A2))))). % range_eq_singletonD
thf(fact_79_image__eqI, axiom,
    ((![B2 : nat, F : nat > nat, X2 : nat, A : set_nat]: ((B2 = (F @ X2)) => ((member_nat @ X2 @ A) => (member_nat @ B2 @ (image_nat_nat @ F @ A))))))). % image_eqI
thf(fact_80_image__eqI, axiom,
    ((![B2 : msg, F : nat > msg, X2 : nat, A : set_nat]: ((B2 = (F @ X2)) => ((member_nat @ X2 @ A) => (member_msg @ B2 @ (image_nat_msg @ F @ A))))))). % image_eqI
thf(fact_81_image__eqI, axiom,
    ((![B2 : agent, F : nat > agent, X2 : nat, A : set_nat]: ((B2 = (F @ X2)) => ((member_nat @ X2 @ A) => (member_agent @ B2 @ (image_nat_agent @ F @ A))))))). % image_eqI
thf(fact_82_image__eqI, axiom,
    ((![B2 : nat, F : msg > nat, X2 : msg, A : set_msg]: ((B2 = (F @ X2)) => ((member_msg @ X2 @ A) => (member_nat @ B2 @ (image_msg_nat @ F @ A))))))). % image_eqI
thf(fact_83_image__eqI, axiom,
    ((![B2 : msg, F : msg > msg, X2 : msg, A : set_msg]: ((B2 = (F @ X2)) => ((member_msg @ X2 @ A) => (member_msg @ B2 @ (image_msg_msg @ F @ A))))))). % image_eqI
thf(fact_84_image__eqI, axiom,
    ((![B2 : agent, F : msg > agent, X2 : msg, A : set_msg]: ((B2 = (F @ X2)) => ((member_msg @ X2 @ A) => (member_agent @ B2 @ (image_msg_agent @ F @ A))))))). % image_eqI
thf(fact_85_image__eqI, axiom,
    ((![B2 : nat, F : agent > nat, X2 : agent, A : set_agent]: ((B2 = (F @ X2)) => ((member_agent @ X2 @ A) => (member_nat @ B2 @ (image_agent_nat @ F @ A))))))). % image_eqI
thf(fact_86_image__eqI, axiom,
    ((![B2 : msg, F : agent > msg, X2 : agent, A : set_agent]: ((B2 = (F @ X2)) => ((member_agent @ X2 @ A) => (member_msg @ B2 @ (image_agent_msg @ F @ A))))))). % image_eqI
thf(fact_87_image__eqI, axiom,
    ((![B2 : agent, F : agent > agent, X2 : agent, A : set_agent]: ((B2 = (F @ X2)) => ((member_agent @ X2 @ A) => (member_agent @ B2 @ (image_agent_agent @ F @ A))))))). % image_eqI
thf(fact_88_image__eqI, axiom,
    ((![B2 : list_event, F : nat > list_event, X2 : nat, A : set_nat]: ((B2 = (F @ X2)) => ((member_nat @ X2 @ A) => (member_list_event @ B2 @ (image_nat_list_event @ F @ A))))))). % image_eqI
thf(fact_89_empty__iff, axiom,
    ((![C : nat]: (~ ((member_nat @ C @ bot_bot_set_nat)))))). % empty_iff
thf(fact_90_empty__iff, axiom,
    ((![C : list_event]: (~ ((member_list_event @ C @ bot_bo1693714908_event)))))). % empty_iff
thf(fact_91_empty__iff, axiom,
    ((![C : agent]: (~ ((member_agent @ C @ bot_bot_set_agent)))))). % empty_iff
thf(fact_92_empty__iff, axiom,
    ((![C : msg]: (~ ((member_msg @ C @ bot_bot_set_msg)))))). % empty_iff
thf(fact_93_all__not__in__conv, axiom,
    ((![A : set_nat]: ((![X5 : nat]: (~ ((member_nat @ X5 @ A)))) = (A = bot_bot_set_nat))))). % all_not_in_conv
thf(fact_94_all__not__in__conv, axiom,
    ((![A : set_list_event]: ((![X5 : list_event]: (~ ((member_list_event @ X5 @ A)))) = (A = bot_bo1693714908_event))))). % all_not_in_conv
thf(fact_95_all__not__in__conv, axiom,
    ((![A : set_agent]: ((![X5 : agent]: (~ ((member_agent @ X5 @ A)))) = (A = bot_bot_set_agent))))). % all_not_in_conv
thf(fact_96_all__not__in__conv, axiom,
    ((![A : set_msg]: ((![X5 : msg]: (~ ((member_msg @ X5 @ A)))) = (A = bot_bot_set_msg))))). % all_not_in_conv
thf(fact_97_Collect__empty__eq, axiom,
    ((![P : msg > $o]: (((collect_msg @ P) = bot_bot_set_msg) = (![X5 : msg]: (~ ((P @ X5)))))))). % Collect_empty_eq
thf(fact_98_empty__Collect__eq, axiom,
    ((![P : msg > $o]: ((bot_bot_set_msg = (collect_msg @ P)) = (![X5 : msg]: (~ ((P @ X5)))))))). % empty_Collect_eq
thf(fact_99_insertCI, axiom,
    ((![A2 : nat, B : set_nat, B2 : nat]: (((~ ((member_nat @ A2 @ B))) => (A2 = B2)) => (member_nat @ A2 @ (insert_nat @ B2 @ B)))))). % insertCI
thf(fact_100_insertCI, axiom,
    ((![A2 : list_event, B : set_list_event, B2 : list_event]: (((~ ((member_list_event @ A2 @ B))) => (A2 = B2)) => (member_list_event @ A2 @ (insert_list_event @ B2 @ B)))))). % insertCI
thf(fact_101_insertCI, axiom,
    ((![A2 : msg, B : set_msg, B2 : msg]: (((~ ((member_msg @ A2 @ B))) => (A2 = B2)) => (member_msg @ A2 @ (insert_msg @ B2 @ B)))))). % insertCI
thf(fact_102_insertCI, axiom,
    ((![A2 : agent, B : set_agent, B2 : agent]: (((~ ((member_agent @ A2 @ B))) => (A2 = B2)) => (member_agent @ A2 @ (insert_agent @ B2 @ B)))))). % insertCI
thf(fact_103_insert__iff, axiom,
    ((![A2 : nat, B2 : nat, A : set_nat]: ((member_nat @ A2 @ (insert_nat @ B2 @ A)) = (((A2 = B2)) | ((member_nat @ A2 @ A))))))). % insert_iff
thf(fact_104_insert__iff, axiom,
    ((![A2 : list_event, B2 : list_event, A : set_list_event]: ((member_list_event @ A2 @ (insert_list_event @ B2 @ A)) = (((A2 = B2)) | ((member_list_event @ A2 @ A))))))). % insert_iff
thf(fact_105_insert__iff, axiom,
    ((![A2 : msg, B2 : msg, A : set_msg]: ((member_msg @ A2 @ (insert_msg @ B2 @ A)) = (((A2 = B2)) | ((member_msg @ A2 @ A))))))). % insert_iff
thf(fact_106_insert__iff, axiom,
    ((![A2 : agent, B2 : agent, A : set_agent]: ((member_agent @ A2 @ (insert_agent @ B2 @ A)) = (((A2 = B2)) | ((member_agent @ A2 @ A))))))). % insert_iff
thf(fact_107_insert__absorb2, axiom,
    ((![X2 : msg, A : set_msg]: ((insert_msg @ X2 @ (insert_msg @ X2 @ A)) = (insert_msg @ X2 @ A))))). % insert_absorb2
thf(fact_108_UNIV__I, axiom,
    ((![X2 : nat]: (member_nat @ X2 @ top_top_set_nat)))). % UNIV_I
thf(fact_109_UNIV__I, axiom,
    ((![X2 : list_event]: (member_list_event @ X2 @ top_to1178833912_event)))). % UNIV_I
thf(fact_110_UNIV__I, axiom,
    ((![X2 : msg]: (member_msg @ X2 @ top_top_set_msg)))). % UNIV_I
thf(fact_111_UNIV__I, axiom,
    ((![X2 : agent]: (member_agent @ X2 @ top_top_set_agent)))). % UNIV_I
thf(fact_112_Key__image__eq, axiom,
    ((![X2 : nat, A : set_nat]: ((member_msg @ (key @ X2) @ (image_nat_msg @ key @ A)) = (member_nat @ X2 @ A))))). % Key_image_eq
thf(fact_113_analz__image__Key, axiom,
    ((![N : set_nat]: ((analz @ (image_nat_msg @ key @ N)) = (image_nat_msg @ key @ N))))). % analz_image_Key
thf(fact_114_parts__image__Key, axiom,
    ((![N : set_nat]: ((parts @ (image_nat_msg @ key @ N)) = (image_nat_msg @ key @ N))))). % parts_image_Key
thf(fact_115_Spy__in__bad, axiom,
    ((member_agent @ spy @ bad))). % Spy_in_bad
thf(fact_116_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_117_Crypt__notin__image__Key, axiom,
    ((![K : nat, X : msg, A : set_nat]: (~ ((member_msg @ (crypt @ K @ X) @ (image_nat_msg @ key @ A))))))). % Crypt_notin_image_Key
thf(fact_118_imageI, axiom,
    ((![X2 : nat, A : set_nat, F : nat > nat]: ((member_nat @ X2 @ A) => (member_nat @ (F @ X2) @ (image_nat_nat @ F @ A)))))). % imageI
thf(fact_119_imageI, axiom,
    ((![X2 : nat, A : set_nat, F : nat > msg]: ((member_nat @ X2 @ A) => (member_msg @ (F @ X2) @ (image_nat_msg @ F @ A)))))). % imageI
thf(fact_120_imageI, axiom,
    ((![X2 : nat, A : set_nat, F : nat > agent]: ((member_nat @ X2 @ A) => (member_agent @ (F @ X2) @ (image_nat_agent @ F @ A)))))). % imageI
thf(fact_121_imageI, axiom,
    ((![X2 : msg, A : set_msg, F : msg > nat]: ((member_msg @ X2 @ A) => (member_nat @ (F @ X2) @ (image_msg_nat @ F @ A)))))). % imageI
thf(fact_122_imageI, axiom,
    ((![X2 : msg, A : set_msg, F : msg > msg]: ((member_msg @ X2 @ A) => (member_msg @ (F @ X2) @ (image_msg_msg @ F @ A)))))). % imageI
thf(fact_123_imageI, axiom,
    ((![X2 : msg, A : set_msg, F : msg > agent]: ((member_msg @ X2 @ A) => (member_agent @ (F @ X2) @ (image_msg_agent @ F @ A)))))). % imageI
thf(fact_124_imageI, axiom,
    ((![X2 : agent, A : set_agent, F : agent > nat]: ((member_agent @ X2 @ A) => (member_nat @ (F @ X2) @ (image_agent_nat @ F @ A)))))). % imageI
thf(fact_125_imageI, axiom,
    ((![X2 : agent, A : set_agent, F : agent > msg]: ((member_agent @ X2 @ A) => (member_msg @ (F @ X2) @ (image_agent_msg @ F @ A)))))). % imageI
thf(fact_126_imageI, axiom,
    ((![X2 : agent, A : set_agent, F : agent > agent]: ((member_agent @ X2 @ A) => (member_agent @ (F @ X2) @ (image_agent_agent @ F @ A)))))). % imageI
thf(fact_127_imageI, axiom,
    ((![X2 : nat, A : set_nat, F : nat > list_event]: ((member_nat @ X2 @ A) => (member_list_event @ (F @ X2) @ (image_nat_list_event @ F @ A)))))). % imageI
thf(fact_128_image__iff, axiom,
    ((![Z : nat, F : agent > nat, A : set_agent]: ((member_nat @ Z @ (image_agent_nat @ F @ A)) = (?[X5 : agent]: (((member_agent @ X5 @ A)) & ((Z = (F @ X5))))))))). % image_iff
thf(fact_129_image__iff, axiom,
    ((![Z : msg, F : nat > msg, A : set_nat]: ((member_msg @ Z @ (image_nat_msg @ F @ A)) = (?[X5 : nat]: (((member_nat @ X5 @ A)) & ((Z = (F @ X5))))))))). % image_iff
thf(fact_130_bex__imageD, axiom,
    ((![F : agent > nat, A : set_agent, P : nat > $o]: ((?[X6 : nat]: ((member_nat @ X6 @ (image_agent_nat @ F @ A)) & (P @ X6))) => (?[X3 : agent]: ((member_agent @ X3 @ A) & (P @ (F @ X3)))))))). % bex_imageD
thf(fact_131_bex__imageD, axiom,
    ((![F : nat > msg, A : set_nat, P : msg > $o]: ((?[X6 : msg]: ((member_msg @ X6 @ (image_nat_msg @ F @ A)) & (P @ X6))) => (?[X3 : nat]: ((member_nat @ X3 @ A) & (P @ (F @ X3)))))))). % bex_imageD
thf(fact_132_image__cong, axiom,
    ((![M : set_nat, N : set_nat, F : nat > msg, G2 : nat > msg]: ((M = N) => ((![X3 : nat]: ((member_nat @ X3 @ N) => ((F @ X3) = (G2 @ X3)))) => ((image_nat_msg @ F @ M) = (image_nat_msg @ G2 @ N))))))). % image_cong
thf(fact_133_image__cong, axiom,
    ((![M : set_agent, N : set_agent, F : agent > nat, G2 : agent > nat]: ((M = N) => ((![X3 : agent]: ((member_agent @ X3 @ N) => ((F @ X3) = (G2 @ X3)))) => ((image_agent_nat @ F @ M) = (image_agent_nat @ G2 @ N))))))). % image_cong
thf(fact_134_ball__imageD, axiom,
    ((![F : agent > nat, A : set_agent, P : nat > $o]: ((![X3 : nat]: ((member_nat @ X3 @ (image_agent_nat @ F @ A)) => (P @ X3))) => (![X6 : agent]: ((member_agent @ X6 @ A) => (P @ (F @ X6)))))))). % ball_imageD
thf(fact_135_ball__imageD, axiom,
    ((![F : nat > msg, A : set_nat, P : msg > $o]: ((![X3 : msg]: ((member_msg @ X3 @ (image_nat_msg @ F @ A)) => (P @ X3))) => (![X6 : nat]: ((member_nat @ X6 @ A) => (P @ (F @ X6)))))))). % ball_imageD
thf(fact_136_rev__image__eqI, axiom,
    ((![X2 : nat, A : set_nat, B2 : nat, F : nat > nat]: ((member_nat @ X2 @ A) => ((B2 = (F @ X2)) => (member_nat @ B2 @ (image_nat_nat @ F @ A))))))). % rev_image_eqI
thf(fact_137_rev__image__eqI, axiom,
    ((![X2 : nat, A : set_nat, B2 : msg, F : nat > msg]: ((member_nat @ X2 @ A) => ((B2 = (F @ X2)) => (member_msg @ B2 @ (image_nat_msg @ F @ A))))))). % rev_image_eqI
thf(fact_138_rev__image__eqI, axiom,
    ((![X2 : nat, A : set_nat, B2 : agent, F : nat > agent]: ((member_nat @ X2 @ A) => ((B2 = (F @ X2)) => (member_agent @ B2 @ (image_nat_agent @ F @ A))))))). % rev_image_eqI
thf(fact_139_rev__image__eqI, axiom,
    ((![X2 : msg, A : set_msg, B2 : nat, F : msg > nat]: ((member_msg @ X2 @ A) => ((B2 = (F @ X2)) => (member_nat @ B2 @ (image_msg_nat @ F @ A))))))). % rev_image_eqI
thf(fact_140_rev__image__eqI, axiom,
    ((![X2 : msg, A : set_msg, B2 : msg, F : msg > msg]: ((member_msg @ X2 @ A) => ((B2 = (F @ X2)) => (member_msg @ B2 @ (image_msg_msg @ F @ A))))))). % rev_image_eqI
thf(fact_141_rev__image__eqI, axiom,
    ((![X2 : msg, A : set_msg, B2 : agent, F : msg > agent]: ((member_msg @ X2 @ A) => ((B2 = (F @ X2)) => (member_agent @ B2 @ (image_msg_agent @ F @ A))))))). % rev_image_eqI
thf(fact_142_rev__image__eqI, axiom,
    ((![X2 : agent, A : set_agent, B2 : nat, F : agent > nat]: ((member_agent @ X2 @ A) => ((B2 = (F @ X2)) => (member_nat @ B2 @ (image_agent_nat @ F @ A))))))). % rev_image_eqI
thf(fact_143_rev__image__eqI, axiom,
    ((![X2 : agent, A : set_agent, B2 : msg, F : agent > msg]: ((member_agent @ X2 @ A) => ((B2 = (F @ X2)) => (member_msg @ B2 @ (image_agent_msg @ F @ A))))))). % rev_image_eqI
thf(fact_144_rev__image__eqI, axiom,
    ((![X2 : agent, A : set_agent, B2 : agent, F : agent > agent]: ((member_agent @ X2 @ A) => ((B2 = (F @ X2)) => (member_agent @ B2 @ (image_agent_agent @ F @ A))))))). % rev_image_eqI
thf(fact_145_rev__image__eqI, axiom,
    ((![X2 : nat, A : set_nat, B2 : list_event, F : nat > list_event]: ((member_nat @ X2 @ A) => ((B2 = (F @ X2)) => (member_list_event @ B2 @ (image_nat_list_event @ F @ A))))))). % rev_image_eqI
thf(fact_146_emptyE, axiom,
    ((![A2 : nat]: (~ ((member_nat @ A2 @ bot_bot_set_nat)))))). % emptyE
thf(fact_147_emptyE, axiom,
    ((![A2 : list_event]: (~ ((member_list_event @ A2 @ bot_bo1693714908_event)))))). % emptyE
thf(fact_148_emptyE, axiom,
    ((![A2 : agent]: (~ ((member_agent @ A2 @ bot_bot_set_agent)))))). % emptyE
thf(fact_149_emptyE, axiom,
    ((![A2 : msg]: (~ ((member_msg @ A2 @ bot_bot_set_msg)))))). % emptyE
thf(fact_150_equals0D, axiom,
    ((![A : set_nat, A2 : nat]: ((A = bot_bot_set_nat) => (~ ((member_nat @ A2 @ A))))))). % equals0D
thf(fact_151_equals0D, axiom,
    ((![A : set_list_event, A2 : list_event]: ((A = bot_bo1693714908_event) => (~ ((member_list_event @ A2 @ A))))))). % equals0D
thf(fact_152_equals0D, axiom,
    ((![A : set_agent, A2 : agent]: ((A = bot_bot_set_agent) => (~ ((member_agent @ A2 @ A))))))). % equals0D
thf(fact_153_equals0D, axiom,
    ((![A : set_msg, A2 : msg]: ((A = bot_bot_set_msg) => (~ ((member_msg @ A2 @ A))))))). % equals0D
thf(fact_154_equals0I, axiom,
    ((![A : set_nat]: ((![Y3 : nat]: (~ ((member_nat @ Y3 @ A)))) => (A = bot_bot_set_nat))))). % equals0I
thf(fact_155_equals0I, axiom,
    ((![A : set_list_event]: ((![Y3 : list_event]: (~ ((member_list_event @ Y3 @ A)))) => (A = bot_bo1693714908_event))))). % equals0I
thf(fact_156_equals0I, axiom,
    ((![A : set_agent]: ((![Y3 : agent]: (~ ((member_agent @ Y3 @ A)))) => (A = bot_bot_set_agent))))). % equals0I
thf(fact_157_equals0I, axiom,
    ((![A : set_msg]: ((![Y3 : msg]: (~ ((member_msg @ Y3 @ A)))) => (A = bot_bot_set_msg))))). % equals0I
thf(fact_158_ex__in__conv, axiom,
    ((![A : set_nat]: ((?[X5 : nat]: (member_nat @ X5 @ A)) = (~ ((A = bot_bot_set_nat))))))). % ex_in_conv
thf(fact_159_ex__in__conv, axiom,
    ((![A : set_list_event]: ((?[X5 : list_event]: (member_list_event @ X5 @ A)) = (~ ((A = bot_bo1693714908_event))))))). % ex_in_conv
thf(fact_160_ex__in__conv, axiom,
    ((![A : set_agent]: ((?[X5 : agent]: (member_agent @ X5 @ A)) = (~ ((A = bot_bot_set_agent))))))). % ex_in_conv
thf(fact_161_ex__in__conv, axiom,
    ((![A : set_msg]: ((?[X5 : msg]: (member_msg @ X5 @ A)) = (~ ((A = bot_bot_set_msg))))))). % ex_in_conv
thf(fact_162_insertE, axiom,
    ((![A2 : nat, B2 : nat, A : set_nat]: ((member_nat @ A2 @ (insert_nat @ B2 @ A)) => ((~ ((A2 = B2))) => (member_nat @ A2 @ A)))))). % insertE
thf(fact_163_insertE, axiom,
    ((![A2 : list_event, B2 : list_event, A : set_list_event]: ((member_list_event @ A2 @ (insert_list_event @ B2 @ A)) => ((~ ((A2 = B2))) => (member_list_event @ A2 @ A)))))). % insertE
thf(fact_164_insertE, axiom,
    ((![A2 : msg, B2 : msg, A : set_msg]: ((member_msg @ A2 @ (insert_msg @ B2 @ A)) => ((~ ((A2 = B2))) => (member_msg @ A2 @ A)))))). % insertE
thf(fact_165_insertE, axiom,
    ((![A2 : agent, B2 : agent, A : set_agent]: ((member_agent @ A2 @ (insert_agent @ B2 @ A)) => ((~ ((A2 = B2))) => (member_agent @ A2 @ A)))))). % insertE
thf(fact_166_insertI1, axiom,
    ((![A2 : nat, B : set_nat]: (member_nat @ A2 @ (insert_nat @ A2 @ B))))). % insertI1
thf(fact_167_insertI1, axiom,
    ((![A2 : list_event, B : set_list_event]: (member_list_event @ A2 @ (insert_list_event @ A2 @ B))))). % insertI1
thf(fact_168_insertI1, axiom,
    ((![A2 : msg, B : set_msg]: (member_msg @ A2 @ (insert_msg @ A2 @ B))))). % insertI1
thf(fact_169_insertI1, axiom,
    ((![A2 : agent, B : set_agent]: (member_agent @ A2 @ (insert_agent @ A2 @ B))))). % insertI1
thf(fact_170_insertI2, axiom,
    ((![A2 : nat, B : set_nat, B2 : nat]: ((member_nat @ A2 @ B) => (member_nat @ A2 @ (insert_nat @ B2 @ B)))))). % insertI2
thf(fact_171_insertI2, axiom,
    ((![A2 : list_event, B : set_list_event, B2 : list_event]: ((member_list_event @ A2 @ B) => (member_list_event @ A2 @ (insert_list_event @ B2 @ B)))))). % insertI2
thf(fact_172_insertI2, axiom,
    ((![A2 : msg, B : set_msg, B2 : msg]: ((member_msg @ A2 @ B) => (member_msg @ A2 @ (insert_msg @ B2 @ B)))))). % insertI2
thf(fact_173_insertI2, axiom,
    ((![A2 : agent, B : set_agent, B2 : agent]: ((member_agent @ A2 @ B) => (member_agent @ A2 @ (insert_agent @ B2 @ B)))))). % insertI2
thf(fact_174_Set_Oset__insert, axiom,
    ((![X2 : nat, A : set_nat]: ((member_nat @ X2 @ A) => (~ ((![B3 : set_nat]: ((A = (insert_nat @ X2 @ B3)) => (member_nat @ X2 @ B3))))))))). % Set.set_insert
thf(fact_175_Set_Oset__insert, axiom,
    ((![X2 : list_event, A : set_list_event]: ((member_list_event @ X2 @ A) => (~ ((![B3 : set_list_event]: ((A = (insert_list_event @ X2 @ B3)) => (member_list_event @ X2 @ B3))))))))). % Set.set_insert
thf(fact_176_Set_Oset__insert, axiom,
    ((![X2 : msg, A : set_msg]: ((member_msg @ X2 @ A) => (~ ((![B3 : set_msg]: ((A = (insert_msg @ X2 @ B3)) => (member_msg @ X2 @ B3))))))))). % Set.set_insert
thf(fact_177_Set_Oset__insert, axiom,
    ((![X2 : agent, A : set_agent]: ((member_agent @ X2 @ A) => (~ ((![B3 : set_agent]: ((A = (insert_agent @ X2 @ B3)) => (member_agent @ X2 @ B3))))))))). % Set.set_insert
thf(fact_178_insert__ident, axiom,
    ((![X2 : nat, A : set_nat, B : set_nat]: ((~ ((member_nat @ X2 @ A))) => ((~ ((member_nat @ X2 @ B))) => (((insert_nat @ X2 @ A) = (insert_nat @ X2 @ B)) = (A = B))))))). % insert_ident
thf(fact_179_insert__ident, axiom,
    ((![X2 : list_event, A : set_list_event, B : set_list_event]: ((~ ((member_list_event @ X2 @ A))) => ((~ ((member_list_event @ X2 @ B))) => (((insert_list_event @ X2 @ A) = (insert_list_event @ X2 @ B)) = (A = B))))))). % insert_ident
thf(fact_180_insert__ident, axiom,
    ((![X2 : msg, A : set_msg, B : set_msg]: ((~ ((member_msg @ X2 @ A))) => ((~ ((member_msg @ X2 @ B))) => (((insert_msg @ X2 @ A) = (insert_msg @ X2 @ B)) = (A = B))))))). % insert_ident
thf(fact_181_insert__ident, axiom,
    ((![X2 : agent, A : set_agent, B : set_agent]: ((~ ((member_agent @ X2 @ A))) => ((~ ((member_agent @ X2 @ B))) => (((insert_agent @ X2 @ A) = (insert_agent @ X2 @ B)) = (A = B))))))). % insert_ident
thf(fact_182_insert__absorb, axiom,
    ((![A2 : nat, A : set_nat]: ((member_nat @ A2 @ A) => ((insert_nat @ A2 @ A) = A))))). % insert_absorb
thf(fact_183_insert__absorb, axiom,
    ((![A2 : list_event, A : set_list_event]: ((member_list_event @ A2 @ A) => ((insert_list_event @ A2 @ A) = A))))). % insert_absorb
thf(fact_184_insert__absorb, axiom,
    ((![A2 : msg, A : set_msg]: ((member_msg @ A2 @ A) => ((insert_msg @ A2 @ A) = A))))). % insert_absorb
thf(fact_185_insert__absorb, axiom,
    ((![A2 : agent, A : set_agent]: ((member_agent @ A2 @ A) => ((insert_agent @ A2 @ A) = A))))). % insert_absorb
thf(fact_186_insert__eq__iff, axiom,
    ((![A2 : nat, A : set_nat, B2 : nat, B : set_nat]: ((~ ((member_nat @ A2 @ A))) => ((~ ((member_nat @ B2 @ B))) => (((insert_nat @ A2 @ A) = (insert_nat @ B2 @ B)) = (((((A2 = B2)) => ((A = B)))) & ((((~ ((A2 = B2)))) => ((?[C2 : set_nat]: (((A = (insert_nat @ B2 @ C2))) & ((((~ ((member_nat @ B2 @ C2)))) & ((((B = (insert_nat @ A2 @ C2))) & ((~ ((member_nat @ A2 @ C2)))))))))))))))))))). % insert_eq_iff
thf(fact_187_insert__eq__iff, axiom,
    ((![A2 : list_event, A : set_list_event, B2 : list_event, B : set_list_event]: ((~ ((member_list_event @ A2 @ A))) => ((~ ((member_list_event @ B2 @ B))) => (((insert_list_event @ A2 @ A) = (insert_list_event @ B2 @ B)) = (((((A2 = B2)) => ((A = B)))) & ((((~ ((A2 = B2)))) => ((?[C2 : set_list_event]: (((A = (insert_list_event @ B2 @ C2))) & ((((~ ((member_list_event @ B2 @ C2)))) & ((((B = (insert_list_event @ A2 @ C2))) & ((~ ((member_list_event @ A2 @ C2)))))))))))))))))))). % insert_eq_iff
thf(fact_188_insert__eq__iff, axiom,
    ((![A2 : msg, A : set_msg, B2 : msg, B : set_msg]: ((~ ((member_msg @ A2 @ A))) => ((~ ((member_msg @ B2 @ B))) => (((insert_msg @ A2 @ A) = (insert_msg @ B2 @ B)) = (((((A2 = B2)) => ((A = B)))) & ((((~ ((A2 = B2)))) => ((?[C2 : set_msg]: (((A = (insert_msg @ B2 @ C2))) & ((((~ ((member_msg @ B2 @ C2)))) & ((((B = (insert_msg @ A2 @ C2))) & ((~ ((member_msg @ A2 @ C2)))))))))))))))))))). % insert_eq_iff
thf(fact_189_insert__eq__iff, axiom,
    ((![A2 : agent, A : set_agent, B2 : agent, B : set_agent]: ((~ ((member_agent @ A2 @ A))) => ((~ ((member_agent @ B2 @ B))) => (((insert_agent @ A2 @ A) = (insert_agent @ B2 @ B)) = (((((A2 = B2)) => ((A = B)))) & ((((~ ((A2 = B2)))) => ((?[C2 : set_agent]: (((A = (insert_agent @ B2 @ C2))) & ((((~ ((member_agent @ B2 @ C2)))) & ((((B = (insert_agent @ A2 @ C2))) & ((~ ((member_agent @ A2 @ C2)))))))))))))))))))). % insert_eq_iff
thf(fact_190_insert__commute, axiom,
    ((![X2 : msg, Y : msg, A : set_msg]: ((insert_msg @ X2 @ (insert_msg @ Y @ A)) = (insert_msg @ Y @ (insert_msg @ X2 @ A)))))). % insert_commute
thf(fact_191_mk__disjoint__insert, axiom,
    ((![A2 : nat, A : set_nat]: ((member_nat @ A2 @ A) => (?[B3 : set_nat]: ((A = (insert_nat @ A2 @ B3)) & (~ ((member_nat @ A2 @ B3))))))))). % mk_disjoint_insert
thf(fact_192_mk__disjoint__insert, axiom,
    ((![A2 : list_event, A : set_list_event]: ((member_list_event @ A2 @ A) => (?[B3 : set_list_event]: ((A = (insert_list_event @ A2 @ B3)) & (~ ((member_list_event @ A2 @ B3))))))))). % mk_disjoint_insert
thf(fact_193_mk__disjoint__insert, axiom,
    ((![A2 : msg, A : set_msg]: ((member_msg @ A2 @ A) => (?[B3 : set_msg]: ((A = (insert_msg @ A2 @ B3)) & (~ ((member_msg @ A2 @ B3))))))))). % mk_disjoint_insert
thf(fact_194_mk__disjoint__insert, axiom,
    ((![A2 : agent, A : set_agent]: ((member_agent @ A2 @ A) => (?[B3 : set_agent]: ((A = (insert_agent @ A2 @ B3)) & (~ ((member_agent @ A2 @ B3))))))))). % mk_disjoint_insert
thf(fact_195_UNIV__eq__I, axiom,
    ((![A : set_nat]: ((![X3 : nat]: (member_nat @ X3 @ A)) => (top_top_set_nat = A))))). % UNIV_eq_I
thf(fact_196_UNIV__eq__I, axiom,
    ((![A : set_list_event]: ((![X3 : list_event]: (member_list_event @ X3 @ A)) => (top_to1178833912_event = A))))). % UNIV_eq_I
thf(fact_197_UNIV__eq__I, axiom,
    ((![A : set_msg]: ((![X3 : msg]: (member_msg @ X3 @ A)) => (top_top_set_msg = A))))). % UNIV_eq_I
thf(fact_198_UNIV__eq__I, axiom,
    ((![A : set_agent]: ((![X3 : agent]: (member_agent @ X3 @ A)) => (top_top_set_agent = A))))). % UNIV_eq_I
thf(fact_199_UNIV__witness, axiom,
    ((?[X3 : nat]: (member_nat @ X3 @ top_top_set_nat)))). % UNIV_witness
thf(fact_200_UNIV__witness, axiom,
    ((?[X3 : list_event]: (member_list_event @ X3 @ top_to1178833912_event)))). % UNIV_witness
thf(fact_201_UNIV__witness, axiom,
    ((?[X3 : msg]: (member_msg @ X3 @ top_top_set_msg)))). % UNIV_witness
thf(fact_202_UNIV__witness, axiom,
    ((?[X3 : agent]: (member_agent @ X3 @ top_top_set_agent)))). % UNIV_witness
thf(fact_203_singletonD, axiom,
    ((![B2 : nat, A2 : nat]: ((member_nat @ B2 @ (insert_nat @ A2 @ bot_bot_set_nat)) => (B2 = A2))))). % singletonD
thf(fact_204_singletonD, axiom,
    ((![B2 : list_event, A2 : list_event]: ((member_list_event @ B2 @ (insert_list_event @ A2 @ bot_bo1693714908_event)) => (B2 = A2))))). % singletonD
thf(fact_205_singletonD, axiom,
    ((![B2 : agent, A2 : agent]: ((member_agent @ B2 @ (insert_agent @ A2 @ bot_bot_set_agent)) => (B2 = A2))))). % singletonD
thf(fact_206_singletonD, axiom,
    ((![B2 : msg, A2 : msg]: ((member_msg @ B2 @ (insert_msg @ A2 @ bot_bot_set_msg)) => (B2 = A2))))). % singletonD
thf(fact_207_singleton__iff, axiom,
    ((![B2 : nat, A2 : nat]: ((member_nat @ B2 @ (insert_nat @ A2 @ bot_bot_set_nat)) = (B2 = A2))))). % singleton_iff
thf(fact_208_singleton__iff, axiom,
    ((![B2 : list_event, A2 : list_event]: ((member_list_event @ B2 @ (insert_list_event @ A2 @ bot_bo1693714908_event)) = (B2 = A2))))). % singleton_iff
thf(fact_209_singleton__iff, axiom,
    ((![B2 : agent, A2 : agent]: ((member_agent @ B2 @ (insert_agent @ A2 @ bot_bot_set_agent)) = (B2 = A2))))). % singleton_iff
thf(fact_210_singleton__iff, axiom,
    ((![B2 : msg, A2 : msg]: ((member_msg @ B2 @ (insert_msg @ A2 @ bot_bot_set_msg)) = (B2 = A2))))). % singleton_iff
thf(fact_211_doubleton__eq__iff, axiom,
    ((![A2 : msg, B2 : msg, C : msg, D : msg]: (((insert_msg @ A2 @ (insert_msg @ B2 @ bot_bot_set_msg)) = (insert_msg @ C @ (insert_msg @ D @ bot_bot_set_msg))) = (((((A2 = C)) & ((B2 = D)))) | ((((A2 = D)) & ((B2 = C))))))))). % doubleton_eq_iff
thf(fact_212_insert__not__empty, axiom,
    ((![A2 : msg, A : set_msg]: (~ (((insert_msg @ A2 @ A) = bot_bot_set_msg)))))). % insert_not_empty
thf(fact_213_singleton__inject, axiom,
    ((![A2 : msg, B2 : msg]: (((insert_msg @ A2 @ bot_bot_set_msg) = (insert_msg @ B2 @ bot_bot_set_msg)) => (A2 = B2))))). % singleton_inject
thf(fact_214_rangeI, axiom,
    ((![F : nat > msg, X2 : nat]: (member_msg @ (F @ X2) @ (image_nat_msg @ F @ top_top_set_nat))))). % rangeI
thf(fact_215_rangeI, axiom,
    ((![F : agent > nat, X2 : agent]: (member_nat @ (F @ X2) @ (image_agent_nat @ F @ top_top_set_agent))))). % rangeI
thf(fact_216_rangeI, axiom,
    ((![F : agent > list_event, X2 : agent]: (member_list_event @ (F @ X2) @ (image_832067507_event @ F @ top_top_set_agent))))). % rangeI
thf(fact_217_rangeI, axiom,
    ((![F : agent > msg, X2 : agent]: (member_msg @ (F @ X2) @ (image_agent_msg @ F @ top_top_set_agent))))). % rangeI
thf(fact_218_rangeI, axiom,
    ((![F : agent > agent, X2 : agent]: (member_agent @ (F @ X2) @ (image_agent_agent @ F @ top_top_set_agent))))). % rangeI
thf(fact_219_range__eqI, axiom,
    ((![B2 : msg, F : nat > msg, X2 : nat]: ((B2 = (F @ X2)) => (member_msg @ B2 @ (image_nat_msg @ F @ top_top_set_nat)))))). % range_eqI
thf(fact_220_range__eqI, axiom,
    ((![B2 : nat, F : agent > nat, X2 : agent]: ((B2 = (F @ X2)) => (member_nat @ B2 @ (image_agent_nat @ F @ top_top_set_agent)))))). % range_eqI
thf(fact_221_range__eqI, axiom,
    ((![B2 : list_event, F : agent > list_event, X2 : agent]: ((B2 = (F @ X2)) => (member_list_event @ B2 @ (image_832067507_event @ F @ top_top_set_agent)))))). % range_eqI
thf(fact_222_range__eqI, axiom,
    ((![B2 : msg, F : agent > msg, X2 : agent]: ((B2 = (F @ X2)) => (member_msg @ B2 @ (image_agent_msg @ F @ top_top_set_agent)))))). % range_eqI
thf(fact_223_range__eqI, axiom,
    ((![B2 : agent, F : agent > agent, X2 : agent]: ((B2 = (F @ X2)) => (member_agent @ B2 @ (image_agent_agent @ F @ top_top_set_agent)))))). % range_eqI
thf(fact_224_empty__not__UNIV, axiom,
    ((~ ((bot_bot_set_msg = top_top_set_msg))))). % empty_not_UNIV
thf(fact_225_empty__not__UNIV, axiom,
    ((~ ((bot_bot_set_agent = top_top_set_agent))))). % empty_not_UNIV
thf(fact_226_insert__UNIV, axiom,
    ((![X2 : msg]: ((insert_msg @ X2 @ top_top_set_msg) = top_top_set_msg)))). % insert_UNIV
thf(fact_227_insert__UNIV, axiom,
    ((![X2 : agent]: ((insert_agent @ X2 @ top_top_set_agent) = top_top_set_agent)))). % insert_UNIV
thf(fact_228_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_229_analz__impI, axiom,
    ((![Y2 : msg, Evs : list_event, Q : $o]: (((~ ((member_msg @ Y2 @ (analz @ (knows @ spy @ Evs))))) => Q) => ((~ ((member_msg @ Y2 @ (analz @ (knows @ spy @ Evs))))) => Q))))). % analz_impI
thf(fact_230_iso__tuple__UNIV__I, axiom,
    ((![X2 : nat]: (member_nat @ X2 @ top_top_set_nat)))). % iso_tuple_UNIV_I
thf(fact_231_iso__tuple__UNIV__I, axiom,
    ((![X2 : list_event]: (member_list_event @ X2 @ top_to1178833912_event)))). % iso_tuple_UNIV_I
thf(fact_232_iso__tuple__UNIV__I, axiom,
    ((![X2 : msg]: (member_msg @ X2 @ top_top_set_msg)))). % iso_tuple_UNIV_I
thf(fact_233_iso__tuple__UNIV__I, axiom,
    ((![X2 : agent]: (member_agent @ X2 @ top_top_set_agent)))). % iso_tuple_UNIV_I
thf(fact_234_analz__spies__pubK, axiom,
    ((![B2 : keymode, A : agent, Evs : list_event]: (member_msg @ (key @ (publicKey @ B2 @ A)) @ (analz @ (knows @ spy @ Evs)))))). % analz_spies_pubK
thf(fact_235_parts__insert__spies, axiom,
    ((![X : msg, Evs : list_event]: ((parts @ (insert_msg @ X @ (knows @ spy @ Evs))) = (sup_sup_set_msg @ (parts @ (insert_msg @ X @ bot_bot_set_msg)) @ (parts @ (knows @ spy @ Evs))))))). % parts_insert_spies
thf(fact_236_publicKey__inject, axiom,
    ((![B2 : keymode, A : agent, C : keymode, A3 : agent]: (((publicKey @ B2 @ A) = (publicKey @ C @ A3)) = (((B2 = C)) & ((A = A3))))))). % publicKey_inject
thf(fact_237_analz__analz__Un, axiom,
    ((![G : set_msg, H : set_msg]: ((analz @ (sup_sup_set_msg @ (analz @ G) @ H)) = (analz @ (sup_sup_set_msg @ G @ H)))))). % analz_analz_Un
thf(fact_238_parts__Un, axiom,
    ((![G : set_msg, H : set_msg]: ((parts @ (sup_sup_set_msg @ G @ H)) = (sup_sup_set_msg @ (parts @ G) @ (parts @ H)))))). % parts_Un
thf(fact_239_publicKey__image__eq, axiom,
    ((![B2 : keymode, X2 : agent, C : keymode, AA : set_agent]: ((member_nat @ (publicKey @ B2 @ X2) @ (image_agent_nat @ (publicKey @ C) @ AA)) = (((B2 = C)) & ((member_agent @ X2 @ AA))))))). % publicKey_image_eq
thf(fact_240_analz__synth, axiom,
    ((![H : set_msg]: ((analz @ (synth @ H)) = (sup_sup_set_msg @ (analz @ H) @ (synth @ H)))))). % analz_synth
thf(fact_241_analz__synth__Un, axiom,
    ((![G : set_msg, H : set_msg]: ((analz @ (sup_sup_set_msg @ (synth @ G) @ H)) = (sup_sup_set_msg @ (analz @ (sup_sup_set_msg @ G @ H)) @ (synth @ G)))))). % analz_synth_Un
thf(fact_242_parts__synth, axiom,
    ((![H : set_msg]: ((parts @ (synth @ H)) = (sup_sup_set_msg @ (parts @ H) @ (synth @ H)))))). % parts_synth
thf(fact_243_spies__pubK, axiom,
    ((![B2 : keymode, A : agent, Evs : list_event]: (member_msg @ (key @ (publicKey @ B2 @ A)) @ (knows @ spy @ Evs))))). % spies_pubK
thf(fact_244_analz__cong, axiom,
    ((![G : set_msg, G3 : set_msg, H : set_msg, H2 : set_msg]: (((analz @ G) = (analz @ G3)) => (((analz @ H) = (analz @ H2)) => ((analz @ (sup_sup_set_msg @ G @ H)) = (analz @ (sup_sup_set_msg @ G3 @ H2)))))))). % analz_cong
thf(fact_245_analz__image__freshK__simps_I63_J, axiom,
    ((![C : msg, G : set_msg, A : set_msg]: ((member_msg @ C @ (analz @ G)) => (member_msg @ C @ (analz @ (sup_sup_set_msg @ A @ G))))))). % analz_image_freshK_simps(63)
thf(fact_246_in__parts__UnE, axiom,
    ((![C : msg, G : set_msg, H : set_msg]: ((member_msg @ C @ (parts @ (sup_sup_set_msg @ G @ H))) => ((~ ((member_msg @ C @ (parts @ G)))) => (member_msg @ C @ (parts @ H))))))). % in_parts_UnE
thf(fact_247_shrK__neq__pubK, axiom,
    ((![B2 : keymode, C3 : agent, A : agent]: (~ (((publicKey @ B2 @ C3) = (shrK @ A))))))). % shrK_neq_pubK
thf(fact_248_injective__publicKey, axiom,
    ((![B2 : keymode, A : agent, C : keymode, A3 : agent]: (((publicKey @ B2 @ A) = (publicKey @ C @ A3)) => ((B2 = C) & (A = A3)))))). % injective_publicKey

% Conjectures (5)
thf(conj_0, hypothesis,
    ((~ ((member_nat @ kab2 @ (image_agent_nat @ shrK @ top_top_set_agent)))))).
thf(conj_1, hypothesis,
    ((member_list_event @ evsf @ nS_Sha1061662329shared))).
thf(conj_2, hypothesis,
    ((((member_msg @ (crypt @ kab @ x) @ (parts @ (knows @ spy @ evsf))) & (member_msg @ (key @ k) @ (parts @ (insert_msg @ x @ bot_bot_set_msg)))) => (member_msg @ (key @ k) @ (parts @ (knows @ spy @ evsf)))))).
thf(conj_3, hypothesis,
    ((member_msg @ xa @ (synth @ (analz @ (knows @ spy @ evsf)))))).
thf(conj_4, conjecture,
    ((((~ ((member_msg @ (crypt @ kab @ x) @ (parts @ (insert_msg @ xa @ (knows @ spy @ evsf)))))) | (~ ((member_msg @ (key @ k) @ (parts @ (insert_msg @ x @ bot_bot_set_msg)))))) | (member_msg @ (key @ k) @ (parts @ (insert_msg @ xa @ (knows @ spy @ evsf))))))).
