% 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_242__5229982_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:23:59.429

% 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 (51)
thf(sy_c_Event_Obad, type,
    bad : set_agent).
thf(sy_c_Event_OinitState, type,
    initState : agent > set_msg).
thf(sy_c_Event_Oknows, type,
    knows : agent > list_event > set_msg).
thf(sy_c_Event_Oused, type,
    used : list_event > set_msg).
thf(sy_c_Message_Oagent_OSpy, type,
    spy : agent).
thf(sy_c_Message_Oanalz, type,
    analz : set_msg > set_msg).
thf(sy_c_Message_OinvKey, type,
    invKey : nat > nat).
thf(sy_c_Message_OkeysFor, type,
    keysFor : set_msg > set_nat).
thf(sy_c_Message_Omsg_OAgent, type,
    agent2 : agent > msg).
thf(sy_c_Message_Omsg_OCrypt, type,
    crypt : nat > msg > msg).
thf(sy_c_Message_Omsg_OKey, type,
    key : nat > msg).
thf(sy_c_Message_Omsg_OMPair, type,
    mPair : msg > msg > msg).
thf(sy_c_Message_Oparts, type,
    parts : set_msg > set_msg).
thf(sy_c_Message_OsymKeys, type,
    symKeys : set_nat).
thf(sy_c_NS__Shared__Mirabelle__xwdrtqxrux_Ons__shared, type,
    nS_Sha1061662329shared : set_list_event).
thf(sy_c_Orderings_Otop__class_Otop_001_062_It__List__Olist_It__Event__Oevent_J_M_Eo_J, type,
    top_top_list_event_o : list_event > $o).
thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Message__Oagent_M_Eo_J, type,
    top_top_agent_o : agent > $o).
thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Message__Omsg_M_Eo_J, type,
    top_top_msg_o : msg > $o).
thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Nat__Onat_M_Eo_J, type,
    top_top_nat_o : nat > $o).
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__List__Olist_It__Event__Oevent_J_001t__Nat__Onat, type,
    image_list_event_nat : (list_event > nat) > set_list_event > set_nat).
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__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_evs, type,
    evs : 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_shrK__image__eq, axiom,
    ((![X : agent, AA : set_agent]: ((member_nat @ (shrK @ X) @ (image_agent_nat @ shrK @ AA)) = (member_agent @ X @ AA))))). % shrK_image_eq
thf(fact_2_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_3_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_4_image__insert, axiom,
    ((![F : msg > nat, A2 : msg, B : set_msg]: ((image_msg_nat @ F @ (insert_msg @ A2 @ B)) = (insert_nat @ (F @ A2) @ (image_msg_nat @ F @ B)))))). % image_insert
thf(fact_5_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_6_image__insert, axiom,
    ((![F : nat > nat, A2 : nat, B : set_nat]: ((image_nat_nat @ F @ (insert_nat @ A2 @ B)) = (insert_nat @ (F @ A2) @ (image_nat_nat @ F @ B)))))). % image_insert
thf(fact_7_image__insert, axiom,
    ((![F : msg > agent, A2 : msg, B : set_msg]: ((image_msg_agent @ F @ (insert_msg @ A2 @ B)) = (insert_agent @ (F @ A2) @ (image_msg_agent @ F @ B)))))). % image_insert
thf(fact_8_image__insert, axiom,
    ((![F : nat > agent, A2 : nat, B : set_nat]: ((image_nat_agent @ F @ (insert_nat @ A2 @ B)) = (insert_agent @ (F @ A2) @ (image_nat_agent @ F @ B)))))). % image_insert
thf(fact_9_image__insert, axiom,
    ((![F : agent > msg, A2 : agent, B : set_agent]: ((image_agent_msg @ F @ (insert_agent @ A2 @ B)) = (insert_msg @ (F @ A2) @ (image_agent_msg @ F @ B)))))). % image_insert
thf(fact_10_image__insert, axiom,
    ((![F : agent > agent, A2 : agent, B : set_agent]: ((image_agent_agent @ F @ (insert_agent @ A2 @ B)) = (insert_agent @ (F @ A2) @ (image_agent_agent @ F @ B)))))). % image_insert
thf(fact_11_image__insert, axiom,
    ((![F : list_event > msg, A2 : list_event, B : set_list_event]: ((image_list_event_msg @ F @ (insert_list_event @ A2 @ B)) = (insert_msg @ (F @ A2) @ (image_list_event_msg @ F @ B)))))). % image_insert
thf(fact_12_insert__image, axiom,
    ((![X : nat, A : set_nat, F : nat > msg]: ((member_nat @ X @ A) => ((insert_msg @ (F @ X) @ (image_nat_msg @ F @ A)) = (image_nat_msg @ F @ A)))))). % insert_image
thf(fact_13_insert__image, axiom,
    ((![X : nat, A : set_nat, F : nat > nat]: ((member_nat @ X @ A) => ((insert_nat @ (F @ X) @ (image_nat_nat @ F @ A)) = (image_nat_nat @ F @ A)))))). % insert_image
thf(fact_14_insert__image, axiom,
    ((![X : msg, A : set_msg, F : msg > msg]: ((member_msg @ X @ A) => ((insert_msg @ (F @ X) @ (image_msg_msg @ F @ A)) = (image_msg_msg @ F @ A)))))). % insert_image
thf(fact_15_insert__image, axiom,
    ((![X : msg, A : set_msg, F : msg > nat]: ((member_msg @ X @ A) => ((insert_nat @ (F @ X) @ (image_msg_nat @ F @ A)) = (image_msg_nat @ F @ A)))))). % insert_image
thf(fact_16_insert__image, axiom,
    ((![X : agent, A : set_agent, F : agent > msg]: ((member_agent @ X @ A) => ((insert_msg @ (F @ X) @ (image_agent_msg @ F @ A)) = (image_agent_msg @ F @ A)))))). % insert_image
thf(fact_17_insert__image, axiom,
    ((![X : agent, A : set_agent, F : agent > nat]: ((member_agent @ X @ A) => ((insert_nat @ (F @ X) @ (image_agent_nat @ F @ A)) = (image_agent_nat @ F @ A)))))). % insert_image
thf(fact_18_insert__image, axiom,
    ((![X : list_event, A : set_list_event, F : list_event > msg]: ((member_list_event @ X @ A) => ((insert_msg @ (F @ X) @ (image_list_event_msg @ F @ A)) = (image_list_event_msg @ F @ A)))))). % insert_image
thf(fact_19_insert__image, axiom,
    ((![X : list_event, A : set_list_event, F : list_event > nat]: ((member_list_event @ X @ A) => ((insert_nat @ (F @ X) @ (image_list_event_nat @ F @ A)) = (image_list_event_nat @ F @ A)))))). % insert_image
thf(fact_20_insert__image, axiom,
    ((![X : nat, A : set_nat, F : nat > agent]: ((member_nat @ X @ A) => ((insert_agent @ (F @ X) @ (image_nat_agent @ F @ A)) = (image_nat_agent @ F @ A)))))). % insert_image
thf(fact_21_insert__image, axiom,
    ((![X : msg, A : set_msg, F : msg > agent]: ((member_msg @ X @ A) => ((insert_agent @ (F @ X) @ (image_msg_agent @ F @ A)) = (image_msg_agent @ F @ A)))))). % insert_image
thf(fact_22_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_23_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_24_shrK__injective, axiom,
    ((![X : agent, Y2 : agent]: (((shrK @ X) = (shrK @ Y2)) = (X = Y2))))). % shrK_injective
thf(fact_25_msg_Oinject_I4_J, axiom,
    ((![X4 : nat, Y4 : nat]: (((key @ X4) = (key @ Y4)) = (X4 = Y4))))). % msg.inject(4)
thf(fact_26_analz__idem, axiom,
    ((![H : set_msg]: ((analz @ (analz @ H)) = (analz @ H))))). % analz_idem
thf(fact_27_UNIV__I, axiom,
    ((![X : list_event]: (member_list_event @ X @ top_to1178833912_event)))). % UNIV_I
thf(fact_28_UNIV__I, axiom,
    ((![X : nat]: (member_nat @ X @ top_top_set_nat)))). % UNIV_I
thf(fact_29_UNIV__I, axiom,
    ((![X : msg]: (member_msg @ X @ top_top_set_msg)))). % UNIV_I
thf(fact_30_UNIV__I, axiom,
    ((![X : agent]: (member_agent @ X @ top_top_set_agent)))). % UNIV_I
thf(fact_31_iso__tuple__UNIV__I, axiom,
    ((![X : agent]: (member_agent @ X @ top_top_set_agent)))). % iso_tuple_UNIV_I
thf(fact_32_iso__tuple__UNIV__I, axiom,
    ((![X : msg]: (member_msg @ X @ top_top_set_msg)))). % iso_tuple_UNIV_I
thf(fact_33_iso__tuple__UNIV__I, axiom,
    ((![X : nat]: (member_nat @ X @ top_top_set_nat)))). % iso_tuple_UNIV_I
thf(fact_34_iso__tuple__UNIV__I, axiom,
    ((![X : list_event]: (member_list_event @ X @ top_to1178833912_event)))). % iso_tuple_UNIV_I
thf(fact_35_image__eqI, axiom,
    ((![B2 : nat, F : nat > nat, X : nat, A : set_nat]: ((B2 = (F @ X)) => ((member_nat @ X @ A) => (member_nat @ B2 @ (image_nat_nat @ F @ A))))))). % image_eqI
thf(fact_36_image__eqI, axiom,
    ((![B2 : msg, F : nat > msg, X : nat, A : set_nat]: ((B2 = (F @ X)) => ((member_nat @ X @ A) => (member_msg @ B2 @ (image_nat_msg @ F @ A))))))). % image_eqI
thf(fact_37_image__eqI, axiom,
    ((![B2 : agent, F : nat > agent, X : nat, A : set_nat]: ((B2 = (F @ X)) => ((member_nat @ X @ A) => (member_agent @ B2 @ (image_nat_agent @ F @ A))))))). % image_eqI
thf(fact_38_image__eqI, axiom,
    ((![B2 : nat, F : msg > nat, X : msg, A : set_msg]: ((B2 = (F @ X)) => ((member_msg @ X @ A) => (member_nat @ B2 @ (image_msg_nat @ F @ A))))))). % image_eqI
thf(fact_39_image__eqI, axiom,
    ((![B2 : msg, F : msg > msg, X : msg, A : set_msg]: ((B2 = (F @ X)) => ((member_msg @ X @ A) => (member_msg @ B2 @ (image_msg_msg @ F @ A))))))). % image_eqI
thf(fact_40_image__eqI, axiom,
    ((![B2 : agent, F : msg > agent, X : msg, A : set_msg]: ((B2 = (F @ X)) => ((member_msg @ X @ A) => (member_agent @ B2 @ (image_msg_agent @ F @ A))))))). % image_eqI
thf(fact_41_image__eqI, axiom,
    ((![B2 : nat, F : agent > nat, X : agent, A : set_agent]: ((B2 = (F @ X)) => ((member_agent @ X @ A) => (member_nat @ B2 @ (image_agent_nat @ F @ A))))))). % image_eqI
thf(fact_42_image__eqI, axiom,
    ((![B2 : msg, F : agent > msg, X : agent, A : set_agent]: ((B2 = (F @ X)) => ((member_agent @ X @ A) => (member_msg @ B2 @ (image_agent_msg @ F @ A))))))). % image_eqI
thf(fact_43_image__eqI, axiom,
    ((![B2 : agent, F : agent > agent, X : agent, A : set_agent]: ((B2 = (F @ X)) => ((member_agent @ X @ A) => (member_agent @ B2 @ (image_agent_agent @ F @ A))))))). % image_eqI
thf(fact_44_image__eqI, axiom,
    ((![B2 : nat, F : list_event > nat, X : list_event, A : set_list_event]: ((B2 = (F @ X)) => ((member_list_event @ X @ A) => (member_nat @ B2 @ (image_list_event_nat @ F @ A))))))). % image_eqI
thf(fact_45_insert__absorb2, axiom,
    ((![X : msg, A : set_msg]: ((insert_msg @ X @ (insert_msg @ X @ A)) = (insert_msg @ X @ A))))). % insert_absorb2
thf(fact_46_insert__absorb2, axiom,
    ((![X : nat, A : set_nat]: ((insert_nat @ X @ (insert_nat @ X @ A)) = (insert_nat @ X @ A))))). % insert_absorb2
thf(fact_47_insert__absorb2, axiom,
    ((![X : agent, A : set_agent]: ((insert_agent @ X @ (insert_agent @ X @ A)) = (insert_agent @ X @ A))))). % insert_absorb2
thf(fact_48_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_49_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_50_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_51_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_52_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_53_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_54_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_55_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_56_Key__image__eq, axiom,
    ((![X : nat, A : set_nat]: ((member_msg @ (key @ X) @ (image_nat_msg @ key @ A)) = (member_nat @ X @ A))))). % Key_image_eq
thf(fact_57_analz__image__Key, axiom,
    ((![N : set_nat]: ((analz @ (image_nat_msg @ key @ N)) = (image_nat_msg @ key @ N))))). % analz_image_Key
thf(fact_58_Spy__in__bad, axiom,
    ((member_agent @ spy @ bad))). % Spy_in_bad
thf(fact_59_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_60_top__set__def, axiom,
    ((top_top_set_agent = (collect_agent @ top_top_agent_o)))). % top_set_def
thf(fact_61_top__set__def, axiom,
    ((top_top_set_msg = (collect_msg @ top_top_msg_o)))). % top_set_def
thf(fact_62_top__set__def, axiom,
    ((top_top_set_nat = (collect_nat @ top_top_nat_o)))). % top_set_def
thf(fact_63_top__set__def, axiom,
    ((top_to1178833912_event = (collect_list_event @ top_top_list_event_o)))). % top_set_def
thf(fact_64_rev__image__eqI, axiom,
    ((![X : nat, A : set_nat, B2 : nat, F : nat > nat]: ((member_nat @ X @ A) => ((B2 = (F @ X)) => (member_nat @ B2 @ (image_nat_nat @ F @ A))))))). % rev_image_eqI
thf(fact_65_rev__image__eqI, axiom,
    ((![X : nat, A : set_nat, B2 : msg, F : nat > msg]: ((member_nat @ X @ A) => ((B2 = (F @ X)) => (member_msg @ B2 @ (image_nat_msg @ F @ A))))))). % rev_image_eqI
thf(fact_66_rev__image__eqI, axiom,
    ((![X : nat, A : set_nat, B2 : agent, F : nat > agent]: ((member_nat @ X @ A) => ((B2 = (F @ X)) => (member_agent @ B2 @ (image_nat_agent @ F @ A))))))). % rev_image_eqI
thf(fact_67_rev__image__eqI, axiom,
    ((![X : msg, A : set_msg, B2 : nat, F : msg > nat]: ((member_msg @ X @ A) => ((B2 = (F @ X)) => (member_nat @ B2 @ (image_msg_nat @ F @ A))))))). % rev_image_eqI
thf(fact_68_rev__image__eqI, axiom,
    ((![X : msg, A : set_msg, B2 : msg, F : msg > msg]: ((member_msg @ X @ A) => ((B2 = (F @ X)) => (member_msg @ B2 @ (image_msg_msg @ F @ A))))))). % rev_image_eqI
thf(fact_69_rev__image__eqI, axiom,
    ((![X : msg, A : set_msg, B2 : agent, F : msg > agent]: ((member_msg @ X @ A) => ((B2 = (F @ X)) => (member_agent @ B2 @ (image_msg_agent @ F @ A))))))). % rev_image_eqI
thf(fact_70_rev__image__eqI, axiom,
    ((![X : agent, A : set_agent, B2 : nat, F : agent > nat]: ((member_agent @ X @ A) => ((B2 = (F @ X)) => (member_nat @ B2 @ (image_agent_nat @ F @ A))))))). % rev_image_eqI
thf(fact_71_rev__image__eqI, axiom,
    ((![X : agent, A : set_agent, B2 : msg, F : agent > msg]: ((member_agent @ X @ A) => ((B2 = (F @ X)) => (member_msg @ B2 @ (image_agent_msg @ F @ A))))))). % rev_image_eqI
thf(fact_72_rev__image__eqI, axiom,
    ((![X : agent, A : set_agent, B2 : agent, F : agent > agent]: ((member_agent @ X @ A) => ((B2 = (F @ X)) => (member_agent @ B2 @ (image_agent_agent @ F @ A))))))). % rev_image_eqI
thf(fact_73_rev__image__eqI, axiom,
    ((![X : list_event, A : set_list_event, B2 : nat, F : list_event > nat]: ((member_list_event @ X @ A) => ((B2 = (F @ X)) => (member_nat @ B2 @ (image_list_event_nat @ F @ A))))))). % rev_image_eqI
thf(fact_74_ball__imageD, axiom,
    ((![F : agent > nat, A : set_agent, P : nat > $o]: ((![X2 : nat]: ((member_nat @ X2 @ (image_agent_nat @ F @ A)) => (P @ X2))) => (![X3 : agent]: ((member_agent @ X3 @ A) => (P @ (F @ X3)))))))). % ball_imageD
thf(fact_75_ball__imageD, axiom,
    ((![F : nat > msg, A : set_nat, P : msg > $o]: ((![X2 : msg]: ((member_msg @ X2 @ (image_nat_msg @ F @ A)) => (P @ X2))) => (![X3 : nat]: ((member_nat @ X3 @ A) => (P @ (F @ X3)))))))). % ball_imageD
thf(fact_76_ball__imageD, axiom,
    ((![F : nat > nat, A : set_nat, P : nat > $o]: ((![X2 : nat]: ((member_nat @ X2 @ (image_nat_nat @ F @ A)) => (P @ X2))) => (![X3 : nat]: ((member_nat @ X3 @ A) => (P @ (F @ X3)))))))). % ball_imageD
thf(fact_77_ball__imageD, axiom,
    ((![F : msg > nat, A : set_msg, P : nat > $o]: ((![X2 : nat]: ((member_nat @ X2 @ (image_msg_nat @ F @ A)) => (P @ X2))) => (![X3 : msg]: ((member_msg @ X3 @ A) => (P @ (F @ X3)))))))). % ball_imageD
thf(fact_78_ball__imageD, axiom,
    ((![F : msg > msg, A : set_msg, P : msg > $o]: ((![X2 : msg]: ((member_msg @ X2 @ (image_msg_msg @ F @ A)) => (P @ X2))) => (![X3 : msg]: ((member_msg @ X3 @ A) => (P @ (F @ X3)))))))). % ball_imageD
thf(fact_79_ball__imageD, axiom,
    ((![F : agent > msg, A : set_agent, P : msg > $o]: ((![X2 : msg]: ((member_msg @ X2 @ (image_agent_msg @ F @ A)) => (P @ X2))) => (![X3 : agent]: ((member_agent @ X3 @ A) => (P @ (F @ X3)))))))). % ball_imageD
thf(fact_80_ball__imageD, axiom,
    ((![F : list_event > nat, A : set_list_event, P : nat > $o]: ((![X2 : nat]: ((member_nat @ X2 @ (image_list_event_nat @ F @ A)) => (P @ X2))) => (![X3 : list_event]: ((member_list_event @ X3 @ A) => (P @ (F @ X3)))))))). % ball_imageD
thf(fact_81_ball__imageD, axiom,
    ((![F : list_event > msg, A : set_list_event, P : msg > $o]: ((![X2 : msg]: ((member_msg @ X2 @ (image_list_event_msg @ F @ A)) => (P @ X2))) => (![X3 : list_event]: ((member_list_event @ X3 @ A) => (P @ (F @ X3)))))))). % ball_imageD
thf(fact_82_image__cong, axiom,
    ((![M : set_list_event, N : set_list_event, F : list_event > nat, G : list_event > nat]: ((M = N) => ((![X2 : list_event]: ((member_list_event @ X2 @ N) => ((F @ X2) = (G @ X2)))) => ((image_list_event_nat @ F @ M) = (image_list_event_nat @ G @ N))))))). % image_cong
thf(fact_83_image__cong, axiom,
    ((![M : set_list_event, N : set_list_event, F : list_event > msg, G : list_event > msg]: ((M = N) => ((![X2 : list_event]: ((member_list_event @ X2 @ N) => ((F @ X2) = (G @ X2)))) => ((image_list_event_msg @ F @ M) = (image_list_event_msg @ G @ N))))))). % image_cong
thf(fact_84_image__cong, axiom,
    ((![M : set_nat, N : set_nat, F : nat > msg, G : nat > msg]: ((M = N) => ((![X2 : nat]: ((member_nat @ X2 @ N) => ((F @ X2) = (G @ X2)))) => ((image_nat_msg @ F @ M) = (image_nat_msg @ G @ N))))))). % image_cong
thf(fact_85_image__cong, axiom,
    ((![M : set_nat, N : set_nat, F : nat > nat, G : nat > nat]: ((M = N) => ((![X2 : nat]: ((member_nat @ X2 @ N) => ((F @ X2) = (G @ X2)))) => ((image_nat_nat @ F @ M) = (image_nat_nat @ G @ N))))))). % image_cong
thf(fact_86_image__cong, axiom,
    ((![M : set_msg, N : set_msg, F : msg > nat, G : msg > nat]: ((M = N) => ((![X2 : msg]: ((member_msg @ X2 @ N) => ((F @ X2) = (G @ X2)))) => ((image_msg_nat @ F @ M) = (image_msg_nat @ G @ N))))))). % image_cong
thf(fact_87_image__cong, axiom,
    ((![M : set_msg, N : set_msg, F : msg > msg, G : msg > msg]: ((M = N) => ((![X2 : msg]: ((member_msg @ X2 @ N) => ((F @ X2) = (G @ X2)))) => ((image_msg_msg @ F @ M) = (image_msg_msg @ G @ N))))))). % image_cong
thf(fact_88_image__cong, axiom,
    ((![M : set_agent, N : set_agent, F : agent > nat, G : agent > nat]: ((M = N) => ((![X2 : agent]: ((member_agent @ X2 @ N) => ((F @ X2) = (G @ X2)))) => ((image_agent_nat @ F @ M) = (image_agent_nat @ G @ N))))))). % image_cong
thf(fact_89_image__cong, axiom,
    ((![M : set_agent, N : set_agent, F : agent > msg, G : agent > msg]: ((M = N) => ((![X2 : agent]: ((member_agent @ X2 @ N) => ((F @ X2) = (G @ X2)))) => ((image_agent_msg @ F @ M) = (image_agent_msg @ G @ N))))))). % image_cong
thf(fact_90_bex__imageD, axiom,
    ((![F : agent > nat, A : set_agent, P : nat > $o]: ((?[X3 : nat]: ((member_nat @ X3 @ (image_agent_nat @ F @ A)) & (P @ X3))) => (?[X2 : agent]: ((member_agent @ X2 @ A) & (P @ (F @ X2)))))))). % bex_imageD
thf(fact_91_bex__imageD, axiom,
    ((![F : nat > msg, A : set_nat, P : msg > $o]: ((?[X3 : msg]: ((member_msg @ X3 @ (image_nat_msg @ F @ A)) & (P @ X3))) => (?[X2 : nat]: ((member_nat @ X2 @ A) & (P @ (F @ X2)))))))). % bex_imageD
thf(fact_92_bex__imageD, axiom,
    ((![F : nat > nat, A : set_nat, P : nat > $o]: ((?[X3 : nat]: ((member_nat @ X3 @ (image_nat_nat @ F @ A)) & (P @ X3))) => (?[X2 : nat]: ((member_nat @ X2 @ A) & (P @ (F @ X2)))))))). % bex_imageD
thf(fact_93_bex__imageD, axiom,
    ((![F : msg > nat, A : set_msg, P : nat > $o]: ((?[X3 : nat]: ((member_nat @ X3 @ (image_msg_nat @ F @ A)) & (P @ X3))) => (?[X2 : msg]: ((member_msg @ X2 @ A) & (P @ (F @ X2)))))))). % bex_imageD
thf(fact_94_bex__imageD, axiom,
    ((![F : msg > msg, A : set_msg, P : msg > $o]: ((?[X3 : msg]: ((member_msg @ X3 @ (image_msg_msg @ F @ A)) & (P @ X3))) => (?[X2 : msg]: ((member_msg @ X2 @ A) & (P @ (F @ X2)))))))). % bex_imageD
thf(fact_95_bex__imageD, axiom,
    ((![F : agent > msg, A : set_agent, P : msg > $o]: ((?[X3 : msg]: ((member_msg @ X3 @ (image_agent_msg @ F @ A)) & (P @ X3))) => (?[X2 : agent]: ((member_agent @ X2 @ A) & (P @ (F @ X2)))))))). % bex_imageD
thf(fact_96_bex__imageD, axiom,
    ((![F : list_event > nat, A : set_list_event, P : nat > $o]: ((?[X3 : nat]: ((member_nat @ X3 @ (image_list_event_nat @ F @ A)) & (P @ X3))) => (?[X2 : list_event]: ((member_list_event @ X2 @ A) & (P @ (F @ X2)))))))). % bex_imageD
thf(fact_97_bex__imageD, axiom,
    ((![F : list_event > msg, A : set_list_event, P : msg > $o]: ((?[X3 : msg]: ((member_msg @ X3 @ (image_list_event_msg @ F @ A)) & (P @ X3))) => (?[X2 : list_event]: ((member_list_event @ X2 @ A) & (P @ (F @ X2)))))))). % bex_imageD
thf(fact_98_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_99_image__iff, axiom,
    ((![Z : nat, F : nat > nat, A : set_nat]: ((member_nat @ Z @ (image_nat_nat @ F @ A)) = (?[X5 : nat]: (((member_nat @ X5 @ A)) & ((Z = (F @ X5))))))))). % image_iff
thf(fact_100_image__iff, axiom,
    ((![Z : nat, F : msg > nat, A : set_msg]: ((member_nat @ Z @ (image_msg_nat @ F @ A)) = (?[X5 : msg]: (((member_msg @ X5 @ A)) & ((Z = (F @ X5))))))))). % image_iff
thf(fact_101_image__iff, axiom,
    ((![Z : nat, F : list_event > nat, A : set_list_event]: ((member_nat @ Z @ (image_list_event_nat @ F @ A)) = (?[X5 : list_event]: (((member_list_event @ X5 @ A)) & ((Z = (F @ X5))))))))). % image_iff
thf(fact_102_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_103_image__iff, axiom,
    ((![Z : msg, F : msg > msg, A : set_msg]: ((member_msg @ Z @ (image_msg_msg @ F @ A)) = (?[X5 : msg]: (((member_msg @ X5 @ A)) & ((Z = (F @ X5))))))))). % image_iff
thf(fact_104_image__iff, axiom,
    ((![Z : msg, F : agent > msg, A : set_agent]: ((member_msg @ Z @ (image_agent_msg @ F @ A)) = (?[X5 : agent]: (((member_agent @ X5 @ A)) & ((Z = (F @ X5))))))))). % image_iff
thf(fact_105_image__iff, axiom,
    ((![Z : msg, F : list_event > msg, A : set_list_event]: ((member_msg @ Z @ (image_list_event_msg @ F @ A)) = (?[X5 : list_event]: (((member_list_event @ X5 @ A)) & ((Z = (F @ X5))))))))). % image_iff
thf(fact_106_imageI, axiom,
    ((![X : nat, A : set_nat, F : nat > nat]: ((member_nat @ X @ A) => (member_nat @ (F @ X) @ (image_nat_nat @ F @ A)))))). % imageI
thf(fact_107_imageI, axiom,
    ((![X : nat, A : set_nat, F : nat > msg]: ((member_nat @ X @ A) => (member_msg @ (F @ X) @ (image_nat_msg @ F @ A)))))). % imageI
thf(fact_108_imageI, axiom,
    ((![X : nat, A : set_nat, F : nat > agent]: ((member_nat @ X @ A) => (member_agent @ (F @ X) @ (image_nat_agent @ F @ A)))))). % imageI
thf(fact_109_imageI, axiom,
    ((![X : msg, A : set_msg, F : msg > nat]: ((member_msg @ X @ A) => (member_nat @ (F @ X) @ (image_msg_nat @ F @ A)))))). % imageI
thf(fact_110_imageI, axiom,
    ((![X : msg, A : set_msg, F : msg > msg]: ((member_msg @ X @ A) => (member_msg @ (F @ X) @ (image_msg_msg @ F @ A)))))). % imageI
thf(fact_111_imageI, axiom,
    ((![X : msg, A : set_msg, F : msg > agent]: ((member_msg @ X @ A) => (member_agent @ (F @ X) @ (image_msg_agent @ F @ A)))))). % imageI
thf(fact_112_imageI, axiom,
    ((![X : agent, A : set_agent, F : agent > nat]: ((member_agent @ X @ A) => (member_nat @ (F @ X) @ (image_agent_nat @ F @ A)))))). % imageI
thf(fact_113_imageI, axiom,
    ((![X : agent, A : set_agent, F : agent > msg]: ((member_agent @ X @ A) => (member_msg @ (F @ X) @ (image_agent_msg @ F @ A)))))). % imageI
thf(fact_114_imageI, axiom,
    ((![X : agent, A : set_agent, F : agent > agent]: ((member_agent @ X @ A) => (member_agent @ (F @ X) @ (image_agent_agent @ F @ A)))))). % imageI
thf(fact_115_imageI, axiom,
    ((![X : list_event, A : set_list_event, F : list_event > nat]: ((member_list_event @ X @ A) => (member_nat @ (F @ X) @ (image_list_event_nat @ F @ A)))))). % imageI
thf(fact_116_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_117_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_118_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_119_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_120_insert__commute, axiom,
    ((![X : msg, Y2 : msg, A : set_msg]: ((insert_msg @ X @ (insert_msg @ Y2 @ A)) = (insert_msg @ Y2 @ (insert_msg @ X @ A)))))). % insert_commute
thf(fact_121_insert__commute, axiom,
    ((![X : nat, Y2 : nat, A : set_nat]: ((insert_nat @ X @ (insert_nat @ Y2 @ A)) = (insert_nat @ Y2 @ (insert_nat @ X @ A)))))). % insert_commute
thf(fact_122_insert__commute, axiom,
    ((![X : agent, Y2 : agent, A : set_agent]: ((insert_agent @ X @ (insert_agent @ Y2 @ A)) = (insert_agent @ Y2 @ (insert_agent @ X @ A)))))). % insert_commute
thf(fact_123_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)))) => ((?[C : set_list_event]: (((A = (insert_list_event @ B2 @ C))) & ((((~ ((member_list_event @ B2 @ C)))) & ((((B = (insert_list_event @ A2 @ C))) & ((~ ((member_list_event @ A2 @ C)))))))))))))))))))). % insert_eq_iff
thf(fact_124_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)))) => ((?[C : set_nat]: (((A = (insert_nat @ B2 @ C))) & ((((~ ((member_nat @ B2 @ C)))) & ((((B = (insert_nat @ A2 @ C))) & ((~ ((member_nat @ A2 @ C)))))))))))))))))))). % insert_eq_iff
thf(fact_125_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)))) => ((?[C : set_msg]: (((A = (insert_msg @ B2 @ C))) & ((((~ ((member_msg @ B2 @ C)))) & ((((B = (insert_msg @ A2 @ C))) & ((~ ((member_msg @ A2 @ C)))))))))))))))))))). % insert_eq_iff
thf(fact_126_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)))) => ((?[C : set_agent]: (((A = (insert_agent @ B2 @ C))) & ((((~ ((member_agent @ B2 @ C)))) & ((((B = (insert_agent @ A2 @ C))) & ((~ ((member_agent @ A2 @ C)))))))))))))))))))). % insert_eq_iff
thf(fact_127_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_128_insert__absorb, axiom,
    ((![A2 : nat, A : set_nat]: ((member_nat @ A2 @ A) => ((insert_nat @ A2 @ A) = A))))). % insert_absorb
thf(fact_129_insert__absorb, axiom,
    ((![A2 : msg, A : set_msg]: ((member_msg @ A2 @ A) => ((insert_msg @ A2 @ A) = A))))). % insert_absorb
thf(fact_130_insert__absorb, axiom,
    ((![A2 : agent, A : set_agent]: ((member_agent @ A2 @ A) => ((insert_agent @ A2 @ A) = A))))). % insert_absorb
thf(fact_131_insert__ident, axiom,
    ((![X : list_event, A : set_list_event, B : set_list_event]: ((~ ((member_list_event @ X @ A))) => ((~ ((member_list_event @ X @ B))) => (((insert_list_event @ X @ A) = (insert_list_event @ X @ B)) = (A = B))))))). % insert_ident
thf(fact_132_insert__ident, axiom,
    ((![X : nat, A : set_nat, B : set_nat]: ((~ ((member_nat @ X @ A))) => ((~ ((member_nat @ X @ B))) => (((insert_nat @ X @ A) = (insert_nat @ X @ B)) = (A = B))))))). % insert_ident
thf(fact_133_insert__ident, axiom,
    ((![X : msg, A : set_msg, B : set_msg]: ((~ ((member_msg @ X @ A))) => ((~ ((member_msg @ X @ B))) => (((insert_msg @ X @ A) = (insert_msg @ X @ B)) = (A = B))))))). % insert_ident
thf(fact_134_insert__ident, axiom,
    ((![X : agent, A : set_agent, B : set_agent]: ((~ ((member_agent @ X @ A))) => ((~ ((member_agent @ X @ B))) => (((insert_agent @ X @ A) = (insert_agent @ X @ B)) = (A = B))))))). % insert_ident
thf(fact_135_Set_Oset__insert, axiom,
    ((![X : list_event, A : set_list_event]: ((member_list_event @ X @ A) => (~ ((![B3 : set_list_event]: ((A = (insert_list_event @ X @ B3)) => (member_list_event @ X @ B3))))))))). % Set.set_insert
thf(fact_136_Set_Oset__insert, axiom,
    ((![X : nat, A : set_nat]: ((member_nat @ X @ A) => (~ ((![B3 : set_nat]: ((A = (insert_nat @ X @ B3)) => (member_nat @ X @ B3))))))))). % Set.set_insert
thf(fact_137_Set_Oset__insert, axiom,
    ((![X : msg, A : set_msg]: ((member_msg @ X @ A) => (~ ((![B3 : set_msg]: ((A = (insert_msg @ X @ B3)) => (member_msg @ X @ B3))))))))). % Set.set_insert
thf(fact_138_Set_Oset__insert, axiom,
    ((![X : agent, A : set_agent]: ((member_agent @ X @ A) => (~ ((![B3 : set_agent]: ((A = (insert_agent @ X @ B3)) => (member_agent @ X @ B3))))))))). % Set.set_insert
thf(fact_139_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_140_insertI2, axiom,
    ((![A2 : nat, B : set_nat, B2 : nat]: ((member_nat @ A2 @ B) => (member_nat @ A2 @ (insert_nat @ B2 @ B)))))). % insertI2
thf(fact_141_insertI2, axiom,
    ((![A2 : msg, B : set_msg, B2 : msg]: ((member_msg @ A2 @ B) => (member_msg @ A2 @ (insert_msg @ B2 @ B)))))). % insertI2
thf(fact_142_insertI2, axiom,
    ((![A2 : agent, B : set_agent, B2 : agent]: ((member_agent @ A2 @ B) => (member_agent @ A2 @ (insert_agent @ B2 @ B)))))). % insertI2
thf(fact_143_insertI1, axiom,
    ((![A2 : list_event, B : set_list_event]: (member_list_event @ A2 @ (insert_list_event @ A2 @ B))))). % insertI1
thf(fact_144_insertI1, axiom,
    ((![A2 : nat, B : set_nat]: (member_nat @ A2 @ (insert_nat @ A2 @ B))))). % insertI1
thf(fact_145_insertI1, axiom,
    ((![A2 : msg, B : set_msg]: (member_msg @ A2 @ (insert_msg @ A2 @ B))))). % insertI1
thf(fact_146_insertI1, axiom,
    ((![A2 : agent, B : set_agent]: (member_agent @ A2 @ (insert_agent @ A2 @ B))))). % insertI1
thf(fact_147_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_148_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_149_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_150_analz__analzD, axiom,
    ((![X6 : msg, H : set_msg]: ((member_msg @ X6 @ (analz @ (analz @ H))) => (member_msg @ X6 @ (analz @ H)))))). % analz_analzD
thf(fact_151_analz_OInj, axiom,
    ((![X6 : msg, H : set_msg]: ((member_msg @ X6 @ H) => (member_msg @ X6 @ (analz @ H)))))). % analz.Inj
thf(fact_152_analz__insert__eq__I, axiom,
    ((![X6 : msg, H : set_msg]: ((![X2 : msg]: ((member_msg @ X2 @ (analz @ (insert_msg @ X6 @ H))) => (member_msg @ X2 @ (insert_msg @ X6 @ (analz @ H))))) => ((analz @ (insert_msg @ X6 @ H)) = (insert_msg @ X6 @ (analz @ H))))))). % analz_insert_eq_I
thf(fact_153_analz__insert__cong, axiom,
    ((![H : set_msg, H2 : set_msg, X6 : msg]: (((analz @ H) = (analz @ H2)) => ((analz @ (insert_msg @ X6 @ H)) = (analz @ (insert_msg @ X6 @ H2))))))). % analz_insert_cong
thf(fact_154_analz__insert__eq, axiom,
    ((![X6 : msg, H : set_msg]: ((member_msg @ X6 @ (analz @ H)) => ((analz @ (insert_msg @ X6 @ H)) = (analz @ H)))))). % analz_insert_eq
thf(fact_155_analz__insertI, axiom,
    ((![C2 : msg, G2 : set_msg, A2 : msg]: ((member_msg @ C2 @ (analz @ G2)) => (member_msg @ C2 @ (analz @ (insert_msg @ A2 @ G2))))))). % analz_insertI
thf(fact_156_analz__cut, axiom,
    ((![Y : msg, X6 : msg, H : set_msg]: ((member_msg @ Y @ (analz @ (insert_msg @ X6 @ H))) => ((member_msg @ X6 @ (analz @ H)) => (member_msg @ Y @ (analz @ H))))))). % analz_cut
thf(fact_157_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_158_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_159_Crypt__Spy__analz__bad, axiom,
    ((![A : agent, X6 : msg, Evs : list_event]: ((member_msg @ (crypt @ (shrK @ A) @ X6) @ (analz @ (knows @ spy @ Evs))) => ((member_agent @ A @ bad) => (member_msg @ X6 @ (analz @ (knows @ spy @ Evs)))))))). % Crypt_Spy_analz_bad
thf(fact_160_Key__not__used, axiom,
    ((![K : nat, Evs : list_event]: ((~ ((member_msg @ (key @ K) @ (used @ Evs)))) => (~ ((member_nat @ K @ (image_agent_nat @ shrK @ top_top_set_agent)))))))). % Key_not_used
thf(fact_161_shrK__in__initState, axiom,
    ((![A : agent]: (member_msg @ (key @ (shrK @ A)) @ (initState @ A))))). % shrK_in_initState
thf(fact_162_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_163_parts__idem, axiom,
    ((![H : set_msg]: ((parts @ (parts @ H)) = (parts @ H))))). % parts_idem
thf(fact_164_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_165_publicKey__inject, axiom,
    ((![B2 : keymode, A : agent, C2 : keymode, A3 : agent]: (((publicKey @ B2 @ A) = (publicKey @ C2 @ A3)) = (((B2 = C2)) & ((A = A3))))))). % publicKey_inject
thf(fact_166_analz__parts, axiom,
    ((![H : set_msg]: ((analz @ (parts @ H)) = (parts @ H))))). % analz_parts
thf(fact_167_parts__analz, axiom,
    ((![H : set_msg]: ((parts @ (analz @ H)) = (parts @ H))))). % parts_analz
thf(fact_168_analz__conj__parts, axiom,
    ((![X6 : msg, H : set_msg]: ((((member_msg @ X6 @ (analz @ H))) & ((member_msg @ X6 @ (parts @ H)))) = (member_msg @ X6 @ (analz @ H)))))). % analz_conj_parts
thf(fact_169_analz__disj__parts, axiom,
    ((![X6 : msg, H : set_msg]: ((((member_msg @ X6 @ (analz @ H))) | ((member_msg @ X6 @ (parts @ H)))) = (member_msg @ X6 @ (parts @ H)))))). % analz_disj_parts
thf(fact_170_parts__cut__eq, axiom,
    ((![X6 : msg, H : set_msg]: ((member_msg @ X6 @ (parts @ H)) => ((parts @ (insert_msg @ X6 @ H)) = (parts @ H)))))). % parts_cut_eq
thf(fact_171_publicKey__image__eq, axiom,
    ((![B2 : keymode, X : agent, C2 : keymode, AA : set_agent]: ((member_nat @ (publicKey @ B2 @ X) @ (image_agent_nat @ (publicKey @ C2) @ AA)) = (((B2 = C2)) & ((member_agent @ X @ AA))))))). % publicKey_image_eq
thf(fact_172_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_173_parts__insert__Crypt, axiom,
    ((![K : nat, X6 : msg, H : set_msg]: ((parts @ (insert_msg @ (crypt @ K @ X6) @ H)) = (insert_msg @ (crypt @ K @ X6) @ (parts @ (insert_msg @ X6 @ H))))))). % parts_insert_Crypt
thf(fact_174_keysFor__insert__Key, axiom,
    ((![K : nat, H : set_msg]: ((keysFor @ (insert_msg @ (key @ K) @ H)) = (keysFor @ H))))). % keysFor_insert_Key
thf(fact_175_parts__image__Key, axiom,
    ((![N : set_nat]: ((parts @ (image_nat_msg @ key @ N)) = (image_nat_msg @ key @ N))))). % parts_image_Key
thf(fact_176_shrK__in__used, axiom,
    ((![A : agent, Evs : list_event]: (member_msg @ (key @ (shrK @ A)) @ (used @ Evs))))). % shrK_in_used
thf(fact_177_publicKey__into__used, axiom,
    ((![B2 : keymode, A : agent, Evs : list_event]: (member_msg @ (key @ (publicKey @ B2 @ A)) @ (used @ Evs))))). % publicKey_into_used
thf(fact_178_publicKey__in__initState, axiom,
    ((![B2 : keymode, A : agent, B : agent]: (member_msg @ (key @ (publicKey @ B2 @ A)) @ (initState @ B))))). % publicKey_in_initState
thf(fact_179_usedI, axiom,
    ((![C2 : msg, Evs : list_event]: ((member_msg @ C2 @ (parts @ (knows @ spy @ Evs))) => (member_msg @ C2 @ (used @ Evs)))))). % usedI
thf(fact_180_spies__pubK, axiom,
    ((![B2 : keymode, A : agent, Evs : list_event]: (member_msg @ (key @ (publicKey @ B2 @ A)) @ (knows @ spy @ Evs))))). % spies_pubK
thf(fact_181_parts_OInj, axiom,
    ((![X6 : msg, H : set_msg]: ((member_msg @ X6 @ H) => (member_msg @ X6 @ (parts @ H)))))). % parts.Inj
thf(fact_182_parts_OBody, axiom,
    ((![K : nat, X6 : msg, H : set_msg]: ((member_msg @ (crypt @ K @ X6) @ (parts @ H)) => (member_msg @ X6 @ (parts @ H)))))). % parts.Body
thf(fact_183_parts__partsD, axiom,
    ((![X6 : msg, H : set_msg]: ((member_msg @ X6 @ (parts @ (parts @ H))) => (member_msg @ X6 @ (parts @ H)))))). % parts_partsD
thf(fact_184_initState__into__used, axiom,
    ((![X6 : msg, B : agent, Evs : list_event]: ((member_msg @ X6 @ (parts @ (initState @ B))) => (member_msg @ X6 @ (used @ Evs)))))). % initState_into_used
thf(fact_185_injective__publicKey, axiom,
    ((![B2 : keymode, A : agent, C2 : keymode, A3 : agent]: (((publicKey @ B2 @ A) = (publicKey @ C2 @ A3)) => ((B2 = C2) & (A = A3)))))). % injective_publicKey
thf(fact_186_Crypt__notin__initState, axiom,
    ((![K : nat, X6 : msg, B : agent]: (~ ((member_msg @ (crypt @ K @ X6) @ (parts @ (initState @ B)))))))). % Crypt_notin_initState
thf(fact_187_analz__into__parts, axiom,
    ((![C2 : msg, H : set_msg]: ((member_msg @ C2 @ (analz @ H)) => (member_msg @ C2 @ (parts @ H)))))). % analz_into_parts
thf(fact_188_not__parts__not__analz, axiom,
    ((![C2 : msg, H : set_msg]: ((~ ((member_msg @ C2 @ (parts @ H)))) => (~ ((member_msg @ C2 @ (analz @ H)))))))). % not_parts_not_analz
thf(fact_189_msg_Odistinct_I35_J, axiom,
    ((![X4 : nat, X71 : nat, X72 : msg]: (~ (((key @ X4) = (crypt @ X71 @ X72))))))). % msg.distinct(35)
thf(fact_190_Crypt__notin__image__Key, axiom,
    ((![K : nat, X6 : msg, A : set_nat]: (~ ((member_msg @ (crypt @ K @ X6) @ (image_nat_msg @ key @ A))))))). % Crypt_notin_image_Key
thf(fact_191_parts__insertI, axiom,
    ((![C2 : msg, G2 : set_msg, A2 : msg]: ((member_msg @ C2 @ (parts @ G2)) => (member_msg @ C2 @ (parts @ (insert_msg @ A2 @ G2))))))). % parts_insertI
thf(fact_192_parts__insert__eq__I, axiom,
    ((![X6 : msg, H : set_msg]: ((![X2 : msg]: ((member_msg @ X2 @ (parts @ (insert_msg @ X6 @ H))) => (member_msg @ X2 @ (insert_msg @ X6 @ (parts @ H))))) => ((parts @ (insert_msg @ X6 @ H)) = (insert_msg @ X6 @ (parts @ H))))))). % parts_insert_eq_I
thf(fact_193_shrK__neq__pubK, axiom,
    ((![B2 : keymode, C3 : agent, A : agent]: (~ (((publicKey @ B2 @ C3) = (shrK @ A))))))). % shrK_neq_pubK
thf(fact_194_pushKeys_I6_J, axiom,
    ((![K : nat, X6 : nat, K2 : msg, A : set_msg]: ((insert_msg @ (key @ K) @ (insert_msg @ (crypt @ X6 @ K2) @ A)) = (insert_msg @ (crypt @ X6 @ K2) @ (insert_msg @ (key @ K) @ A)))))). % pushKeys(6)
thf(fact_195_neq__shrK, axiom,
    ((![S : nat, Evs : list_event, B : agent]: ((~ ((member_msg @ (key @ S) @ (used @ Evs)))) => (~ ((S = (shrK @ B)))))))). % neq_shrK
thf(fact_196_shrK__neq, axiom,
    ((![K : nat, Evs : list_event, B : agent]: ((~ ((member_msg @ (key @ K) @ (used @ Evs)))) => (~ (((shrK @ B) = K))))))). % shrK_neq
thf(fact_197_publicKey__notin__image__shrK, axiom,
    ((![B2 : keymode, X : agent, AA : set_agent]: (~ ((member_nat @ (publicKey @ B2 @ X) @ (image_agent_nat @ shrK @ AA))))))). % publicKey_notin_image_shrK
thf(fact_198_shrK__notin__image__publicKey, axiom,
    ((![X : agent, B2 : keymode, AA : set_agent]: (~ ((member_nat @ (shrK @ X) @ (image_agent_nat @ (publicKey @ B2) @ AA))))))). % shrK_notin_image_publicKey
thf(fact_199_analz__shrK__Decrypt, axiom,
    ((![A : agent, X6 : msg, H : set_msg]: ((member_msg @ (crypt @ (shrK @ A) @ X6) @ (analz @ H)) => ((member_msg @ (key @ (shrK @ A)) @ (analz @ H)) => (member_msg @ X6 @ (analz @ H))))))). % analz_shrK_Decrypt
thf(fact_200_new__keys__not__used, axiom,
    ((![K : nat, Evs : list_event]: ((~ ((member_msg @ (key @ K) @ (used @ Evs)))) => ((member_nat @ K @ symKeys) => ((member_list_event @ Evs @ nS_Sha1061662329shared) => (~ ((member_nat @ K @ (keysFor @ (parts @ (knows @ spy @ Evs)))))))))))). % new_keys_not_used
thf(fact_201_Spy__spies__bad__privateKey, axiom,
    ((![A : agent, B2 : keymode, Evs : list_event]: ((member_agent @ A @ bad) => (member_msg @ (key @ (invKey @ (publicKey @ B2 @ A))) @ (knows @ spy @ Evs)))))). % Spy_spies_bad_privateKey
thf(fact_202_analz__Crypt__if, axiom,
    ((![K : nat, H : set_msg, X6 : msg]: (((member_msg @ (key @ (invKey @ K)) @ (analz @ H)) => ((analz @ (insert_msg @ (crypt @ K @ X6) @ H)) = (insert_msg @ (crypt @ K @ X6) @ (analz @ (insert_msg @ X6 @ H))))) & ((~ ((member_msg @ (key @ (invKey @ K)) @ (analz @ H)))) => ((analz @ (insert_msg @ (crypt @ K @ X6) @ H)) = (insert_msg @ (crypt @ K @ X6) @ (analz @ H)))))))). % analz_Crypt_if
thf(fact_203_cert__A__form, axiom,
    ((![A : agent, NA : msg, B : agent, K : nat, X6 : msg, Evs : list_event]: ((member_msg @ (crypt @ (shrK @ A) @ (mPair @ NA @ (mPair @ (agent2 @ B) @ (mPair @ (key @ K) @ X6)))) @ (parts @ (knows @ spy @ Evs))) => ((~ ((member_agent @ A @ bad))) => ((member_list_event @ Evs @ nS_Sha1061662329shared) => ((~ ((member_nat @ K @ (image_agent_nat @ shrK @ top_top_set_agent)))) & (X6 = (crypt @ (shrK @ B) @ (mPair @ (key @ K) @ (agent2 @ A))))))))))). % cert_A_form
thf(fact_204_msg_Oinject_I6_J, axiom,
    ((![X61 : msg, X62 : msg, Y61 : msg, Y62 : msg]: (((mPair @ X61 @ X62) = (mPair @ Y61 @ Y62)) = (((X61 = Y61)) & ((X62 = Y62))))))). % msg.inject(6)
thf(fact_205_msg_Oinject_I1_J, axiom,
    ((![X1 : agent, Y1 : agent]: (((agent2 @ X1) = (agent2 @ Y1)) = (X1 = Y1))))). % msg.inject(1)
thf(fact_206_invKey__image__eq, axiom,
    ((![X : nat, A : set_nat]: ((member_nat @ (invKey @ X) @ (image_nat_nat @ invKey @ A)) = (member_nat @ X @ A))))). % invKey_image_eq
thf(fact_207_invKey__eq, axiom,
    ((![K : nat, K2 : nat]: (((invKey @ K) = (invKey @ K2)) = (K = K2))))). % invKey_eq
thf(fact_208_invKey, axiom,
    ((![K : nat]: ((invKey @ (invKey @ K)) = K)))). % invKey
thf(fact_209_invKey__shrK, axiom,
    ((![A : agent]: ((invKey @ (shrK @ A)) = (shrK @ A))))). % invKey_shrK
thf(fact_210_sym__shrK, axiom,
    ((![X6 : agent]: (member_nat @ (shrK @ X6) @ symKeys)))). % sym_shrK
thf(fact_211_symKeys__invKey__iff, axiom,
    ((![K : nat]: ((member_nat @ (invKey @ K) @ symKeys) = (member_nat @ K @ symKeys))))). % symKeys_invKey_iff
thf(fact_212_invKey__K, axiom,
    ((![K : nat]: ((member_nat @ K @ symKeys) => ((invKey @ K) = K))))). % invKey_K
thf(fact_213_analz__insert__MPair, axiom,
    ((![X6 : msg, Y : msg, H : set_msg]: ((analz @ (insert_msg @ (mPair @ X6 @ Y) @ H)) = (insert_msg @ (mPair @ X6 @ Y) @ (analz @ (insert_msg @ X6 @ (insert_msg @ Y @ H)))))))). % analz_insert_MPair
thf(fact_214_parts__insert__MPair, axiom,
    ((![X6 : msg, Y : msg, H : set_msg]: ((parts @ (insert_msg @ (mPair @ X6 @ Y) @ H)) = (insert_msg @ (mPair @ X6 @ Y) @ (parts @ (insert_msg @ X6 @ (insert_msg @ Y @ H)))))))). % parts_insert_MPair
thf(fact_215_analz__insert__Agent, axiom,
    ((![Agt : agent, H : set_msg]: ((analz @ (insert_msg @ (agent2 @ Agt) @ H)) = (insert_msg @ (agent2 @ Agt) @ (analz @ H)))))). % analz_insert_Agent
thf(fact_216_parts__insert__Agent, axiom,
    ((![Agt : agent, H : set_msg]: ((parts @ (insert_msg @ (agent2 @ Agt) @ H)) = (insert_msg @ (agent2 @ Agt) @ (parts @ H)))))). % parts_insert_Agent
thf(fact_217_keysFor__insert__MPair, axiom,
    ((![X6 : msg, Y : msg, H : set_msg]: ((keysFor @ (insert_msg @ (mPair @ X6 @ Y) @ H)) = (keysFor @ H))))). % keysFor_insert_MPair
thf(fact_218_keysFor__insert__Agent, axiom,
    ((![A : agent, H : set_msg]: ((keysFor @ (insert_msg @ (agent2 @ A) @ H)) = (keysFor @ H))))). % keysFor_insert_Agent
thf(fact_219_privateKey__image__eq, axiom,
    ((![B2 : keymode, A : agent, C2 : keymode, AS : set_agent]: ((member_nat @ (invKey @ (publicKey @ B2 @ A)) @ (image_nat_nat @ invKey @ (image_agent_nat @ (publicKey @ C2) @ AS))) = (((B2 = C2)) & ((member_agent @ A @ AS))))))). % privateKey_image_eq
thf(fact_220_keysFor__insert__Crypt, axiom,
    ((![K : nat, X6 : msg, H : set_msg]: ((keysFor @ (insert_msg @ (crypt @ K @ X6) @ H)) = (insert_nat @ (invKey @ K) @ (keysFor @ H)))))). % keysFor_insert_Crypt
thf(fact_221_privateKey__into__used, axiom,
    ((![B2 : keymode, A : agent, Evs : list_event]: (member_msg @ (key @ (invKey @ (publicKey @ B2 @ A))) @ (used @ Evs))))). % privateKey_into_used
thf(fact_222_priK__in__initState, axiom,
    ((![B2 : keymode, A : agent]: (member_msg @ (key @ (invKey @ (publicKey @ B2 @ A))) @ (initState @ A))))). % priK_in_initState
thf(fact_223_msg_Odistinct_I41_J, axiom,
    ((![X61 : msg, X62 : msg, X71 : nat, X72 : msg]: (~ (((mPair @ X61 @ X62) = (crypt @ X71 @ X72))))))). % msg.distinct(41)
thf(fact_224_parts_OFst, axiom,
    ((![X6 : msg, Y : msg, H : set_msg]: ((member_msg @ (mPair @ X6 @ Y) @ (parts @ H)) => (member_msg @ X6 @ (parts @ H)))))). % parts.Fst
thf(fact_225_parts_OSnd, axiom,
    ((![X6 : msg, Y : msg, H : set_msg]: ((member_msg @ (mPair @ X6 @ Y) @ (parts @ H)) => (member_msg @ Y @ (parts @ H)))))). % parts.Snd
thf(fact_226_MPair__parts, axiom,
    ((![X6 : msg, Y : msg, H : set_msg]: ((member_msg @ (mPair @ X6 @ Y) @ (parts @ H)) => (~ (((member_msg @ X6 @ (parts @ H)) => (~ ((member_msg @ Y @ (parts @ H))))))))))). % MPair_parts
thf(fact_227_not__symKeys__priK, axiom,
    ((![B2 : keymode, A : agent]: (~ ((member_nat @ (invKey @ (publicKey @ B2 @ A)) @ symKeys)))))). % not_symKeys_priK
thf(fact_228_analz_OFst, axiom,
    ((![X6 : msg, Y : msg, H : set_msg]: ((member_msg @ (mPair @ X6 @ Y) @ (analz @ H)) => (member_msg @ X6 @ (analz @ H)))))). % analz.Fst
thf(fact_229_analz_OSnd, axiom,
    ((![X6 : msg, Y : msg, H : set_msg]: ((member_msg @ (mPair @ X6 @ Y) @ (analz @ H)) => (member_msg @ Y @ (analz @ H)))))). % analz.Snd
thf(fact_230_MPair__analz, axiom,
    ((![X6 : msg, Y : msg, H : set_msg]: ((member_msg @ (mPair @ X6 @ Y) @ (analz @ H)) => (~ (((member_msg @ X6 @ (analz @ H)) => (~ ((member_msg @ Y @ (analz @ H))))))))))). % MPair_analz
thf(fact_231_msg_Odistinct_I33_J, axiom,
    ((![X4 : nat, X61 : msg, X62 : msg]: (~ (((key @ X4) = (mPair @ X61 @ X62))))))). % msg.distinct(33)
thf(fact_232_symKeys__neq__imp__neq, axiom,
    ((![K : nat, K2 : nat]: ((~ (((member_nat @ K @ symKeys) = (member_nat @ K2 @ symKeys)))) => (~ ((K = K2))))))). % symKeys_neq_imp_neq
thf(fact_233_msg_Odistinct_I9_J, axiom,
    ((![X1 : agent, X61 : msg, X62 : msg]: (~ (((agent2 @ X1) = (mPair @ X61 @ X62))))))). % msg.distinct(9)
thf(fact_234_msg_Odistinct_I5_J, axiom,
    ((![X1 : agent, X4 : nat]: (~ (((agent2 @ X1) = (key @ X4))))))). % msg.distinct(5)
thf(fact_235_msg_Odistinct_I11_J, axiom,
    ((![X1 : agent, X71 : nat, X72 : msg]: (~ (((agent2 @ X1) = (crypt @ X71 @ X72))))))). % msg.distinct(11)
thf(fact_236_MPair__used__D, axiom,
    ((![X6 : msg, Y : msg, H : list_event]: ((member_msg @ (mPair @ X6 @ Y) @ (used @ H)) => ((member_msg @ X6 @ (used @ H)) & (member_msg @ Y @ (used @ H))))))). % MPair_used_D
thf(fact_237_MPair__used, axiom,
    ((![X6 : msg, Y : msg, H : list_event]: ((member_msg @ (mPair @ X6 @ Y) @ (used @ H)) => (~ (((member_msg @ X6 @ (used @ H)) => (~ ((member_msg @ Y @ (used @ H))))))))))). % MPair_used
thf(fact_238_publicKey__neq__privateKey, axiom,
    ((![C2 : keymode, A3 : agent, B2 : keymode, A : agent]: (~ (((publicKey @ C2 @ A3) = (invKey @ (publicKey @ B2 @ A)))))))). % publicKey_neq_privateKey
thf(fact_239_analz_Oinducts, axiom,
    ((![X : msg, H : set_msg, P : msg > $o]: ((member_msg @ X @ (analz @ H)) => ((![X7 : msg]: ((member_msg @ X7 @ H) => (P @ X7))) => ((![X7 : msg, Y3 : msg]: ((member_msg @ (mPair @ X7 @ Y3) @ (analz @ H)) => ((P @ (mPair @ X7 @ Y3)) => (P @ X7)))) => ((![X7 : msg, Y3 : msg]: ((member_msg @ (mPair @ X7 @ Y3) @ (analz @ H)) => ((P @ (mPair @ X7 @ Y3)) => (P @ Y3)))) => ((![K3 : nat, X7 : msg]: ((member_msg @ (crypt @ K3 @ X7) @ (analz @ H)) => ((P @ (crypt @ K3 @ X7)) => ((member_msg @ (key @ (invKey @ K3)) @ (analz @ H)) => ((P @ (key @ (invKey @ K3))) => (P @ X7)))))) => (P @ X))))))))). % analz.inducts
thf(fact_240_analz_Osimps, axiom,
    ((![A2 : msg, H : set_msg]: ((member_msg @ A2 @ (analz @ H)) = (((?[X8 : msg]: (((A2 = X8)) & ((member_msg @ X8 @ H))))) | ((((?[X8 : msg]: (?[Y5 : msg]: (((A2 = X8)) & ((member_msg @ (mPair @ X8 @ Y5) @ (analz @ H))))))) | ((((?[X8 : msg]: (?[Y5 : msg]: (((A2 = Y5)) & ((member_msg @ (mPair @ X8 @ Y5) @ (analz @ H))))))) | ((?[K4 : nat]: (?[X8 : msg]: (((A2 = X8)) & ((((member_msg @ (crypt @ K4 @ X8) @ (analz @ H))) & ((member_msg @ (key @ (invKey @ K4)) @ (analz @ H)))))))))))))))))). % analz.simps
thf(fact_241_analz_Ocases, axiom,
    ((![A2 : msg, H : set_msg]: ((member_msg @ A2 @ (analz @ H)) => ((~ ((member_msg @ A2 @ H))) => ((![Y3 : msg]: (~ ((member_msg @ (mPair @ A2 @ Y3) @ (analz @ H))))) => ((![X7 : msg]: (~ ((member_msg @ (mPair @ X7 @ A2) @ (analz @ H))))) => (~ ((![K3 : nat]: ((member_msg @ (crypt @ K3 @ A2) @ (analz @ H)) => (~ ((member_msg @ (key @ (invKey @ K3)) @ (analz @ H))))))))))))))). % analz.cases
thf(fact_242_not__symKeys__pubK, axiom,
    ((![B2 : keymode, A : agent]: (~ ((member_nat @ (publicKey @ B2 @ A) @ symKeys)))))). % not_symKeys_pubK
thf(fact_243_pushKeys_I5_J, axiom,
    ((![K : nat, X6 : msg, Y : msg, A : set_msg]: ((insert_msg @ (key @ K) @ (insert_msg @ (mPair @ X6 @ Y) @ A)) = (insert_msg @ (mPair @ X6 @ Y) @ (insert_msg @ (key @ K) @ A)))))). % pushKeys(5)
thf(fact_244_analz__trivial, axiom,
    ((![H : set_msg]: ((![X7 : msg, Y3 : msg]: (~ ((member_msg @ (mPair @ X7 @ Y3) @ H)))) => ((![X7 : msg, K3 : nat]: (~ ((member_msg @ (crypt @ K3 @ X7) @ H)))) => ((analz @ H) = H)))))). % analz_trivial
thf(fact_245_pushCrypts_I6_J, axiom,
    ((![X6 : nat, K : msg, X9 : msg, Y : msg, A : set_msg]: ((insert_msg @ (crypt @ X6 @ K) @ (insert_msg @ (mPair @ X9 @ Y) @ A)) = (insert_msg @ (mPair @ X9 @ Y) @ (insert_msg @ (crypt @ X6 @ K) @ A)))))). % pushCrypts(6)
thf(fact_246_parts_Oinducts, axiom,
    ((![X : msg, H : set_msg, P : msg > $o]: ((member_msg @ X @ (parts @ H)) => ((![X7 : msg]: ((member_msg @ X7 @ H) => (P @ X7))) => ((![X7 : msg, Y3 : msg]: ((member_msg @ (mPair @ X7 @ Y3) @ (parts @ H)) => ((P @ (mPair @ X7 @ Y3)) => (P @ X7)))) => ((![X7 : msg, Y3 : msg]: ((member_msg @ (mPair @ X7 @ Y3) @ (parts @ H)) => ((P @ (mPair @ X7 @ Y3)) => (P @ Y3)))) => ((![K3 : nat, X7 : msg]: ((member_msg @ (crypt @ K3 @ X7) @ (parts @ H)) => ((P @ (crypt @ K3 @ X7)) => (P @ X7)))) => (P @ X))))))))). % parts.inducts
thf(fact_247_parts_Osimps, axiom,
    ((![A2 : msg, H : set_msg]: ((member_msg @ A2 @ (parts @ H)) = (((?[X8 : msg]: (((A2 = X8)) & ((member_msg @ X8 @ H))))) | ((((?[X8 : msg]: (?[Y5 : msg]: (((A2 = X8)) & ((member_msg @ (mPair @ X8 @ Y5) @ (parts @ H))))))) | ((((?[X8 : msg]: (?[Y5 : msg]: (((A2 = Y5)) & ((member_msg @ (mPair @ X8 @ Y5) @ (parts @ H))))))) | ((?[K4 : nat]: (?[X8 : msg]: (((A2 = X8)) & ((member_msg @ (crypt @ K4 @ X8) @ (parts @ H)))))))))))))))). % parts.simps
thf(fact_248_parts_Ocases, axiom,
    ((![A2 : msg, H : set_msg]: ((member_msg @ A2 @ (parts @ H)) => ((~ ((member_msg @ A2 @ H))) => ((![Y3 : msg]: (~ ((member_msg @ (mPair @ A2 @ Y3) @ (parts @ H))))) => ((![X7 : msg]: (~ ((member_msg @ (mPair @ X7 @ A2) @ (parts @ H))))) => (~ ((![K3 : nat]: (~ ((member_msg @ (crypt @ K3 @ A2) @ (parts @ H)))))))))))))). % parts.cases

% Conjectures (3)
thf(conj_0, hypothesis,
    ((member_list_event @ evs @ nS_Sha1061662329shared))).
thf(conj_1, hypothesis,
    ((~ ((member_nat @ kab @ (image_agent_nat @ shrK @ top_top_set_agent)))))).
thf(conj_2, conjecture,
    (((member_msg @ (key @ k) @ (analz @ (insert_msg @ (key @ kab) @ (knows @ spy @ evs)))) = (((k = kab)) | ((member_msg @ (key @ k) @ (analz @ (knows @ spy @ evs)))))))).
