% 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_144__5229068_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:23:43.461

% Could-be-implicit typings (7)
thf(ty_n_t__Set__Oset_It__List__Olist_It__Event__Oevent_J_J, type,
    set_list_event : $tType).
thf(ty_n_t__List__Olist_It__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__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 (39)
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_Lattices_Osup__class_Osup_001t__Set__Oset_It__List__Olist_It__Event__Oevent_J_J, type,
    sup_su1529884788_event : set_list_event > set_list_event > set_list_event).
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_Lattices_Osup__class_Osup_001t__Set__Oset_It__Nat__Onat_J, type,
    sup_sup_set_nat : set_nat > set_nat > set_nat).
thf(sy_c_Message_Oagent_OSpy, type,
    spy : agent).
thf(sy_c_Message_Oanalz, type,
    analz : set_msg > set_msg).
thf(sy_c_Message_OinvKey, type,
    invKey : nat > nat).
thf(sy_c_Message_OkeysFor, type,
    keysFor : set_msg > set_nat).
thf(sy_c_Message_Omsg_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_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_001_062_It__Message__Omsg_M_Eo_J, type,
    bot_bot_msg_o : msg > $o).
thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Nat__Onat_M_Eo_J, type,
    bot_bot_nat_o : nat > $o).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__List__Olist_It__Event__Oevent_J_J, type,
    bot_bo1693714908_event : set_list_event).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Message__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_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__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__Omsg, type,
    insert_msg : msg > set_msg > set_msg).
thf(sy_c_Set_Oinsert_001t__Nat__Onat, type,
    insert_nat : nat > set_nat > set_nat).
thf(sy_c_Set_Ois__empty_001t__Message__Omsg, type,
    is_empty_msg : set_msg > $o).
thf(sy_c_Set_Ois__empty_001t__Nat__Onat, type,
    is_empty_nat : set_nat > $o).
thf(sy_c_Set_Ois__singleton_001t__List__Olist_It__Event__Oevent_J, type,
    is_sin1717822750_event : set_list_event > $o).
thf(sy_c_Set_Ois__singleton_001t__Message__Omsg, type,
    is_singleton_msg : set_msg > $o).
thf(sy_c_Set_Ois__singleton_001t__Nat__Onat, type,
    is_singleton_nat : set_nat > $o).
thf(sy_c_Set_Othe__elem_001t__Message__Omsg, type,
    the_elem_msg : set_msg > msg).
thf(sy_c_Set_Othe__elem_001t__Nat__Onat, type,
    the_elem_nat : set_nat > 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__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_X, type,
    x : msg).
thf(sy_v_evsf, type,
    evsf : list_event).

% Relevant facts (249)
thf(fact_0_usedI, axiom,
    ((![C : msg, Evs : list_event]: ((member_msg @ C @ (parts @ (knows @ spy @ Evs))) => (member_msg @ C @ (used @ Evs)))))). % usedI
thf(fact_1_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_2_keysFor__insert__Key, axiom,
    ((![K : nat, H : set_msg]: ((keysFor @ (insert_msg @ (key @ K) @ H)) = (keysFor @ H))))). % keysFor_insert_Key
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__Key, axiom,
    ((![K : nat, H : set_msg]: ((parts @ (insert_msg @ (key @ K) @ H)) = (insert_msg @ (key @ K) @ (parts @ H)))))). % parts_insert_Key
thf(fact_5_parts__empty, axiom,
    (((parts @ bot_bot_set_msg) = bot_bot_set_msg))). % parts_empty
thf(fact_6_analz__empty, axiom,
    (((analz @ bot_bot_set_msg) = bot_bot_set_msg))). % analz_empty
thf(fact_7_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_8_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_9_analz__parts, axiom,
    ((![H : set_msg]: ((analz @ (parts @ H)) = (parts @ H))))). % analz_parts
thf(fact_10_parts__analz, axiom,
    ((![H : set_msg]: ((parts @ (analz @ H)) = (parts @ H))))). % parts_analz
thf(fact_11_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_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_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_16_analz__analzD, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ (analz @ (analz @ H))) => (member_msg @ X @ (analz @ H)))))). % analz_analzD
thf(fact_17_analz_OInj, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ H) => (member_msg @ X @ (analz @ H)))))). % analz.Inj
thf(fact_18_parts__partsD, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ (parts @ (parts @ H))) => (member_msg @ X @ (parts @ H)))))). % parts_partsD
thf(fact_19_parts_OInj, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ H) => (member_msg @ X @ (parts @ H)))))). % parts.Inj
thf(fact_20_synth__synthD, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ (synth @ (synth @ H))) => (member_msg @ X @ (synth @ H)))))). % synth_synthD
thf(fact_21_synth__idem, axiom,
    ((![H : set_msg]: ((synth @ (synth @ H)) = (synth @ H))))). % synth_idem
thf(fact_22_synth_OInj, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ H) => (member_msg @ X @ (synth @ H)))))). % synth.Inj
thf(fact_23_analz__insert__eq__I, axiom,
    ((![X : msg, H : set_msg]: ((![X2 : msg]: ((member_msg @ X2 @ (analz @ (insert_msg @ X @ H))) => (member_msg @ X2 @ (insert_msg @ X @ (analz @ H))))) => ((analz @ (insert_msg @ X @ H)) = (insert_msg @ X @ (analz @ H))))))). % analz_insert_eq_I
thf(fact_24_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_25_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_26_analz__insertI, axiom,
    ((![C : msg, G : set_msg, A : msg]: ((member_msg @ C @ (analz @ G)) => (member_msg @ C @ (analz @ (insert_msg @ A @ G))))))). % analz_insertI
thf(fact_27_analz__cut, axiom,
    ((![Y : msg, X : msg, H : set_msg]: ((member_msg @ Y @ (analz @ (insert_msg @ X @ H))) => ((member_msg @ X @ (analz @ H)) => (member_msg @ Y @ (analz @ H))))))). % analz_cut
thf(fact_28_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_29_analz__into__parts, axiom,
    ((![C : msg, H : set_msg]: ((member_msg @ C @ (analz @ H)) => (member_msg @ C @ (parts @ H)))))). % analz_into_parts
thf(fact_30_parts__insert__eq__I, axiom,
    ((![X : msg, H : set_msg]: ((![X2 : msg]: ((member_msg @ X2 @ (parts @ (insert_msg @ X @ H))) => (member_msg @ X2 @ (insert_msg @ X @ (parts @ H))))) => ((parts @ (insert_msg @ X @ H)) = (insert_msg @ X @ (parts @ H))))))). % parts_insert_eq_I
thf(fact_31_parts__insertI, axiom,
    ((![C : msg, G : set_msg, A : msg]: ((member_msg @ C @ (parts @ G)) => (member_msg @ C @ (parts @ (insert_msg @ A @ G))))))). % parts_insertI
thf(fact_32_synth__cut, axiom,
    ((![Y : msg, X : msg, H : set_msg]: ((member_msg @ Y @ (synth @ (insert_msg @ X @ H))) => ((member_msg @ X @ (synth @ H)) => (member_msg @ Y @ (synth @ H))))))). % synth_cut
thf(fact_33_parts__emptyE, axiom,
    ((![X : msg]: (~ ((member_msg @ X @ (parts @ bot_bot_set_msg))))))). % parts_emptyE
thf(fact_34_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_35_parts__singleton, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ (parts @ H)) => (?[X2 : msg]: ((member_msg @ X2 @ H) & (member_msg @ X @ (parts @ (insert_msg @ X2 @ bot_bot_set_msg))))))))). % parts_singleton
thf(fact_36_syan__impI, axiom,
    ((![Y : msg, Evs : list_event, Q : $o]: (((~ ((member_msg @ Y @ (synth @ (analz @ (knows @ spy @ Evs)))))) => Q) => ((~ ((member_msg @ Y @ (synth @ (analz @ (knows @ spy @ Evs)))))) => Q))))). % syan_impI
thf(fact_37_singletonI, axiom,
    ((![A : list_event]: (member_list_event @ A @ (insert_list_event @ A @ bot_bo1693714908_event))))). % singletonI
thf(fact_38_singletonI, axiom,
    ((![A : msg]: (member_msg @ A @ (insert_msg @ A @ bot_bot_set_msg))))). % singletonI
thf(fact_39_singletonI, axiom,
    ((![A : nat]: (member_nat @ A @ (insert_nat @ A @ bot_bot_set_nat))))). % singletonI
thf(fact_40_insert__absorb2, axiom,
    ((![X3 : msg, A2 : set_msg]: ((insert_msg @ X3 @ (insert_msg @ X3 @ A2)) = (insert_msg @ X3 @ A2))))). % insert_absorb2
thf(fact_41_insert__iff, axiom,
    ((![A : nat, B : nat, A2 : set_nat]: ((member_nat @ A @ (insert_nat @ B @ A2)) = (((A = B)) | ((member_nat @ A @ A2))))))). % insert_iff
thf(fact_42_insert__iff, axiom,
    ((![A : list_event, B : list_event, A2 : set_list_event]: ((member_list_event @ A @ (insert_list_event @ B @ A2)) = (((A = B)) | ((member_list_event @ A @ A2))))))). % insert_iff
thf(fact_43_insert__iff, axiom,
    ((![A : msg, B : msg, A2 : set_msg]: ((member_msg @ A @ (insert_msg @ B @ A2)) = (((A = B)) | ((member_msg @ A @ A2))))))). % insert_iff
thf(fact_44_insertCI, axiom,
    ((![A : nat, B2 : set_nat, B : nat]: (((~ ((member_nat @ A @ B2))) => (A = B)) => (member_nat @ A @ (insert_nat @ B @ B2)))))). % insertCI
thf(fact_45_insertCI, axiom,
    ((![A : list_event, B2 : set_list_event, B : list_event]: (((~ ((member_list_event @ A @ B2))) => (A = B)) => (member_list_event @ A @ (insert_list_event @ B @ B2)))))). % insertCI
thf(fact_46_insertCI, axiom,
    ((![A : msg, B2 : set_msg, B : msg]: (((~ ((member_msg @ A @ B2))) => (A = B)) => (member_msg @ A @ (insert_msg @ B @ B2)))))). % insertCI
thf(fact_47_empty__Collect__eq, axiom,
    ((![P : msg > $o]: ((bot_bot_set_msg = (collect_msg @ P)) = (![X5 : msg]: (~ ((P @ X5)))))))). % empty_Collect_eq
thf(fact_48_empty__Collect__eq, axiom,
    ((![P : nat > $o]: ((bot_bot_set_nat = (collect_nat @ P)) = (![X5 : nat]: (~ ((P @ X5)))))))). % empty_Collect_eq
thf(fact_49_Collect__empty__eq, axiom,
    ((![P : msg > $o]: (((collect_msg @ P) = bot_bot_set_msg) = (![X5 : msg]: (~ ((P @ X5)))))))). % Collect_empty_eq
thf(fact_50_Collect__empty__eq, axiom,
    ((![P : nat > $o]: (((collect_nat @ P) = bot_bot_set_nat) = (![X5 : nat]: (~ ((P @ X5)))))))). % Collect_empty_eq
thf(fact_51_all__not__in__conv, axiom,
    ((![A2 : set_list_event]: ((![X5 : list_event]: (~ ((member_list_event @ X5 @ A2)))) = (A2 = bot_bo1693714908_event))))). % all_not_in_conv
thf(fact_52_all__not__in__conv, axiom,
    ((![A2 : set_msg]: ((![X5 : msg]: (~ ((member_msg @ X5 @ A2)))) = (A2 = bot_bot_set_msg))))). % all_not_in_conv
thf(fact_53_all__not__in__conv, axiom,
    ((![A2 : set_nat]: ((![X5 : nat]: (~ ((member_nat @ X5 @ A2)))) = (A2 = bot_bot_set_nat))))). % all_not_in_conv
thf(fact_54_empty__iff, axiom,
    ((![C : list_event]: (~ ((member_list_event @ C @ bot_bo1693714908_event)))))). % empty_iff
thf(fact_55_empty__iff, axiom,
    ((![C : msg]: (~ ((member_msg @ C @ bot_bot_set_msg)))))). % empty_iff
thf(fact_56_empty__iff, axiom,
    ((![C : nat]: (~ ((member_nat @ C @ bot_bot_set_nat)))))). % empty_iff
thf(fact_57_mem__Collect__eq, axiom,
    ((![A : nat, P : nat > $o]: ((member_nat @ A @ (collect_nat @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_58_mem__Collect__eq, axiom,
    ((![A : list_event, P : list_event > $o]: ((member_list_event @ A @ (collect_list_event @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_59_mem__Collect__eq, axiom,
    ((![A : msg, P : msg > $o]: ((member_msg @ A @ (collect_msg @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_60_Collect__mem__eq, axiom,
    ((![A2 : set_nat]: ((collect_nat @ (^[X5 : nat]: (member_nat @ X5 @ A2))) = A2)))). % Collect_mem_eq
thf(fact_61_Collect__mem__eq, axiom,
    ((![A2 : set_list_event]: ((collect_list_event @ (^[X5 : list_event]: (member_list_event @ X5 @ A2))) = A2)))). % Collect_mem_eq
thf(fact_62_Collect__mem__eq, axiom,
    ((![A2 : set_msg]: ((collect_msg @ (^[X5 : msg]: (member_msg @ X5 @ A2))) = A2)))). % Collect_mem_eq
thf(fact_63_singleton__inject, axiom,
    ((![A : msg, B : msg]: (((insert_msg @ A @ bot_bot_set_msg) = (insert_msg @ B @ bot_bot_set_msg)) => (A = B))))). % singleton_inject
thf(fact_64_singleton__inject, axiom,
    ((![A : nat, B : nat]: (((insert_nat @ A @ bot_bot_set_nat) = (insert_nat @ B @ bot_bot_set_nat)) => (A = B))))). % singleton_inject
thf(fact_65_keysFor__empty, axiom,
    (((keysFor @ bot_bot_set_msg) = bot_bot_set_nat))). % keysFor_empty
thf(fact_66_bot__set__def, axiom,
    ((bot_bot_set_msg = (collect_msg @ bot_bot_msg_o)))). % bot_set_def
thf(fact_67_bot__set__def, axiom,
    ((bot_bot_set_nat = (collect_nat @ bot_bot_nat_o)))). % bot_set_def
thf(fact_68_emptyE, axiom,
    ((![A : list_event]: (~ ((member_list_event @ A @ bot_bo1693714908_event)))))). % emptyE
thf(fact_69_emptyE, axiom,
    ((![A : msg]: (~ ((member_msg @ A @ bot_bot_set_msg)))))). % emptyE
thf(fact_70_emptyE, axiom,
    ((![A : nat]: (~ ((member_nat @ A @ bot_bot_set_nat)))))). % emptyE
thf(fact_71_equals0D, axiom,
    ((![A2 : set_list_event, A : list_event]: ((A2 = bot_bo1693714908_event) => (~ ((member_list_event @ A @ A2))))))). % equals0D
thf(fact_72_equals0D, axiom,
    ((![A2 : set_msg, A : msg]: ((A2 = bot_bot_set_msg) => (~ ((member_msg @ A @ A2))))))). % equals0D
thf(fact_73_equals0D, axiom,
    ((![A2 : set_nat, A : nat]: ((A2 = bot_bot_set_nat) => (~ ((member_nat @ A @ A2))))))). % equals0D
thf(fact_74_equals0I, axiom,
    ((![A2 : set_list_event]: ((![Y2 : list_event]: (~ ((member_list_event @ Y2 @ A2)))) => (A2 = bot_bo1693714908_event))))). % equals0I
thf(fact_75_equals0I, axiom,
    ((![A2 : set_msg]: ((![Y2 : msg]: (~ ((member_msg @ Y2 @ A2)))) => (A2 = bot_bot_set_msg))))). % equals0I
thf(fact_76_equals0I, axiom,
    ((![A2 : set_nat]: ((![Y2 : nat]: (~ ((member_nat @ Y2 @ A2)))) => (A2 = bot_bot_set_nat))))). % equals0I
thf(fact_77_ex__in__conv, axiom,
    ((![A2 : set_list_event]: ((?[X5 : list_event]: (member_list_event @ X5 @ A2)) = (~ ((A2 = bot_bo1693714908_event))))))). % ex_in_conv
thf(fact_78_ex__in__conv, axiom,
    ((![A2 : set_msg]: ((?[X5 : msg]: (member_msg @ X5 @ A2)) = (~ ((A2 = bot_bot_set_msg))))))). % ex_in_conv
thf(fact_79_ex__in__conv, axiom,
    ((![A2 : set_nat]: ((?[X5 : nat]: (member_nat @ X5 @ A2)) = (~ ((A2 = bot_bot_set_nat))))))). % ex_in_conv
thf(fact_80_insertE, axiom,
    ((![A : nat, B : nat, A2 : set_nat]: ((member_nat @ A @ (insert_nat @ B @ A2)) => ((~ ((A = B))) => (member_nat @ A @ A2)))))). % insertE
thf(fact_81_insertE, axiom,
    ((![A : list_event, B : list_event, A2 : set_list_event]: ((member_list_event @ A @ (insert_list_event @ B @ A2)) => ((~ ((A = B))) => (member_list_event @ A @ A2)))))). % insertE
thf(fact_82_insertE, axiom,
    ((![A : msg, B : msg, A2 : set_msg]: ((member_msg @ A @ (insert_msg @ B @ A2)) => ((~ ((A = B))) => (member_msg @ A @ A2)))))). % insertE
thf(fact_83_insertI1, axiom,
    ((![A : nat, B2 : set_nat]: (member_nat @ A @ (insert_nat @ A @ B2))))). % insertI1
thf(fact_84_insertI1, axiom,
    ((![A : list_event, B2 : set_list_event]: (member_list_event @ A @ (insert_list_event @ A @ B2))))). % insertI1
thf(fact_85_insertI1, axiom,
    ((![A : msg, B2 : set_msg]: (member_msg @ A @ (insert_msg @ A @ B2))))). % insertI1
thf(fact_86_insertI2, axiom,
    ((![A : nat, B2 : set_nat, B : nat]: ((member_nat @ A @ B2) => (member_nat @ A @ (insert_nat @ B @ B2)))))). % insertI2
thf(fact_87_insertI2, axiom,
    ((![A : list_event, B2 : set_list_event, B : list_event]: ((member_list_event @ A @ B2) => (member_list_event @ A @ (insert_list_event @ B @ B2)))))). % insertI2
thf(fact_88_insertI2, axiom,
    ((![A : msg, B2 : set_msg, B : msg]: ((member_msg @ A @ B2) => (member_msg @ A @ (insert_msg @ B @ B2)))))). % insertI2
thf(fact_89_Set_Oset__insert, axiom,
    ((![X3 : nat, A2 : set_nat]: ((member_nat @ X3 @ A2) => (~ ((![B3 : set_nat]: ((A2 = (insert_nat @ X3 @ B3)) => (member_nat @ X3 @ B3))))))))). % Set.set_insert
thf(fact_90_Set_Oset__insert, axiom,
    ((![X3 : list_event, A2 : set_list_event]: ((member_list_event @ X3 @ A2) => (~ ((![B3 : set_list_event]: ((A2 = (insert_list_event @ X3 @ B3)) => (member_list_event @ X3 @ B3))))))))). % Set.set_insert
thf(fact_91_Set_Oset__insert, axiom,
    ((![X3 : msg, A2 : set_msg]: ((member_msg @ X3 @ A2) => (~ ((![B3 : set_msg]: ((A2 = (insert_msg @ X3 @ B3)) => (member_msg @ X3 @ B3))))))))). % Set.set_insert
thf(fact_92_insert__ident, axiom,
    ((![X3 : nat, A2 : set_nat, B2 : set_nat]: ((~ ((member_nat @ X3 @ A2))) => ((~ ((member_nat @ X3 @ B2))) => (((insert_nat @ X3 @ A2) = (insert_nat @ X3 @ B2)) = (A2 = B2))))))). % insert_ident
thf(fact_93_insert__ident, axiom,
    ((![X3 : list_event, A2 : set_list_event, B2 : set_list_event]: ((~ ((member_list_event @ X3 @ A2))) => ((~ ((member_list_event @ X3 @ B2))) => (((insert_list_event @ X3 @ A2) = (insert_list_event @ X3 @ B2)) = (A2 = B2))))))). % insert_ident
thf(fact_94_insert__ident, axiom,
    ((![X3 : msg, A2 : set_msg, B2 : set_msg]: ((~ ((member_msg @ X3 @ A2))) => ((~ ((member_msg @ X3 @ B2))) => (((insert_msg @ X3 @ A2) = (insert_msg @ X3 @ B2)) = (A2 = B2))))))). % insert_ident
thf(fact_95_insert__absorb, axiom,
    ((![A : nat, A2 : set_nat]: ((member_nat @ A @ A2) => ((insert_nat @ A @ A2) = A2))))). % insert_absorb
thf(fact_96_insert__absorb, axiom,
    ((![A : list_event, A2 : set_list_event]: ((member_list_event @ A @ A2) => ((insert_list_event @ A @ A2) = A2))))). % insert_absorb
thf(fact_97_insert__absorb, axiom,
    ((![A : msg, A2 : set_msg]: ((member_msg @ A @ A2) => ((insert_msg @ A @ A2) = A2))))). % insert_absorb
thf(fact_98_insert__eq__iff, axiom,
    ((![A : nat, A2 : set_nat, B : nat, B2 : set_nat]: ((~ ((member_nat @ A @ A2))) => ((~ ((member_nat @ B @ B2))) => (((insert_nat @ A @ A2) = (insert_nat @ B @ B2)) = (((((A = B)) => ((A2 = B2)))) & ((((~ ((A = B)))) => ((?[C2 : set_nat]: (((A2 = (insert_nat @ B @ C2))) & ((((~ ((member_nat @ B @ C2)))) & ((((B2 = (insert_nat @ A @ C2))) & ((~ ((member_nat @ A @ C2)))))))))))))))))))). % insert_eq_iff
thf(fact_99_insert__eq__iff, axiom,
    ((![A : list_event, A2 : set_list_event, B : list_event, B2 : set_list_event]: ((~ ((member_list_event @ A @ A2))) => ((~ ((member_list_event @ B @ B2))) => (((insert_list_event @ A @ A2) = (insert_list_event @ B @ B2)) = (((((A = B)) => ((A2 = B2)))) & ((((~ ((A = B)))) => ((?[C2 : set_list_event]: (((A2 = (insert_list_event @ B @ C2))) & ((((~ ((member_list_event @ B @ C2)))) & ((((B2 = (insert_list_event @ A @ C2))) & ((~ ((member_list_event @ A @ C2)))))))))))))))))))). % insert_eq_iff
thf(fact_100_insert__eq__iff, axiom,
    ((![A : msg, A2 : set_msg, B : msg, B2 : set_msg]: ((~ ((member_msg @ A @ A2))) => ((~ ((member_msg @ B @ B2))) => (((insert_msg @ A @ A2) = (insert_msg @ B @ B2)) = (((((A = B)) => ((A2 = B2)))) & ((((~ ((A = B)))) => ((?[C2 : set_msg]: (((A2 = (insert_msg @ B @ C2))) & ((((~ ((member_msg @ B @ C2)))) & ((((B2 = (insert_msg @ A @ C2))) & ((~ ((member_msg @ A @ C2)))))))))))))))))))). % insert_eq_iff
thf(fact_101_insert__commute, axiom,
    ((![X3 : msg, Y3 : msg, A2 : set_msg]: ((insert_msg @ X3 @ (insert_msg @ Y3 @ A2)) = (insert_msg @ Y3 @ (insert_msg @ X3 @ A2)))))). % insert_commute
thf(fact_102_mk__disjoint__insert, axiom,
    ((![A : nat, A2 : set_nat]: ((member_nat @ A @ A2) => (?[B3 : set_nat]: ((A2 = (insert_nat @ A @ B3)) & (~ ((member_nat @ A @ B3))))))))). % mk_disjoint_insert
thf(fact_103_mk__disjoint__insert, axiom,
    ((![A : list_event, A2 : set_list_event]: ((member_list_event @ A @ A2) => (?[B3 : set_list_event]: ((A2 = (insert_list_event @ A @ B3)) & (~ ((member_list_event @ A @ B3))))))))). % mk_disjoint_insert
thf(fact_104_mk__disjoint__insert, axiom,
    ((![A : msg, A2 : set_msg]: ((member_msg @ A @ A2) => (?[B3 : set_msg]: ((A2 = (insert_msg @ A @ B3)) & (~ ((member_msg @ A @ B3))))))))). % mk_disjoint_insert
thf(fact_105_singletonD, axiom,
    ((![B : list_event, A : list_event]: ((member_list_event @ B @ (insert_list_event @ A @ bot_bo1693714908_event)) => (B = A))))). % singletonD
thf(fact_106_singletonD, axiom,
    ((![B : msg, A : msg]: ((member_msg @ B @ (insert_msg @ A @ bot_bot_set_msg)) => (B = A))))). % singletonD
thf(fact_107_singletonD, axiom,
    ((![B : nat, A : nat]: ((member_nat @ B @ (insert_nat @ A @ bot_bot_set_nat)) => (B = A))))). % singletonD
thf(fact_108_singleton__iff, axiom,
    ((![B : list_event, A : list_event]: ((member_list_event @ B @ (insert_list_event @ A @ bot_bo1693714908_event)) = (B = A))))). % singleton_iff
thf(fact_109_singleton__iff, axiom,
    ((![B : msg, A : msg]: ((member_msg @ B @ (insert_msg @ A @ bot_bot_set_msg)) = (B = A))))). % singleton_iff
thf(fact_110_singleton__iff, axiom,
    ((![B : nat, A : nat]: ((member_nat @ B @ (insert_nat @ A @ bot_bot_set_nat)) = (B = A))))). % singleton_iff
thf(fact_111_doubleton__eq__iff, axiom,
    ((![A : msg, B : msg, C : msg, D : msg]: (((insert_msg @ A @ (insert_msg @ B @ bot_bot_set_msg)) = (insert_msg @ C @ (insert_msg @ D @ bot_bot_set_msg))) = (((((A = C)) & ((B = D)))) | ((((A = D)) & ((B = C))))))))). % doubleton_eq_iff
thf(fact_112_doubleton__eq__iff, axiom,
    ((![A : nat, B : nat, C : nat, D : nat]: (((insert_nat @ A @ (insert_nat @ B @ bot_bot_set_nat)) = (insert_nat @ C @ (insert_nat @ D @ bot_bot_set_nat))) = (((((A = C)) & ((B = D)))) | ((((A = D)) & ((B = C))))))))). % doubleton_eq_iff
thf(fact_113_insert__not__empty, axiom,
    ((![A : msg, A2 : set_msg]: (~ (((insert_msg @ A @ A2) = bot_bot_set_msg)))))). % insert_not_empty
thf(fact_114_insert__not__empty, axiom,
    ((![A : nat, A2 : set_nat]: (~ (((insert_nat @ A @ A2) = bot_bot_set_nat)))))). % insert_not_empty
thf(fact_115_the__elem__eq, axiom,
    ((![X3 : msg]: ((the_elem_msg @ (insert_msg @ X3 @ bot_bot_set_msg)) = X3)))). % the_elem_eq
thf(fact_116_the__elem__eq, axiom,
    ((![X3 : nat]: ((the_elem_nat @ (insert_nat @ X3 @ bot_bot_set_nat)) = X3)))). % the_elem_eq
thf(fact_117_is__singletonI, axiom,
    ((![X3 : msg]: (is_singleton_msg @ (insert_msg @ X3 @ bot_bot_set_msg))))). % is_singletonI
thf(fact_118_is__singletonI, axiom,
    ((![X3 : nat]: (is_singleton_nat @ (insert_nat @ X3 @ bot_bot_set_nat))))). % is_singletonI
thf(fact_119_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_120_Fake__parts__sing__imp__Un, axiom,
    ((![C : msg, X : msg, H : set_msg]: ((member_msg @ C @ (parts @ (insert_msg @ X @ bot_bot_set_msg))) => ((member_msg @ X @ (synth @ (analz @ H))) => (member_msg @ C @ (sup_sup_set_msg @ (synth @ (analz @ H)) @ (parts @ H)))))))). % Fake_parts_sing_imp_Un
thf(fact_121_Set_Ois__empty__def, axiom,
    ((is_empty_msg = (^[A3 : set_msg]: (A3 = bot_bot_set_msg))))). % Set.is_empty_def
thf(fact_122_Set_Ois__empty__def, axiom,
    ((is_empty_nat = (^[A3 : set_nat]: (A3 = bot_bot_set_nat))))). % Set.is_empty_def
thf(fact_123_is__singletonE, axiom,
    ((![A2 : set_msg]: ((is_singleton_msg @ A2) => (~ ((![X2 : msg]: (~ ((A2 = (insert_msg @ X2 @ bot_bot_set_msg))))))))))). % is_singletonE
thf(fact_124_is__singletonE, axiom,
    ((![A2 : set_nat]: ((is_singleton_nat @ A2) => (~ ((![X2 : nat]: (~ ((A2 = (insert_nat @ X2 @ bot_bot_set_nat))))))))))). % is_singletonE
thf(fact_125_Un__iff, axiom,
    ((![C : list_event, A2 : set_list_event, B2 : set_list_event]: ((member_list_event @ C @ (sup_su1529884788_event @ A2 @ B2)) = (((member_list_event @ C @ A2)) | ((member_list_event @ C @ B2))))))). % Un_iff
thf(fact_126_Un__iff, axiom,
    ((![C : msg, A2 : set_msg, B2 : set_msg]: ((member_msg @ C @ (sup_sup_set_msg @ A2 @ B2)) = (((member_msg @ C @ A2)) | ((member_msg @ C @ B2))))))). % Un_iff
thf(fact_127_Un__iff, axiom,
    ((![C : nat, A2 : set_nat, B2 : set_nat]: ((member_nat @ C @ (sup_sup_set_nat @ A2 @ B2)) = (((member_nat @ C @ A2)) | ((member_nat @ C @ B2))))))). % Un_iff
thf(fact_128_UnCI, axiom,
    ((![C : list_event, B2 : set_list_event, A2 : set_list_event]: (((~ ((member_list_event @ C @ B2))) => (member_list_event @ C @ A2)) => (member_list_event @ C @ (sup_su1529884788_event @ A2 @ B2)))))). % UnCI
thf(fact_129_UnCI, axiom,
    ((![C : msg, B2 : set_msg, A2 : set_msg]: (((~ ((member_msg @ C @ B2))) => (member_msg @ C @ A2)) => (member_msg @ C @ (sup_sup_set_msg @ A2 @ B2)))))). % UnCI
thf(fact_130_UnCI, axiom,
    ((![C : nat, B2 : set_nat, A2 : set_nat]: (((~ ((member_nat @ C @ B2))) => (member_nat @ C @ A2)) => (member_nat @ C @ (sup_sup_set_nat @ A2 @ B2)))))). % UnCI
thf(fact_131_Un__empty, axiom,
    ((![A2 : set_msg, B2 : set_msg]: (((sup_sup_set_msg @ A2 @ B2) = bot_bot_set_msg) = (((A2 = bot_bot_set_msg)) & ((B2 = bot_bot_set_msg))))))). % Un_empty
thf(fact_132_Un__empty, axiom,
    ((![A2 : set_nat, B2 : set_nat]: (((sup_sup_set_nat @ A2 @ B2) = bot_bot_set_nat) = (((A2 = bot_bot_set_nat)) & ((B2 = bot_bot_set_nat))))))). % Un_empty
thf(fact_133_Un__insert__right, axiom,
    ((![A2 : set_msg, A : msg, B2 : set_msg]: ((sup_sup_set_msg @ A2 @ (insert_msg @ A @ B2)) = (insert_msg @ A @ (sup_sup_set_msg @ A2 @ B2)))))). % Un_insert_right
thf(fact_134_Un__insert__right, axiom,
    ((![A2 : set_nat, A : nat, B2 : set_nat]: ((sup_sup_set_nat @ A2 @ (insert_nat @ A @ B2)) = (insert_nat @ A @ (sup_sup_set_nat @ A2 @ B2)))))). % Un_insert_right
thf(fact_135_Un__insert__left, axiom,
    ((![A : msg, B2 : set_msg, C3 : set_msg]: ((sup_sup_set_msg @ (insert_msg @ A @ B2) @ C3) = (insert_msg @ A @ (sup_sup_set_msg @ B2 @ C3)))))). % Un_insert_left
thf(fact_136_Un__insert__left, axiom,
    ((![A : nat, B2 : set_nat, C3 : set_nat]: ((sup_sup_set_nat @ (insert_nat @ A @ B2) @ C3) = (insert_nat @ A @ (sup_sup_set_nat @ B2 @ C3)))))). % Un_insert_left
thf(fact_137_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_138_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_139_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_140_analz__synth, axiom,
    ((![H : set_msg]: ((analz @ (synth @ H)) = (sup_sup_set_msg @ (analz @ H) @ (synth @ H)))))). % analz_synth
thf(fact_141_parts__synth, axiom,
    ((![H : set_msg]: ((parts @ (synth @ H)) = (sup_sup_set_msg @ (parts @ H) @ (synth @ H)))))). % parts_synth
thf(fact_142_Un__left__commute, axiom,
    ((![A2 : set_msg, B2 : set_msg, C3 : set_msg]: ((sup_sup_set_msg @ A2 @ (sup_sup_set_msg @ B2 @ C3)) = (sup_sup_set_msg @ B2 @ (sup_sup_set_msg @ A2 @ C3)))))). % Un_left_commute
thf(fact_143_Un__left__commute, axiom,
    ((![A2 : set_nat, B2 : set_nat, C3 : set_nat]: ((sup_sup_set_nat @ A2 @ (sup_sup_set_nat @ B2 @ C3)) = (sup_sup_set_nat @ B2 @ (sup_sup_set_nat @ A2 @ C3)))))). % Un_left_commute
thf(fact_144_Un__left__absorb, axiom,
    ((![A2 : set_msg, B2 : set_msg]: ((sup_sup_set_msg @ A2 @ (sup_sup_set_msg @ A2 @ B2)) = (sup_sup_set_msg @ A2 @ B2))))). % Un_left_absorb
thf(fact_145_Un__left__absorb, axiom,
    ((![A2 : set_nat, B2 : set_nat]: ((sup_sup_set_nat @ A2 @ (sup_sup_set_nat @ A2 @ B2)) = (sup_sup_set_nat @ A2 @ B2))))). % Un_left_absorb
thf(fact_146_Un__commute, axiom,
    ((sup_sup_set_msg = (^[A3 : set_msg]: (^[B4 : set_msg]: (sup_sup_set_msg @ B4 @ A3)))))). % Un_commute
thf(fact_147_Un__commute, axiom,
    ((sup_sup_set_nat = (^[A3 : set_nat]: (^[B4 : set_nat]: (sup_sup_set_nat @ B4 @ A3)))))). % Un_commute
thf(fact_148_Un__absorb, axiom,
    ((![A2 : set_msg]: ((sup_sup_set_msg @ A2 @ A2) = A2)))). % Un_absorb
thf(fact_149_Un__absorb, axiom,
    ((![A2 : set_nat]: ((sup_sup_set_nat @ A2 @ A2) = A2)))). % Un_absorb
thf(fact_150_Un__assoc, axiom,
    ((![A2 : set_msg, B2 : set_msg, C3 : set_msg]: ((sup_sup_set_msg @ (sup_sup_set_msg @ A2 @ B2) @ C3) = (sup_sup_set_msg @ A2 @ (sup_sup_set_msg @ B2 @ C3)))))). % Un_assoc
thf(fact_151_Un__assoc, axiom,
    ((![A2 : set_nat, B2 : set_nat, C3 : set_nat]: ((sup_sup_set_nat @ (sup_sup_set_nat @ A2 @ B2) @ C3) = (sup_sup_set_nat @ A2 @ (sup_sup_set_nat @ B2 @ C3)))))). % Un_assoc
thf(fact_152_ball__Un, axiom,
    ((![A2 : set_msg, B2 : set_msg, P : msg > $o]: ((![X5 : msg]: (((member_msg @ X5 @ (sup_sup_set_msg @ A2 @ B2))) => ((P @ X5)))) = (((![X5 : msg]: (((member_msg @ X5 @ A2)) => ((P @ X5))))) & ((![X5 : msg]: (((member_msg @ X5 @ B2)) => ((P @ X5)))))))))). % ball_Un
thf(fact_153_ball__Un, axiom,
    ((![A2 : set_nat, B2 : set_nat, P : nat > $o]: ((![X5 : nat]: (((member_nat @ X5 @ (sup_sup_set_nat @ A2 @ B2))) => ((P @ X5)))) = (((![X5 : nat]: (((member_nat @ X5 @ A2)) => ((P @ X5))))) & ((![X5 : nat]: (((member_nat @ X5 @ B2)) => ((P @ X5)))))))))). % ball_Un
thf(fact_154_bex__Un, axiom,
    ((![A2 : set_msg, B2 : set_msg, P : msg > $o]: ((?[X5 : msg]: (((member_msg @ X5 @ (sup_sup_set_msg @ A2 @ B2))) & ((P @ X5)))) = (((?[X5 : msg]: (((member_msg @ X5 @ A2)) & ((P @ X5))))) | ((?[X5 : msg]: (((member_msg @ X5 @ B2)) & ((P @ X5)))))))))). % bex_Un
thf(fact_155_bex__Un, axiom,
    ((![A2 : set_nat, B2 : set_nat, P : nat > $o]: ((?[X5 : nat]: (((member_nat @ X5 @ (sup_sup_set_nat @ A2 @ B2))) & ((P @ X5)))) = (((?[X5 : nat]: (((member_nat @ X5 @ A2)) & ((P @ X5))))) | ((?[X5 : nat]: (((member_nat @ X5 @ B2)) & ((P @ X5)))))))))). % bex_Un
thf(fact_156_UnI2, axiom,
    ((![C : list_event, B2 : set_list_event, A2 : set_list_event]: ((member_list_event @ C @ B2) => (member_list_event @ C @ (sup_su1529884788_event @ A2 @ B2)))))). % UnI2
thf(fact_157_UnI2, axiom,
    ((![C : msg, B2 : set_msg, A2 : set_msg]: ((member_msg @ C @ B2) => (member_msg @ C @ (sup_sup_set_msg @ A2 @ B2)))))). % UnI2
thf(fact_158_UnI2, axiom,
    ((![C : nat, B2 : set_nat, A2 : set_nat]: ((member_nat @ C @ B2) => (member_nat @ C @ (sup_sup_set_nat @ A2 @ B2)))))). % UnI2
thf(fact_159_UnI1, axiom,
    ((![C : list_event, A2 : set_list_event, B2 : set_list_event]: ((member_list_event @ C @ A2) => (member_list_event @ C @ (sup_su1529884788_event @ A2 @ B2)))))). % UnI1
thf(fact_160_UnI1, axiom,
    ((![C : msg, A2 : set_msg, B2 : set_msg]: ((member_msg @ C @ A2) => (member_msg @ C @ (sup_sup_set_msg @ A2 @ B2)))))). % UnI1
thf(fact_161_UnI1, axiom,
    ((![C : nat, A2 : set_nat, B2 : set_nat]: ((member_nat @ C @ A2) => (member_nat @ C @ (sup_sup_set_nat @ A2 @ B2)))))). % UnI1
thf(fact_162_UnE, axiom,
    ((![C : list_event, A2 : set_list_event, B2 : set_list_event]: ((member_list_event @ C @ (sup_su1529884788_event @ A2 @ B2)) => ((~ ((member_list_event @ C @ A2))) => (member_list_event @ C @ B2)))))). % UnE
thf(fact_163_UnE, axiom,
    ((![C : msg, A2 : set_msg, B2 : set_msg]: ((member_msg @ C @ (sup_sup_set_msg @ A2 @ B2)) => ((~ ((member_msg @ C @ A2))) => (member_msg @ C @ B2)))))). % UnE
thf(fact_164_UnE, axiom,
    ((![C : nat, A2 : set_nat, B2 : set_nat]: ((member_nat @ C @ (sup_sup_set_nat @ A2 @ B2)) => ((~ ((member_nat @ C @ A2))) => (member_nat @ C @ B2)))))). % UnE
thf(fact_165_Un__empty__right, axiom,
    ((![A2 : set_msg]: ((sup_sup_set_msg @ A2 @ bot_bot_set_msg) = A2)))). % Un_empty_right
thf(fact_166_Un__empty__right, axiom,
    ((![A2 : set_nat]: ((sup_sup_set_nat @ A2 @ bot_bot_set_nat) = A2)))). % Un_empty_right
thf(fact_167_Un__empty__left, axiom,
    ((![B2 : set_msg]: ((sup_sup_set_msg @ bot_bot_set_msg @ B2) = B2)))). % Un_empty_left
thf(fact_168_Un__empty__left, axiom,
    ((![B2 : set_nat]: ((sup_sup_set_nat @ bot_bot_set_nat @ B2) = B2)))). % Un_empty_left
thf(fact_169_analz__cong, axiom,
    ((![G : set_msg, G2 : set_msg, H : set_msg, H2 : set_msg]: (((analz @ G) = (analz @ G2)) => (((analz @ H) = (analz @ H2)) => ((analz @ (sup_sup_set_msg @ G @ H)) = (analz @ (sup_sup_set_msg @ G2 @ H2)))))))). % analz_cong
thf(fact_170_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_171_singleton__Un__iff, axiom,
    ((![X3 : msg, A2 : set_msg, B2 : set_msg]: (((insert_msg @ X3 @ bot_bot_set_msg) = (sup_sup_set_msg @ A2 @ B2)) = (((((A2 = bot_bot_set_msg)) & ((B2 = (insert_msg @ X3 @ bot_bot_set_msg))))) | ((((((A2 = (insert_msg @ X3 @ bot_bot_set_msg))) & ((B2 = bot_bot_set_msg)))) | ((((A2 = (insert_msg @ X3 @ bot_bot_set_msg))) & ((B2 = (insert_msg @ X3 @ bot_bot_set_msg)))))))))))). % singleton_Un_iff
thf(fact_172_singleton__Un__iff, axiom,
    ((![X3 : nat, A2 : set_nat, B2 : set_nat]: (((insert_nat @ X3 @ bot_bot_set_nat) = (sup_sup_set_nat @ A2 @ B2)) = (((((A2 = bot_bot_set_nat)) & ((B2 = (insert_nat @ X3 @ bot_bot_set_nat))))) | ((((((A2 = (insert_nat @ X3 @ bot_bot_set_nat))) & ((B2 = bot_bot_set_nat)))) | ((((A2 = (insert_nat @ X3 @ bot_bot_set_nat))) & ((B2 = (insert_nat @ X3 @ bot_bot_set_nat)))))))))))). % singleton_Un_iff
thf(fact_173_Un__singleton__iff, axiom,
    ((![A2 : set_msg, B2 : set_msg, X3 : msg]: (((sup_sup_set_msg @ A2 @ B2) = (insert_msg @ X3 @ bot_bot_set_msg)) = (((((A2 = bot_bot_set_msg)) & ((B2 = (insert_msg @ X3 @ bot_bot_set_msg))))) | ((((((A2 = (insert_msg @ X3 @ bot_bot_set_msg))) & ((B2 = bot_bot_set_msg)))) | ((((A2 = (insert_msg @ X3 @ bot_bot_set_msg))) & ((B2 = (insert_msg @ X3 @ bot_bot_set_msg)))))))))))). % Un_singleton_iff
thf(fact_174_Un__singleton__iff, axiom,
    ((![A2 : set_nat, B2 : set_nat, X3 : nat]: (((sup_sup_set_nat @ A2 @ B2) = (insert_nat @ X3 @ bot_bot_set_nat)) = (((((A2 = bot_bot_set_nat)) & ((B2 = (insert_nat @ X3 @ bot_bot_set_nat))))) | ((((((A2 = (insert_nat @ X3 @ bot_bot_set_nat))) & ((B2 = bot_bot_set_nat)))) | ((((A2 = (insert_nat @ X3 @ bot_bot_set_nat))) & ((B2 = (insert_nat @ X3 @ bot_bot_set_nat)))))))))))). % Un_singleton_iff
thf(fact_175_insert__is__Un, axiom,
    ((insert_msg = (^[A4 : msg]: (sup_sup_set_msg @ (insert_msg @ A4 @ bot_bot_set_msg)))))). % insert_is_Un
thf(fact_176_insert__is__Un, axiom,
    ((insert_nat = (^[A4 : nat]: (sup_sup_set_nat @ (insert_nat @ A4 @ bot_bot_set_nat)))))). % insert_is_Un
thf(fact_177_parts__cut, axiom,
    ((![Y : msg, X : msg, G : set_msg, H : set_msg]: ((member_msg @ Y @ (parts @ (insert_msg @ X @ G))) => ((member_msg @ X @ (parts @ H)) => (member_msg @ Y @ (parts @ (sup_sup_set_msg @ G @ H)))))))). % parts_cut
thf(fact_178_is__singleton__the__elem, axiom,
    ((is_singleton_msg = (^[A3 : set_msg]: (A3 = (insert_msg @ (the_elem_msg @ A3) @ bot_bot_set_msg)))))). % is_singleton_the_elem
thf(fact_179_is__singleton__the__elem, axiom,
    ((is_singleton_nat = (^[A3 : set_nat]: (A3 = (insert_nat @ (the_elem_nat @ A3) @ bot_bot_set_nat)))))). % is_singleton_the_elem
thf(fact_180_is__singletonI_H, axiom,
    ((![A2 : set_list_event]: ((~ ((A2 = bot_bo1693714908_event))) => ((![X2 : list_event, Y2 : list_event]: ((member_list_event @ X2 @ A2) => ((member_list_event @ Y2 @ A2) => (X2 = Y2)))) => (is_sin1717822750_event @ A2)))))). % is_singletonI'
thf(fact_181_is__singletonI_H, axiom,
    ((![A2 : set_msg]: ((~ ((A2 = bot_bot_set_msg))) => ((![X2 : msg, Y2 : msg]: ((member_msg @ X2 @ A2) => ((member_msg @ Y2 @ A2) => (X2 = Y2)))) => (is_singleton_msg @ A2)))))). % is_singletonI'
thf(fact_182_is__singletonI_H, axiom,
    ((![A2 : set_nat]: ((~ ((A2 = bot_bot_set_nat))) => ((![X2 : nat, Y2 : nat]: ((member_nat @ X2 @ A2) => ((member_nat @ Y2 @ A2) => (X2 = Y2)))) => (is_singleton_nat @ A2)))))). % is_singletonI'
thf(fact_183_parts__insert2, axiom,
    ((![X : msg, Y : msg, H : set_msg]: ((parts @ (insert_msg @ X @ (insert_msg @ Y @ H))) = (sup_sup_set_msg @ (sup_sup_set_msg @ (parts @ (insert_msg @ X @ bot_bot_set_msg)) @ (parts @ (insert_msg @ Y @ bot_bot_set_msg))) @ (parts @ H)))))). % parts_insert2
thf(fact_184_parts__insert, axiom,
    ((![X : msg, H : set_msg]: ((parts @ (insert_msg @ X @ H)) = (sup_sup_set_msg @ (parts @ (insert_msg @ X @ bot_bot_set_msg)) @ (parts @ H)))))). % parts_insert
thf(fact_185_Fake__parts__insert__in__Un, axiom,
    ((![Z : msg, X : msg, H : set_msg]: ((member_msg @ Z @ (parts @ (insert_msg @ X @ H))) => ((member_msg @ X @ (synth @ (analz @ H))) => (member_msg @ Z @ (sup_sup_set_msg @ (synth @ (analz @ H)) @ (parts @ H)))))))). % Fake_parts_insert_in_Un
thf(fact_186_parts__insert__knows__A, axiom,
    ((![X : msg, A2 : agent, Evs : list_event]: ((parts @ (insert_msg @ X @ (knows @ A2 @ Evs))) = (sup_sup_set_msg @ (parts @ (insert_msg @ X @ bot_bot_set_msg)) @ (parts @ (knows @ A2 @ Evs))))))). % parts_insert_knows_A
thf(fact_187_is__singleton__def, axiom,
    ((is_singleton_msg = (^[A3 : set_msg]: (?[X5 : msg]: (A3 = (insert_msg @ X5 @ bot_bot_set_msg))))))). % is_singleton_def
thf(fact_188_is__singleton__def, axiom,
    ((is_singleton_nat = (^[A3 : set_nat]: (?[X5 : nat]: (A3 = (insert_nat @ X5 @ bot_bot_set_nat))))))). % is_singleton_def
thf(fact_189_sup__bot__left, axiom,
    ((![X3 : set_msg]: ((sup_sup_set_msg @ bot_bot_set_msg @ X3) = X3)))). % sup_bot_left
thf(fact_190_sup__bot__left, axiom,
    ((![X3 : set_nat]: ((sup_sup_set_nat @ bot_bot_set_nat @ X3) = X3)))). % sup_bot_left
thf(fact_191_sup__bot__right, axiom,
    ((![X3 : set_msg]: ((sup_sup_set_msg @ X3 @ bot_bot_set_msg) = X3)))). % sup_bot_right
thf(fact_192_sup__bot__right, axiom,
    ((![X3 : set_nat]: ((sup_sup_set_nat @ X3 @ bot_bot_set_nat) = X3)))). % sup_bot_right
thf(fact_193_bot__eq__sup__iff, axiom,
    ((![X3 : set_msg, Y3 : set_msg]: ((bot_bot_set_msg = (sup_sup_set_msg @ X3 @ Y3)) = (((X3 = bot_bot_set_msg)) & ((Y3 = bot_bot_set_msg))))))). % bot_eq_sup_iff
thf(fact_194_bot__eq__sup__iff, axiom,
    ((![X3 : set_nat, Y3 : set_nat]: ((bot_bot_set_nat = (sup_sup_set_nat @ X3 @ Y3)) = (((X3 = bot_bot_set_nat)) & ((Y3 = bot_bot_set_nat))))))). % bot_eq_sup_iff
thf(fact_195_sup__eq__bot__iff, axiom,
    ((![X3 : set_msg, Y3 : set_msg]: (((sup_sup_set_msg @ X3 @ Y3) = bot_bot_set_msg) = (((X3 = bot_bot_set_msg)) & ((Y3 = bot_bot_set_msg))))))). % sup_eq_bot_iff
thf(fact_196_sup__eq__bot__iff, axiom,
    ((![X3 : set_nat, Y3 : set_nat]: (((sup_sup_set_nat @ X3 @ Y3) = bot_bot_set_nat) = (((X3 = bot_bot_set_nat)) & ((Y3 = bot_bot_set_nat))))))). % sup_eq_bot_iff
thf(fact_197_sup_Oright__idem, axiom,
    ((![A : set_msg, B : set_msg]: ((sup_sup_set_msg @ (sup_sup_set_msg @ A @ B) @ B) = (sup_sup_set_msg @ A @ B))))). % sup.right_idem
thf(fact_198_sup_Oright__idem, axiom,
    ((![A : set_nat, B : set_nat]: ((sup_sup_set_nat @ (sup_sup_set_nat @ A @ B) @ B) = (sup_sup_set_nat @ A @ B))))). % sup.right_idem
thf(fact_199_sup__left__idem, axiom,
    ((![X3 : set_msg, Y3 : set_msg]: ((sup_sup_set_msg @ X3 @ (sup_sup_set_msg @ X3 @ Y3)) = (sup_sup_set_msg @ X3 @ Y3))))). % sup_left_idem
thf(fact_200_sup__left__idem, axiom,
    ((![X3 : set_nat, Y3 : set_nat]: ((sup_sup_set_nat @ X3 @ (sup_sup_set_nat @ X3 @ Y3)) = (sup_sup_set_nat @ X3 @ Y3))))). % sup_left_idem
thf(fact_201_sup_Oleft__idem, axiom,
    ((![A : set_msg, B : set_msg]: ((sup_sup_set_msg @ A @ (sup_sup_set_msg @ A @ B)) = (sup_sup_set_msg @ A @ B))))). % sup.left_idem
thf(fact_202_sup_Oleft__idem, axiom,
    ((![A : set_nat, B : set_nat]: ((sup_sup_set_nat @ A @ (sup_sup_set_nat @ A @ B)) = (sup_sup_set_nat @ A @ B))))). % sup.left_idem
thf(fact_203_sup__idem, axiom,
    ((![X3 : set_msg]: ((sup_sup_set_msg @ X3 @ X3) = X3)))). % sup_idem
thf(fact_204_sup__idem, axiom,
    ((![X3 : set_nat]: ((sup_sup_set_nat @ X3 @ X3) = X3)))). % sup_idem
thf(fact_205_sup_Oidem, axiom,
    ((![A : set_msg]: ((sup_sup_set_msg @ A @ A) = A)))). % sup.idem
thf(fact_206_sup_Oidem, axiom,
    ((![A : set_nat]: ((sup_sup_set_nat @ A @ A) = A)))). % sup.idem
thf(fact_207_sup__bot_Oright__neutral, axiom,
    ((![A : set_msg]: ((sup_sup_set_msg @ A @ bot_bot_set_msg) = A)))). % sup_bot.right_neutral
thf(fact_208_sup__bot_Oright__neutral, axiom,
    ((![A : set_nat]: ((sup_sup_set_nat @ A @ bot_bot_set_nat) = A)))). % sup_bot.right_neutral
thf(fact_209_sup__bot_Oneutr__eq__iff, axiom,
    ((![A : set_msg, B : set_msg]: ((bot_bot_set_msg = (sup_sup_set_msg @ A @ B)) = (((A = bot_bot_set_msg)) & ((B = bot_bot_set_msg))))))). % sup_bot.neutr_eq_iff
thf(fact_210_sup__bot_Oneutr__eq__iff, axiom,
    ((![A : set_nat, B : set_nat]: ((bot_bot_set_nat = (sup_sup_set_nat @ A @ B)) = (((A = bot_bot_set_nat)) & ((B = bot_bot_set_nat))))))). % sup_bot.neutr_eq_iff
thf(fact_211_sup__bot_Oleft__neutral, axiom,
    ((![A : set_msg]: ((sup_sup_set_msg @ bot_bot_set_msg @ A) = A)))). % sup_bot.left_neutral
thf(fact_212_sup__bot_Oleft__neutral, axiom,
    ((![A : set_nat]: ((sup_sup_set_nat @ bot_bot_set_nat @ A) = A)))). % sup_bot.left_neutral
thf(fact_213_sup__bot_Oeq__neutr__iff, axiom,
    ((![A : set_msg, B : set_msg]: (((sup_sup_set_msg @ A @ B) = bot_bot_set_msg) = (((A = bot_bot_set_msg)) & ((B = bot_bot_set_msg))))))). % sup_bot.eq_neutr_iff
thf(fact_214_sup__bot_Oeq__neutr__iff, axiom,
    ((![A : set_nat, B : set_nat]: (((sup_sup_set_nat @ A @ B) = bot_bot_set_nat) = (((A = bot_bot_set_nat)) & ((B = bot_bot_set_nat))))))). % sup_bot.eq_neutr_iff
thf(fact_215_keysFor__Un, axiom,
    ((![H : set_msg, H2 : set_msg]: ((keysFor @ (sup_sup_set_msg @ H @ H2)) = (sup_sup_set_nat @ (keysFor @ H) @ (keysFor @ H2)))))). % keysFor_Un
thf(fact_216_sup__left__commute, axiom,
    ((![X3 : set_msg, Y3 : set_msg, Z2 : set_msg]: ((sup_sup_set_msg @ X3 @ (sup_sup_set_msg @ Y3 @ Z2)) = (sup_sup_set_msg @ Y3 @ (sup_sup_set_msg @ X3 @ Z2)))))). % sup_left_commute
thf(fact_217_sup__left__commute, axiom,
    ((![X3 : set_nat, Y3 : set_nat, Z2 : set_nat]: ((sup_sup_set_nat @ X3 @ (sup_sup_set_nat @ Y3 @ Z2)) = (sup_sup_set_nat @ Y3 @ (sup_sup_set_nat @ X3 @ Z2)))))). % sup_left_commute
thf(fact_218_sup_Oleft__commute, axiom,
    ((![B : set_msg, A : set_msg, C : set_msg]: ((sup_sup_set_msg @ B @ (sup_sup_set_msg @ A @ C)) = (sup_sup_set_msg @ A @ (sup_sup_set_msg @ B @ C)))))). % sup.left_commute
thf(fact_219_sup_Oleft__commute, axiom,
    ((![B : set_nat, A : set_nat, C : set_nat]: ((sup_sup_set_nat @ B @ (sup_sup_set_nat @ A @ C)) = (sup_sup_set_nat @ A @ (sup_sup_set_nat @ B @ C)))))). % sup.left_commute
thf(fact_220_sup__commute, axiom,
    ((sup_sup_set_msg = (^[X5 : set_msg]: (^[Y5 : set_msg]: (sup_sup_set_msg @ Y5 @ X5)))))). % sup_commute
thf(fact_221_sup__commute, axiom,
    ((sup_sup_set_nat = (^[X5 : set_nat]: (^[Y5 : set_nat]: (sup_sup_set_nat @ Y5 @ X5)))))). % sup_commute
thf(fact_222_sup_Ocommute, axiom,
    ((sup_sup_set_msg = (^[A4 : set_msg]: (^[B5 : set_msg]: (sup_sup_set_msg @ B5 @ A4)))))). % sup.commute
thf(fact_223_sup_Ocommute, axiom,
    ((sup_sup_set_nat = (^[A4 : set_nat]: (^[B5 : set_nat]: (sup_sup_set_nat @ B5 @ A4)))))). % sup.commute
thf(fact_224_sup__assoc, axiom,
    ((![X3 : set_msg, Y3 : set_msg, Z2 : set_msg]: ((sup_sup_set_msg @ (sup_sup_set_msg @ X3 @ Y3) @ Z2) = (sup_sup_set_msg @ X3 @ (sup_sup_set_msg @ Y3 @ Z2)))))). % sup_assoc
thf(fact_225_sup__assoc, axiom,
    ((![X3 : set_nat, Y3 : set_nat, Z2 : set_nat]: ((sup_sup_set_nat @ (sup_sup_set_nat @ X3 @ Y3) @ Z2) = (sup_sup_set_nat @ X3 @ (sup_sup_set_nat @ Y3 @ Z2)))))). % sup_assoc
thf(fact_226_sup_Oassoc, axiom,
    ((![A : set_msg, B : set_msg, C : set_msg]: ((sup_sup_set_msg @ (sup_sup_set_msg @ A @ B) @ C) = (sup_sup_set_msg @ A @ (sup_sup_set_msg @ B @ C)))))). % sup.assoc
thf(fact_227_sup_Oassoc, axiom,
    ((![A : set_nat, B : set_nat, C : set_nat]: ((sup_sup_set_nat @ (sup_sup_set_nat @ A @ B) @ C) = (sup_sup_set_nat @ A @ (sup_sup_set_nat @ B @ C)))))). % sup.assoc
thf(fact_228_boolean__algebra__cancel_Osup2, axiom,
    ((![B2 : set_msg, K2 : set_msg, B : set_msg, A : set_msg]: ((B2 = (sup_sup_set_msg @ K2 @ B)) => ((sup_sup_set_msg @ A @ B2) = (sup_sup_set_msg @ K2 @ (sup_sup_set_msg @ A @ B))))))). % boolean_algebra_cancel.sup2
thf(fact_229_boolean__algebra__cancel_Osup2, axiom,
    ((![B2 : set_nat, K2 : set_nat, B : set_nat, A : set_nat]: ((B2 = (sup_sup_set_nat @ K2 @ B)) => ((sup_sup_set_nat @ A @ B2) = (sup_sup_set_nat @ K2 @ (sup_sup_set_nat @ A @ B))))))). % boolean_algebra_cancel.sup2
thf(fact_230_boolean__algebra__cancel_Osup1, axiom,
    ((![A2 : set_msg, K2 : set_msg, A : set_msg, B : set_msg]: ((A2 = (sup_sup_set_msg @ K2 @ A)) => ((sup_sup_set_msg @ A2 @ B) = (sup_sup_set_msg @ K2 @ (sup_sup_set_msg @ A @ B))))))). % boolean_algebra_cancel.sup1
thf(fact_231_boolean__algebra__cancel_Osup1, axiom,
    ((![A2 : set_nat, K2 : set_nat, A : set_nat, B : set_nat]: ((A2 = (sup_sup_set_nat @ K2 @ A)) => ((sup_sup_set_nat @ A2 @ B) = (sup_sup_set_nat @ K2 @ (sup_sup_set_nat @ A @ B))))))). % boolean_algebra_cancel.sup1
thf(fact_232_inf__sup__aci_I5_J, axiom,
    ((sup_sup_set_msg = (^[X5 : set_msg]: (^[Y5 : set_msg]: (sup_sup_set_msg @ Y5 @ X5)))))). % inf_sup_aci(5)
thf(fact_233_inf__sup__aci_I5_J, axiom,
    ((sup_sup_set_nat = (^[X5 : set_nat]: (^[Y5 : set_nat]: (sup_sup_set_nat @ Y5 @ X5)))))). % inf_sup_aci(5)
thf(fact_234_inf__sup__aci_I6_J, axiom,
    ((![X3 : set_msg, Y3 : set_msg, Z2 : set_msg]: ((sup_sup_set_msg @ (sup_sup_set_msg @ X3 @ Y3) @ Z2) = (sup_sup_set_msg @ X3 @ (sup_sup_set_msg @ Y3 @ Z2)))))). % inf_sup_aci(6)
thf(fact_235_inf__sup__aci_I6_J, axiom,
    ((![X3 : set_nat, Y3 : set_nat, Z2 : set_nat]: ((sup_sup_set_nat @ (sup_sup_set_nat @ X3 @ Y3) @ Z2) = (sup_sup_set_nat @ X3 @ (sup_sup_set_nat @ Y3 @ Z2)))))). % inf_sup_aci(6)
thf(fact_236_inf__sup__aci_I7_J, axiom,
    ((![X3 : set_msg, Y3 : set_msg, Z2 : set_msg]: ((sup_sup_set_msg @ X3 @ (sup_sup_set_msg @ Y3 @ Z2)) = (sup_sup_set_msg @ Y3 @ (sup_sup_set_msg @ X3 @ Z2)))))). % inf_sup_aci(7)
thf(fact_237_inf__sup__aci_I7_J, axiom,
    ((![X3 : set_nat, Y3 : set_nat, Z2 : set_nat]: ((sup_sup_set_nat @ X3 @ (sup_sup_set_nat @ Y3 @ Z2)) = (sup_sup_set_nat @ Y3 @ (sup_sup_set_nat @ X3 @ Z2)))))). % inf_sup_aci(7)
thf(fact_238_inf__sup__aci_I8_J, axiom,
    ((![X3 : set_msg, Y3 : set_msg]: ((sup_sup_set_msg @ X3 @ (sup_sup_set_msg @ X3 @ Y3)) = (sup_sup_set_msg @ X3 @ Y3))))). % inf_sup_aci(8)
thf(fact_239_inf__sup__aci_I8_J, axiom,
    ((![X3 : set_nat, Y3 : set_nat]: ((sup_sup_set_nat @ X3 @ (sup_sup_set_nat @ X3 @ Y3)) = (sup_sup_set_nat @ X3 @ Y3))))). % inf_sup_aci(8)
thf(fact_240_bot__empty__eq, axiom,
    ((bot_bot_nat_o = (^[X5 : nat]: (member_nat @ X5 @ bot_bot_set_nat))))). % bot_empty_eq
thf(fact_241_keysFor__parts__insert, axiom,
    ((![K : nat, X : msg, G : set_msg, H : set_msg]: ((member_nat @ K @ (keysFor @ (parts @ (insert_msg @ X @ G)))) => ((member_msg @ X @ (synth @ (analz @ H))) => ((member_nat @ K @ (keysFor @ (parts @ (sup_sup_set_msg @ G @ H)))) | (member_msg @ (key @ (invKey @ K)) @ (parts @ H)))))))). % keysFor_parts_insert
thf(fact_242_analz__image__freshK__simps_I63_J, axiom,
    ((![C : msg, G : set_msg, A2 : set_msg]: ((member_msg @ C @ (analz @ G)) => (member_msg @ C @ (analz @ (sup_sup_set_msg @ A2 @ G))))))). % analz_image_freshK_simps(63)
thf(fact_243_invKey, axiom,
    ((![K : nat]: ((invKey @ (invKey @ K)) = K)))). % invKey
thf(fact_244_invKey__eq, axiom,
    ((![K : nat, K3 : nat]: (((invKey @ K) = (invKey @ K3)) = (K = K3))))). % invKey_eq
thf(fact_245_symKeys__invKey__iff, axiom,
    ((![K : nat]: ((member_nat @ (invKey @ K) @ symKeys) = (member_nat @ K @ symKeys))))). % symKeys_invKey_iff
thf(fact_246_invKey__K, axiom,
    ((![K : nat]: ((member_nat @ K @ symKeys) => ((invKey @ K) = K))))). % invKey_K
thf(fact_247_symKeys__neq__imp__neq, axiom,
    ((![K : nat, K3 : nat]: ((~ (((member_nat @ K @ symKeys) = (member_nat @ K3 @ symKeys)))) => (~ ((K = K3))))))). % symKeys_neq_imp_neq
thf(fact_248_keysFor__parts__initState, axiom,
    ((![C3 : agent]: ((keysFor @ (parts @ (initState @ C3))) = bot_bot_set_nat)))). % keysFor_parts_initState

% Conjectures (5)
thf(conj_0, hypothesis,
    ((member_nat @ k @ symKeys))).
thf(conj_1, hypothesis,
    ((member_list_event @ evsf @ nS_Sha1061662329shared))).
thf(conj_2, hypothesis,
    (((~ ((member_msg @ (key @ k) @ (used @ evsf)))) => (~ ((member_nat @ k @ (keysFor @ (parts @ (knows @ spy @ evsf))))))))).
thf(conj_3, hypothesis,
    ((member_msg @ x @ (synth @ (analz @ (knows @ spy @ evsf)))))).
thf(conj_4, conjecture,
    ((((member_msg @ (key @ k) @ (parts @ (insert_msg @ x @ bot_bot_set_msg))) | (member_msg @ (key @ k) @ (used @ evsf))) | (~ ((member_nat @ k @ (keysFor @ (parts @ (insert_msg @ x @ (knows @ spy @ evsf)))))))))).
