% 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_173__5229360_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:23:48.421

% 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 (57)
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_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__Oagent_J, type,
    sup_sup_set_agent : set_agent > set_agent > set_agent).
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_Oanalzp, type,
    analzp : (msg > $o) > msg > $o).
thf(sy_c_Message_OinvKey, type,
    invKey : nat > nat).
thf(sy_c_Message_OkeysFor, type,
    keysFor : set_msg > set_nat).
thf(sy_c_Message_Omsg_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_Okeymode_OEncryption, type,
    encryption : keymode).
thf(sy_c_Public_Okeymode_OSignature, type,
    signature : keymode).
thf(sy_c_Public_OpublicKey, type,
    publicKey : keymode > agent > nat).
thf(sy_c_Public_OshrK, type,
    shrK : agent > nat).
thf(sy_c_Set_OCollect_001t__List__Olist_It__Event__Oevent_J, type,
    collect_list_event : (list_event > $o) > set_list_event).
thf(sy_c_Set_OCollect_001t__Message__Oagent, type,
    collect_agent : (agent > $o) > set_agent).
thf(sy_c_Set_OCollect_001t__Message__Omsg, type,
    collect_msg : (msg > $o) > set_msg).
thf(sy_c_Set_OCollect_001t__Nat__Onat, type,
    collect_nat : (nat > $o) > set_nat).
thf(sy_c_Set_Oimage_001t__Message__Oagent_001t__List__Olist_It__Event__Oevent_J, type,
    image_832067507_event : (agent > list_event) > set_agent > set_list_event).
thf(sy_c_Set_Oimage_001t__Message__Oagent_001t__Message__Oagent, type,
    image_agent_agent : (agent > agent) > set_agent > set_agent).
thf(sy_c_Set_Oimage_001t__Message__Oagent_001t__Message__Omsg, type,
    image_agent_msg : (agent > msg) > set_agent > set_msg).
thf(sy_c_Set_Oimage_001t__Message__Oagent_001t__Nat__Onat, type,
    image_agent_nat : (agent > nat) > set_agent > set_nat).
thf(sy_c_Set_Oimage_001t__Message__Omsg_001t__List__Olist_It__Event__Oevent_J, type,
    image_msg_list_event : (msg > list_event) > set_msg > set_list_event).
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_member_001t__List__Olist_It__Event__Oevent_J, type,
    member_list_event : list_event > set_list_event > $o).
thf(sy_c_member_001t__Message__Oagent, type,
    member_agent : agent > set_agent > $o).
thf(sy_c_member_001t__Message__Omsg, type,
    member_msg : msg > set_msg > $o).
thf(sy_c_member_001t__Nat__Onat, type,
    member_nat : nat > set_nat > $o).
thf(sy_v_A, type,
    a : agent).
thf(sy_v_B, type,
    b : agent).
thf(sy_v_K, type,
    k : nat).
thf(sy_v_NA, type,
    na : msg).
thf(sy_v_X, type,
    x : msg).
thf(sy_v_evs, type,
    evs : list_event).

% Relevant facts (244)
thf(fact_0_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_1_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_2_shrK__in__knows, axiom,
    ((![A : agent, Evs : list_event]: (member_msg @ (key @ (shrK @ A)) @ (knows @ A @ Evs))))). % shrK_in_knows
thf(fact_3_Spy__in__bad, axiom,
    ((member_agent @ spy @ bad))). % Spy_in_bad
thf(fact_4_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_5_parts_Ocases, axiom,
    ((![A2 : msg, H : set_msg]: ((member_msg @ A2 @ (parts @ H)) => ((~ ((member_msg @ A2 @ H))) => ((![Y : msg]: (~ ((member_msg @ (mPair @ A2 @ Y) @ (parts @ H))))) => ((![X2 : msg]: (~ ((member_msg @ (mPair @ X2 @ A2) @ (parts @ H))))) => (~ ((![K : nat]: (~ ((member_msg @ (crypt @ K @ A2) @ (parts @ H)))))))))))))). % parts.cases
thf(fact_6_parts_Osimps, axiom,
    ((![A2 : msg, H : set_msg]: ((member_msg @ A2 @ (parts @ H)) = (((?[X3 : msg]: (((A2 = X3)) & ((member_msg @ X3 @ H))))) | ((((?[X3 : msg]: (?[Y2 : msg]: (((A2 = X3)) & ((member_msg @ (mPair @ X3 @ Y2) @ (parts @ H))))))) | ((((?[X3 : msg]: (?[Y2 : msg]: (((A2 = Y2)) & ((member_msg @ (mPair @ X3 @ Y2) @ (parts @ H))))))) | ((?[K2 : nat]: (?[X3 : msg]: (((A2 = X3)) & ((member_msg @ (crypt @ K2 @ X3) @ (parts @ H)))))))))))))))). % parts.simps
thf(fact_7_parts_Oinducts, axiom,
    ((![X : msg, H : set_msg, P : msg > $o]: ((member_msg @ X @ (parts @ H)) => ((![X2 : msg]: ((member_msg @ X2 @ H) => (P @ X2))) => ((![X2 : msg, Y : msg]: ((member_msg @ (mPair @ X2 @ Y) @ (parts @ H)) => ((P @ (mPair @ X2 @ Y)) => (P @ X2)))) => ((![X2 : msg, Y : msg]: ((member_msg @ (mPair @ X2 @ Y) @ (parts @ H)) => ((P @ (mPair @ X2 @ Y)) => (P @ Y)))) => ((![K : nat, X2 : msg]: ((member_msg @ (crypt @ K @ X2) @ (parts @ H)) => ((P @ (crypt @ K @ X2)) => (P @ X2)))) => (P @ X))))))))). % parts.inducts
thf(fact_8_shrK__injective, axiom,
    ((![X : agent, Y3 : agent]: (((shrK @ X) = (shrK @ Y3)) = (X = Y3))))). % shrK_injective
thf(fact_9_msg_Oinject_I1_J, axiom,
    ((![X1 : agent, Y1 : agent]: (((agent2 @ X1) = (agent2 @ Y1)) = (X1 = Y1))))). % msg.inject(1)
thf(fact_10_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_11_msg_Oinject_I4_J, axiom,
    ((![X4 : nat, Y4 : nat]: (((key @ X4) = (key @ Y4)) = (X4 = Y4))))). % msg.inject(4)
thf(fact_12_parts__idem, axiom,
    ((![H : set_msg]: ((parts @ (parts @ H)) = (parts @ H))))). % parts_idem
thf(fact_13_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_14_parts__partsD, axiom,
    ((![X5 : msg, H : set_msg]: ((member_msg @ X5 @ (parts @ (parts @ H))) => (member_msg @ X5 @ (parts @ H)))))). % parts_partsD
thf(fact_15_parts_OInj, axiom,
    ((![X5 : msg, H : set_msg]: ((member_msg @ X5 @ H) => (member_msg @ X5 @ (parts @ H)))))). % parts.Inj
thf(fact_16_MPair__parts, axiom,
    ((![X5 : msg, Y5 : msg, H : set_msg]: ((member_msg @ (mPair @ X5 @ Y5) @ (parts @ H)) => (~ (((member_msg @ X5 @ (parts @ H)) => (~ ((member_msg @ Y5 @ (parts @ H))))))))))). % MPair_parts
thf(fact_17_parts_OSnd, axiom,
    ((![X5 : msg, Y5 : msg, H : set_msg]: ((member_msg @ (mPair @ X5 @ Y5) @ (parts @ H)) => (member_msg @ Y5 @ (parts @ H)))))). % parts.Snd
thf(fact_18_parts_OFst, axiom,
    ((![X5 : msg, Y5 : msg, H : set_msg]: ((member_msg @ (mPair @ X5 @ Y5) @ (parts @ H)) => (member_msg @ X5 @ (parts @ H)))))). % parts.Fst
thf(fact_19_msg_Odistinct_I33_J, axiom,
    ((![X4 : nat, X61 : msg, X62 : msg]: (~ (((key @ X4) = (mPair @ X61 @ X62))))))). % msg.distinct(33)
thf(fact_20_msg_Odistinct_I41_J, axiom,
    ((![X61 : msg, X62 : msg, X71 : nat, X72 : msg]: (~ (((mPair @ X61 @ X62) = (crypt @ X71 @ X72))))))). % msg.distinct(41)
thf(fact_21_parts_OBody, axiom,
    ((![K3 : nat, X5 : msg, H : set_msg]: ((member_msg @ (crypt @ K3 @ X5) @ (parts @ H)) => (member_msg @ X5 @ (parts @ H)))))). % parts.Body
thf(fact_22_msg_Odistinct_I35_J, axiom,
    ((![X4 : nat, X71 : nat, X72 : msg]: (~ (((key @ X4) = (crypt @ X71 @ X72))))))). % msg.distinct(35)
thf(fact_23_msg_Odistinct_I9_J, axiom,
    ((![X1 : agent, X61 : msg, X62 : msg]: (~ (((agent2 @ X1) = (mPair @ X61 @ X62))))))). % msg.distinct(9)
thf(fact_24_msg_Odistinct_I5_J, axiom,
    ((![X1 : agent, X4 : nat]: (~ (((agent2 @ X1) = (key @ X4))))))). % msg.distinct(5)
thf(fact_25_msg_Odistinct_I11_J, axiom,
    ((![X1 : agent, X71 : nat, X72 : msg]: (~ (((agent2 @ X1) = (crypt @ X71 @ X72))))))). % msg.distinct(11)
thf(fact_26_iso__tuple__UNIV__I, axiom,
    ((![X : msg]: (member_msg @ X @ top_top_set_msg)))). % iso_tuple_UNIV_I
thf(fact_27_iso__tuple__UNIV__I, axiom,
    ((![X : list_event]: (member_list_event @ X @ top_to1178833912_event)))). % iso_tuple_UNIV_I
thf(fact_28_iso__tuple__UNIV__I, axiom,
    ((![X : nat]: (member_nat @ X @ top_top_set_nat)))). % iso_tuple_UNIV_I
thf(fact_29_iso__tuple__UNIV__I, axiom,
    ((![X : agent]: (member_agent @ X @ top_top_set_agent)))). % iso_tuple_UNIV_I
thf(fact_30_UNIV__I, axiom,
    ((![X : msg]: (member_msg @ X @ top_top_set_msg)))). % UNIV_I
thf(fact_31_UNIV__I, axiom,
    ((![X : list_event]: (member_list_event @ X @ top_to1178833912_event)))). % UNIV_I
thf(fact_32_UNIV__I, axiom,
    ((![X : nat]: (member_nat @ X @ top_top_set_nat)))). % UNIV_I
thf(fact_33_UNIV__I, axiom,
    ((![X : agent]: (member_agent @ X @ top_top_set_agent)))). % UNIV_I
thf(fact_34_image__eqI, axiom,
    ((![B : msg, F : msg > msg, X : msg, A : set_msg]: ((B = (F @ X)) => ((member_msg @ X @ A) => (member_msg @ B @ (image_msg_msg @ F @ A))))))). % image_eqI
thf(fact_35_image__eqI, axiom,
    ((![B : agent, F : msg > agent, X : msg, A : set_msg]: ((B = (F @ X)) => ((member_msg @ X @ A) => (member_agent @ B @ (image_msg_agent @ F @ A))))))). % image_eqI
thf(fact_36_image__eqI, axiom,
    ((![B : nat, F : msg > nat, X : msg, A : set_msg]: ((B = (F @ X)) => ((member_msg @ X @ A) => (member_nat @ B @ (image_msg_nat @ F @ A))))))). % image_eqI
thf(fact_37_image__eqI, axiom,
    ((![B : msg, F : agent > msg, X : agent, A : set_agent]: ((B = (F @ X)) => ((member_agent @ X @ A) => (member_msg @ B @ (image_agent_msg @ F @ A))))))). % image_eqI
thf(fact_38_image__eqI, axiom,
    ((![B : agent, F : agent > agent, X : agent, A : set_agent]: ((B = (F @ X)) => ((member_agent @ X @ A) => (member_agent @ B @ (image_agent_agent @ F @ A))))))). % image_eqI
thf(fact_39_image__eqI, axiom,
    ((![B : nat, F : agent > nat, X : agent, A : set_agent]: ((B = (F @ X)) => ((member_agent @ X @ A) => (member_nat @ B @ (image_agent_nat @ F @ A))))))). % image_eqI
thf(fact_40_image__eqI, axiom,
    ((![B : msg, F : nat > msg, X : nat, A : set_nat]: ((B = (F @ X)) => ((member_nat @ X @ A) => (member_msg @ B @ (image_nat_msg @ F @ A))))))). % image_eqI
thf(fact_41_image__eqI, axiom,
    ((![B : agent, F : nat > agent, X : nat, A : set_nat]: ((B = (F @ X)) => ((member_nat @ X @ A) => (member_agent @ B @ (image_nat_agent @ F @ A))))))). % image_eqI
thf(fact_42_image__eqI, axiom,
    ((![B : nat, F : nat > nat, X : nat, A : set_nat]: ((B = (F @ X)) => ((member_nat @ X @ A) => (member_nat @ B @ (image_nat_nat @ F @ A))))))). % image_eqI
thf(fact_43_image__eqI, axiom,
    ((![B : list_event, F : msg > list_event, X : msg, A : set_msg]: ((B = (F @ X)) => ((member_msg @ X @ A) => (member_list_event @ B @ (image_msg_list_event @ F @ A))))))). % image_eqI
thf(fact_44_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_45_range__eqI, axiom,
    ((![B : msg, F : nat > msg, X : nat]: ((B = (F @ X)) => (member_msg @ B @ (image_nat_msg @ F @ top_top_set_nat)))))). % range_eqI
thf(fact_46_range__eqI, axiom,
    ((![B : nat, F : nat > nat, X : nat]: ((B = (F @ X)) => (member_nat @ B @ (image_nat_nat @ F @ top_top_set_nat)))))). % range_eqI
thf(fact_47_range__eqI, axiom,
    ((![B : msg, F : agent > msg, X : agent]: ((B = (F @ X)) => (member_msg @ B @ (image_agent_msg @ F @ top_top_set_agent)))))). % range_eqI
thf(fact_48_range__eqI, axiom,
    ((![B : agent, F : agent > agent, X : agent]: ((B = (F @ X)) => (member_agent @ B @ (image_agent_agent @ F @ top_top_set_agent)))))). % range_eqI
thf(fact_49_range__eqI, axiom,
    ((![B : list_event, F : agent > list_event, X : agent]: ((B = (F @ X)) => (member_list_event @ B @ (image_832067507_event @ F @ top_top_set_agent)))))). % range_eqI
thf(fact_50_range__eqI, axiom,
    ((![B : nat, F : agent > nat, X : agent]: ((B = (F @ X)) => (member_nat @ B @ (image_agent_nat @ F @ top_top_set_agent)))))). % range_eqI
thf(fact_51_surj__def, axiom,
    ((![F : nat > msg]: (((image_nat_msg @ F @ top_top_set_nat) = top_top_set_msg) = (![Y6 : msg]: (?[X6 : nat]: (Y6 = (F @ X6)))))))). % surj_def
thf(fact_52_surj__def, axiom,
    ((![F : nat > nat]: (((image_nat_nat @ F @ top_top_set_nat) = top_top_set_nat) = (![Y6 : nat]: (?[X6 : nat]: (Y6 = (F @ X6)))))))). % surj_def
thf(fact_53_surj__def, axiom,
    ((![F : agent > nat]: (((image_agent_nat @ F @ top_top_set_agent) = top_top_set_nat) = (![Y6 : nat]: (?[X6 : agent]: (Y6 = (F @ X6)))))))). % surj_def
thf(fact_54_surj__def, axiom,
    ((![F : agent > agent]: (((image_agent_agent @ F @ top_top_set_agent) = top_top_set_agent) = (![Y6 : agent]: (?[X6 : agent]: (Y6 = (F @ X6)))))))). % surj_def
thf(fact_55_rangeI, axiom,
    ((![F : nat > msg, X : nat]: (member_msg @ (F @ X) @ (image_nat_msg @ F @ top_top_set_nat))))). % rangeI
thf(fact_56_rangeI, axiom,
    ((![F : nat > nat, X : nat]: (member_nat @ (F @ X) @ (image_nat_nat @ F @ top_top_set_nat))))). % rangeI
thf(fact_57_rangeI, axiom,
    ((![F : agent > msg, X : agent]: (member_msg @ (F @ X) @ (image_agent_msg @ F @ top_top_set_agent))))). % rangeI
thf(fact_58_rangeI, axiom,
    ((![F : agent > agent, X : agent]: (member_agent @ (F @ X) @ (image_agent_agent @ F @ top_top_set_agent))))). % rangeI
thf(fact_59_rangeI, axiom,
    ((![F : agent > list_event, X : agent]: (member_list_event @ (F @ X) @ (image_832067507_event @ F @ top_top_set_agent))))). % rangeI
thf(fact_60_rangeI, axiom,
    ((![F : agent > nat, X : agent]: (member_nat @ (F @ X) @ (image_agent_nat @ F @ top_top_set_agent))))). % rangeI
thf(fact_61_surjI, axiom,
    ((![G : nat > msg, F : msg > nat]: ((![X7 : msg]: ((G @ (F @ X7)) = X7)) => ((image_nat_msg @ G @ top_top_set_nat) = top_top_set_msg))))). % surjI
thf(fact_62_surjI, axiom,
    ((![G : nat > nat, F : nat > nat]: ((![X7 : nat]: ((G @ (F @ X7)) = X7)) => ((image_nat_nat @ G @ top_top_set_nat) = top_top_set_nat))))). % surjI
thf(fact_63_surjI, axiom,
    ((![G : agent > nat, F : nat > agent]: ((![X7 : nat]: ((G @ (F @ X7)) = X7)) => ((image_agent_nat @ G @ top_top_set_agent) = top_top_set_nat))))). % surjI
thf(fact_64_surjI, axiom,
    ((![G : agent > agent, F : agent > agent]: ((![X7 : agent]: ((G @ (F @ X7)) = X7)) => ((image_agent_agent @ G @ top_top_set_agent) = top_top_set_agent))))). % surjI
thf(fact_65_surjE, axiom,
    ((![F : nat > msg, Y3 : msg]: (((image_nat_msg @ F @ top_top_set_nat) = top_top_set_msg) => (~ ((![X7 : nat]: (~ ((Y3 = (F @ X7))))))))))). % surjE
thf(fact_66_surjE, axiom,
    ((![F : nat > nat, Y3 : nat]: (((image_nat_nat @ F @ top_top_set_nat) = top_top_set_nat) => (~ ((![X7 : nat]: (~ ((Y3 = (F @ X7))))))))))). % surjE
thf(fact_67_surjE, axiom,
    ((![F : agent > nat, Y3 : nat]: (((image_agent_nat @ F @ top_top_set_agent) = top_top_set_nat) => (~ ((![X7 : agent]: (~ ((Y3 = (F @ X7))))))))))). % surjE
thf(fact_68_surjE, axiom,
    ((![F : agent > agent, Y3 : agent]: (((image_agent_agent @ F @ top_top_set_agent) = top_top_set_agent) => (~ ((![X7 : agent]: (~ ((Y3 = (F @ X7))))))))))). % surjE
thf(fact_69_analz__idem, axiom,
    ((![H : set_msg]: ((analz @ (analz @ H)) = (analz @ H))))). % analz_idem
thf(fact_70_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_71_analz__parts, axiom,
    ((![H : set_msg]: ((analz @ (parts @ H)) = (parts @ H))))). % analz_parts
thf(fact_72_parts__analz, axiom,
    ((![H : set_msg]: ((parts @ (analz @ H)) = (parts @ H))))). % parts_analz
thf(fact_73_analz__conj__parts, axiom,
    ((![X5 : msg, H : set_msg]: ((((member_msg @ X5 @ (analz @ H))) & ((member_msg @ X5 @ (parts @ H)))) = (member_msg @ X5 @ (analz @ H)))))). % analz_conj_parts
thf(fact_74_analz__disj__parts, axiom,
    ((![X5 : msg, H : set_msg]: ((((member_msg @ X5 @ (analz @ H))) | ((member_msg @ X5 @ (parts @ H)))) = (member_msg @ X5 @ (parts @ H)))))). % analz_disj_parts
thf(fact_75_analz__image__Key, axiom,
    ((![N : set_nat]: ((analz @ (image_nat_msg @ key @ N)) = (image_nat_msg @ key @ N))))). % analz_image_Key
thf(fact_76_parts__image__Key, axiom,
    ((![N : set_nat]: ((parts @ (image_nat_msg @ key @ N)) = (image_nat_msg @ key @ N))))). % parts_image_Key
thf(fact_77_analz_OInj, axiom,
    ((![X5 : msg, H : set_msg]: ((member_msg @ X5 @ H) => (member_msg @ X5 @ (analz @ H)))))). % analz.Inj
thf(fact_78_mem__Collect__eq, axiom,
    ((![A2 : msg, P : msg > $o]: ((member_msg @ A2 @ (collect_msg @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_79_mem__Collect__eq, axiom,
    ((![A2 : agent, P : agent > $o]: ((member_agent @ A2 @ (collect_agent @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_80_mem__Collect__eq, axiom,
    ((![A2 : list_event, P : list_event > $o]: ((member_list_event @ A2 @ (collect_list_event @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_81_mem__Collect__eq, axiom,
    ((![A2 : nat, P : nat > $o]: ((member_nat @ A2 @ (collect_nat @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_82_Collect__mem__eq, axiom,
    ((![A : set_msg]: ((collect_msg @ (^[X6 : msg]: (member_msg @ X6 @ A))) = A)))). % Collect_mem_eq
thf(fact_83_Collect__mem__eq, axiom,
    ((![A : set_agent]: ((collect_agent @ (^[X6 : agent]: (member_agent @ X6 @ A))) = A)))). % Collect_mem_eq
thf(fact_84_Collect__mem__eq, axiom,
    ((![A : set_list_event]: ((collect_list_event @ (^[X6 : list_event]: (member_list_event @ X6 @ A))) = A)))). % Collect_mem_eq
thf(fact_85_Collect__mem__eq, axiom,
    ((![A : set_nat]: ((collect_nat @ (^[X6 : nat]: (member_nat @ X6 @ A))) = A)))). % Collect_mem_eq
thf(fact_86_analz__analzD, axiom,
    ((![X5 : msg, H : set_msg]: ((member_msg @ X5 @ (analz @ (analz @ H))) => (member_msg @ X5 @ (analz @ H)))))). % analz_analzD
thf(fact_87_top__set__def, axiom,
    ((top_top_set_agent = (collect_agent @ top_top_agent_o)))). % top_set_def
thf(fact_88_analz_OFst, axiom,
    ((![X5 : msg, Y5 : msg, H : set_msg]: ((member_msg @ (mPair @ X5 @ Y5) @ (analz @ H)) => (member_msg @ X5 @ (analz @ H)))))). % analz.Fst
thf(fact_89_analz_OSnd, axiom,
    ((![X5 : msg, Y5 : msg, H : set_msg]: ((member_msg @ (mPair @ X5 @ Y5) @ (analz @ H)) => (member_msg @ Y5 @ (analz @ H)))))). % analz.Snd
thf(fact_90_MPair__analz, axiom,
    ((![X5 : msg, Y5 : msg, H : set_msg]: ((member_msg @ (mPair @ X5 @ Y5) @ (analz @ H)) => (~ (((member_msg @ X5 @ (analz @ H)) => (~ ((member_msg @ Y5 @ (analz @ H))))))))))). % MPair_analz
thf(fact_91_analz__into__parts, axiom,
    ((![C : msg, H : set_msg]: ((member_msg @ C @ (analz @ H)) => (member_msg @ C @ (parts @ H)))))). % analz_into_parts
thf(fact_92_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_93_analz__trivial, axiom,
    ((![H : set_msg]: ((![X2 : msg, Y : msg]: (~ ((member_msg @ (mPair @ X2 @ Y) @ H)))) => ((![X2 : msg, K : nat]: (~ ((member_msg @ (crypt @ K @ X2) @ H)))) => ((analz @ H) = H)))))). % analz_trivial
thf(fact_94_Crypt__notin__image__Key, axiom,
    ((![K3 : nat, X5 : msg, A : set_nat]: (~ ((member_msg @ (crypt @ K3 @ X5) @ (image_nat_msg @ key @ A))))))). % Crypt_notin_image_Key
thf(fact_95_analz__impI, axiom,
    ((![Y5 : msg, Evs : list_event, Q : $o]: (((~ ((member_msg @ Y5 @ (analz @ (knows @ spy @ Evs))))) => Q) => ((~ ((member_msg @ Y5 @ (analz @ (knows @ spy @ Evs))))) => Q))))). % analz_impI
thf(fact_96_analz__shrK__Decrypt, axiom,
    ((![A : agent, X5 : msg, H : set_msg]: ((member_msg @ (crypt @ (shrK @ A) @ X5) @ (analz @ H)) => ((member_msg @ (key @ (shrK @ A)) @ (analz @ H)) => (member_msg @ X5 @ (analz @ H))))))). % analz_shrK_Decrypt
thf(fact_97_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_98_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_99_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_100_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_101_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_102_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_103_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_104_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_105_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_106_imageI, axiom,
    ((![X : msg, A : set_msg, F : msg > list_event]: ((member_msg @ X @ A) => (member_list_event @ (F @ X) @ (image_msg_list_event @ F @ A)))))). % imageI
thf(fact_107_image__iff, axiom,
    ((![Z : msg, F : nat > msg, A : set_nat]: ((member_msg @ Z @ (image_nat_msg @ F @ A)) = (?[X6 : nat]: (((member_nat @ X6 @ A)) & ((Z = (F @ X6))))))))). % image_iff
thf(fact_108_image__iff, axiom,
    ((![Z : nat, F : agent > nat, A : set_agent]: ((member_nat @ Z @ (image_agent_nat @ F @ A)) = (?[X6 : agent]: (((member_agent @ X6 @ A)) & ((Z = (F @ X6))))))))). % image_iff
thf(fact_109_image__iff, axiom,
    ((![Z : nat, F : nat > nat, A : set_nat]: ((member_nat @ Z @ (image_nat_nat @ F @ A)) = (?[X6 : nat]: (((member_nat @ X6 @ A)) & ((Z = (F @ X6))))))))). % image_iff
thf(fact_110_bex__imageD, axiom,
    ((![F : agent > nat, A : set_agent, P : nat > $o]: ((?[X8 : nat]: ((member_nat @ X8 @ (image_agent_nat @ F @ A)) & (P @ X8))) => (?[X7 : agent]: ((member_agent @ X7 @ A) & (P @ (F @ X7)))))))). % bex_imageD
thf(fact_111_bex__imageD, axiom,
    ((![F : nat > msg, A : set_nat, P : msg > $o]: ((?[X8 : msg]: ((member_msg @ X8 @ (image_nat_msg @ F @ A)) & (P @ X8))) => (?[X7 : nat]: ((member_nat @ X7 @ A) & (P @ (F @ X7)))))))). % bex_imageD
thf(fact_112_bex__imageD, axiom,
    ((![F : nat > nat, A : set_nat, P : nat > $o]: ((?[X8 : nat]: ((member_nat @ X8 @ (image_nat_nat @ F @ A)) & (P @ X8))) => (?[X7 : nat]: ((member_nat @ X7 @ A) & (P @ (F @ X7)))))))). % bex_imageD
thf(fact_113_image__cong, axiom,
    ((![M : set_agent, N : set_agent, F : agent > nat, G : agent > nat]: ((M = N) => ((![X7 : agent]: ((member_agent @ X7 @ N) => ((F @ X7) = (G @ X7)))) => ((image_agent_nat @ F @ M) = (image_agent_nat @ G @ N))))))). % image_cong
thf(fact_114_image__cong, axiom,
    ((![M : set_nat, N : set_nat, F : nat > msg, G : nat > msg]: ((M = N) => ((![X7 : nat]: ((member_nat @ X7 @ N) => ((F @ X7) = (G @ X7)))) => ((image_nat_msg @ F @ M) = (image_nat_msg @ G @ N))))))). % image_cong
thf(fact_115_image__cong, axiom,
    ((![M : set_nat, N : set_nat, F : nat > nat, G : nat > nat]: ((M = N) => ((![X7 : nat]: ((member_nat @ X7 @ N) => ((F @ X7) = (G @ X7)))) => ((image_nat_nat @ F @ M) = (image_nat_nat @ G @ N))))))). % image_cong
thf(fact_116_ball__imageD, axiom,
    ((![F : agent > nat, A : set_agent, P : nat > $o]: ((![X7 : nat]: ((member_nat @ X7 @ (image_agent_nat @ F @ A)) => (P @ X7))) => (![X8 : agent]: ((member_agent @ X8 @ A) => (P @ (F @ X8)))))))). % ball_imageD
thf(fact_117_ball__imageD, axiom,
    ((![F : nat > msg, A : set_nat, P : msg > $o]: ((![X7 : msg]: ((member_msg @ X7 @ (image_nat_msg @ F @ A)) => (P @ X7))) => (![X8 : nat]: ((member_nat @ X8 @ A) => (P @ (F @ X8)))))))). % ball_imageD
thf(fact_118_ball__imageD, axiom,
    ((![F : nat > nat, A : set_nat, P : nat > $o]: ((![X7 : nat]: ((member_nat @ X7 @ (image_nat_nat @ F @ A)) => (P @ X7))) => (![X8 : nat]: ((member_nat @ X8 @ A) => (P @ (F @ X8)))))))). % ball_imageD
thf(fact_119_rev__image__eqI, axiom,
    ((![X : msg, A : set_msg, B : msg, F : msg > msg]: ((member_msg @ X @ A) => ((B = (F @ X)) => (member_msg @ B @ (image_msg_msg @ F @ A))))))). % rev_image_eqI
thf(fact_120_rev__image__eqI, axiom,
    ((![X : msg, A : set_msg, B : agent, F : msg > agent]: ((member_msg @ X @ A) => ((B = (F @ X)) => (member_agent @ B @ (image_msg_agent @ F @ A))))))). % rev_image_eqI
thf(fact_121_rev__image__eqI, axiom,
    ((![X : msg, A : set_msg, B : nat, F : msg > nat]: ((member_msg @ X @ A) => ((B = (F @ X)) => (member_nat @ B @ (image_msg_nat @ F @ A))))))). % rev_image_eqI
thf(fact_122_rev__image__eqI, axiom,
    ((![X : agent, A : set_agent, B : msg, F : agent > msg]: ((member_agent @ X @ A) => ((B = (F @ X)) => (member_msg @ B @ (image_agent_msg @ F @ A))))))). % rev_image_eqI
thf(fact_123_rev__image__eqI, axiom,
    ((![X : agent, A : set_agent, B : agent, F : agent > agent]: ((member_agent @ X @ A) => ((B = (F @ X)) => (member_agent @ B @ (image_agent_agent @ F @ A))))))). % rev_image_eqI
thf(fact_124_rev__image__eqI, axiom,
    ((![X : agent, A : set_agent, B : nat, F : agent > nat]: ((member_agent @ X @ A) => ((B = (F @ X)) => (member_nat @ B @ (image_agent_nat @ F @ A))))))). % rev_image_eqI
thf(fact_125_rev__image__eqI, axiom,
    ((![X : nat, A : set_nat, B : msg, F : nat > msg]: ((member_nat @ X @ A) => ((B = (F @ X)) => (member_msg @ B @ (image_nat_msg @ F @ A))))))). % rev_image_eqI
thf(fact_126_rev__image__eqI, axiom,
    ((![X : nat, A : set_nat, B : agent, F : nat > agent]: ((member_nat @ X @ A) => ((B = (F @ X)) => (member_agent @ B @ (image_nat_agent @ F @ A))))))). % rev_image_eqI
thf(fact_127_rev__image__eqI, axiom,
    ((![X : nat, A : set_nat, B : nat, F : nat > nat]: ((member_nat @ X @ A) => ((B = (F @ X)) => (member_nat @ B @ (image_nat_nat @ F @ A))))))). % rev_image_eqI
thf(fact_128_rev__image__eqI, axiom,
    ((![X : msg, A : set_msg, B : list_event, F : msg > list_event]: ((member_msg @ X @ A) => ((B = (F @ X)) => (member_list_event @ B @ (image_msg_list_event @ F @ A))))))). % rev_image_eqI
thf(fact_129_UNIV__eq__I, axiom,
    ((![A : set_msg]: ((![X7 : msg]: (member_msg @ X7 @ A)) => (top_top_set_msg = A))))). % UNIV_eq_I
thf(fact_130_UNIV__eq__I, axiom,
    ((![A : set_list_event]: ((![X7 : list_event]: (member_list_event @ X7 @ A)) => (top_to1178833912_event = A))))). % UNIV_eq_I
thf(fact_131_UNIV__eq__I, axiom,
    ((![A : set_nat]: ((![X7 : nat]: (member_nat @ X7 @ A)) => (top_top_set_nat = A))))). % UNIV_eq_I
thf(fact_132_UNIV__eq__I, axiom,
    ((![A : set_agent]: ((![X7 : agent]: (member_agent @ X7 @ A)) => (top_top_set_agent = A))))). % UNIV_eq_I
thf(fact_133_UNIV__witness, axiom,
    ((?[X7 : msg]: (member_msg @ X7 @ top_top_set_msg)))). % UNIV_witness
thf(fact_134_UNIV__witness, axiom,
    ((?[X7 : list_event]: (member_list_event @ X7 @ top_to1178833912_event)))). % UNIV_witness
thf(fact_135_UNIV__witness, axiom,
    ((?[X7 : nat]: (member_nat @ X7 @ top_top_set_nat)))). % UNIV_witness
thf(fact_136_UNIV__witness, axiom,
    ((?[X7 : agent]: (member_agent @ X7 @ top_top_set_agent)))). % UNIV_witness
thf(fact_137_Crypt__Spy__analz__bad, axiom,
    ((![A : agent, X5 : msg, Evs : list_event]: ((member_msg @ (crypt @ (shrK @ A) @ X5) @ (analz @ (knows @ spy @ Evs))) => ((member_agent @ A @ bad) => (member_msg @ X5 @ (analz @ (knows @ spy @ Evs)))))))). % Crypt_Spy_analz_bad
thf(fact_138_surjD, axiom,
    ((![F : nat > msg, Y3 : msg]: (((image_nat_msg @ F @ top_top_set_nat) = top_top_set_msg) => (?[X7 : nat]: (Y3 = (F @ X7))))))). % surjD
thf(fact_139_surjD, axiom,
    ((![F : nat > nat, Y3 : nat]: (((image_nat_nat @ F @ top_top_set_nat) = top_top_set_nat) => (?[X7 : nat]: (Y3 = (F @ X7))))))). % surjD
thf(fact_140_surjD, axiom,
    ((![F : agent > nat, Y3 : nat]: (((image_agent_nat @ F @ top_top_set_agent) = top_top_set_nat) => (?[X7 : agent]: (Y3 = (F @ X7))))))). % surjD
thf(fact_141_surjD, axiom,
    ((![F : agent > agent, Y3 : agent]: (((image_agent_agent @ F @ top_top_set_agent) = top_top_set_agent) => (?[X7 : agent]: (Y3 = (F @ X7))))))). % surjD
thf(fact_142_analz__spies__pubK, axiom,
    ((![B : keymode, A : agent, Evs : list_event]: (member_msg @ (key @ (publicKey @ B @ A)) @ (analz @ (knows @ spy @ Evs)))))). % analz_spies_pubK
thf(fact_143_Key__not__used, axiom,
    ((![K3 : nat, Evs : list_event]: ((~ ((member_msg @ (key @ K3) @ (used @ Evs)))) => (~ ((member_nat @ K3 @ (image_agent_nat @ shrK @ top_top_set_agent)))))))). % Key_not_used
thf(fact_144_analz__symKeys__Decrypt, axiom,
    ((![K3 : nat, X5 : msg, H : set_msg]: ((member_msg @ (crypt @ K3 @ X5) @ (analz @ H)) => ((member_nat @ K3 @ symKeys) => ((member_msg @ (key @ K3) @ (analz @ H)) => (member_msg @ X5 @ (analz @ H)))))))). % analz_symKeys_Decrypt
thf(fact_145_shrK__in__initState, axiom,
    ((![A : agent]: (member_msg @ (key @ (shrK @ A)) @ (initState @ A))))). % shrK_in_initState
thf(fact_146_spies__pubK, axiom,
    ((![B : keymode, A : agent, Evs : list_event]: (member_msg @ (key @ (publicKey @ B @ A)) @ (knows @ spy @ Evs))))). % spies_pubK
thf(fact_147_usedI, axiom,
    ((![C : msg, Evs : list_event]: ((member_msg @ C @ (parts @ (knows @ spy @ Evs))) => (member_msg @ C @ (used @ Evs)))))). % usedI
thf(fact_148_analz_Ocases, axiom,
    ((![A2 : msg, H : set_msg]: ((member_msg @ A2 @ (analz @ H)) => ((~ ((member_msg @ A2 @ H))) => ((![Y : msg]: (~ ((member_msg @ (mPair @ A2 @ Y) @ (analz @ H))))) => ((![X2 : msg]: (~ ((member_msg @ (mPair @ X2 @ A2) @ (analz @ H))))) => (~ ((![K : nat]: ((member_msg @ (crypt @ K @ A2) @ (analz @ H)) => (~ ((member_msg @ (key @ (invKey @ K)) @ (analz @ H))))))))))))))). % analz.cases
thf(fact_149_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_150_invKey__eq, axiom,
    ((![K3 : nat, K4 : nat]: (((invKey @ K3) = (invKey @ K4)) = (K3 = K4))))). % invKey_eq
thf(fact_151_invKey, axiom,
    ((![K3 : nat]: ((invKey @ (invKey @ K3)) = K3)))). % invKey
thf(fact_152_publicKey__inject, axiom,
    ((![B : keymode, A : agent, C : keymode, A3 : agent]: (((publicKey @ B @ A) = (publicKey @ C @ A3)) = (((B = C)) & ((A = A3))))))). % publicKey_inject
thf(fact_153_invKey__shrK, axiom,
    ((![A : agent]: ((invKey @ (shrK @ A)) = (shrK @ A))))). % invKey_shrK
thf(fact_154_symKeys__invKey__iff, axiom,
    ((![K3 : nat]: ((member_nat @ (invKey @ K3) @ symKeys) = (member_nat @ K3 @ symKeys))))). % symKeys_invKey_iff
thf(fact_155_invKey__K, axiom,
    ((![K3 : nat]: ((member_nat @ K3 @ symKeys) => ((invKey @ K3) = K3))))). % invKey_K
thf(fact_156_publicKey__image__eq, axiom,
    ((![B : keymode, X : agent, C : keymode, AA : set_agent]: ((member_nat @ (publicKey @ B @ X) @ (image_agent_nat @ (publicKey @ C) @ AA)) = (((B = C)) & ((member_agent @ X @ AA))))))). % publicKey_image_eq
thf(fact_157_sym__shrK, axiom,
    ((![X5 : agent]: (member_nat @ (shrK @ X5) @ symKeys)))). % sym_shrK
thf(fact_158_shrK__in__used, axiom,
    ((![A : agent, Evs : list_event]: (member_msg @ (key @ (shrK @ A)) @ (used @ Evs))))). % shrK_in_used
thf(fact_159_publicKey__into__used, axiom,
    ((![B : keymode, A : agent, Evs : list_event]: (member_msg @ (key @ (publicKey @ B @ A)) @ (used @ Evs))))). % publicKey_into_used
thf(fact_160_publicKey__in__initState, axiom,
    ((![B : keymode, A : agent, B2 : agent]: (member_msg @ (key @ (publicKey @ B @ A)) @ (initState @ B2))))). % publicKey_in_initState
thf(fact_161_privateKey__image__eq, axiom,
    ((![B : keymode, A : agent, C : keymode, AS : set_agent]: ((member_nat @ (invKey @ (publicKey @ B @ A)) @ (image_nat_nat @ invKey @ (image_agent_nat @ (publicKey @ C) @ AS))) = (((B = C)) & ((member_agent @ A @ AS))))))). % privateKey_image_eq
thf(fact_162_privateKey__into__used, axiom,
    ((![B : keymode, A : agent, Evs : list_event]: (member_msg @ (key @ (invKey @ (publicKey @ B @ A))) @ (used @ Evs))))). % privateKey_into_used
thf(fact_163_priK__in__initState, axiom,
    ((![B : keymode, A : agent]: (member_msg @ (key @ (invKey @ (publicKey @ B @ A))) @ (initState @ A))))). % priK_in_initState
thf(fact_164_Spy__spies__bad__privateKey, axiom,
    ((![A : agent, B : keymode, Evs : list_event]: ((member_agent @ A @ bad) => (member_msg @ (key @ (invKey @ (publicKey @ B @ A))) @ (knows @ spy @ Evs)))))). % Spy_spies_bad_privateKey
thf(fact_165_publicKey__notin__image__privateKey, axiom,
    ((![B : keymode, A : agent, C : keymode, AS : set_agent]: (~ ((member_nat @ (publicKey @ B @ A) @ (image_nat_nat @ invKey @ (image_agent_nat @ (publicKey @ C) @ AS)))))))). % publicKey_notin_image_privateKey
thf(fact_166_shrK__neq__priK, axiom,
    ((![B : keymode, C2 : agent, A : agent]: (~ (((invKey @ (publicKey @ B @ C2)) = (shrK @ A))))))). % shrK_neq_priK
thf(fact_167_privateKey__notin__image__publicKey, axiom,
    ((![B : keymode, X : agent, C : keymode, AA : set_agent]: (~ ((member_nat @ (invKey @ (publicKey @ B @ X)) @ (image_agent_nat @ (publicKey @ C) @ AA))))))). % privateKey_notin_image_publicKey
thf(fact_168_initState__into__used, axiom,
    ((![X5 : msg, B2 : agent, Evs : list_event]: ((member_msg @ X5 @ (parts @ (initState @ B2))) => (member_msg @ X5 @ (used @ Evs)))))). % initState_into_used
thf(fact_169_publicKey__neq__privateKey, axiom,
    ((![C : keymode, A3 : agent, B : keymode, A : agent]: (~ (((publicKey @ C @ A3) = (invKey @ (publicKey @ B @ A)))))))). % publicKey_neq_privateKey
thf(fact_170_symKeys__neq__imp__neq, axiom,
    ((![K3 : nat, K4 : nat]: ((~ (((member_nat @ K3 @ symKeys) = (member_nat @ K4 @ symKeys)))) => (~ ((K3 = K4))))))). % symKeys_neq_imp_neq
thf(fact_171_injective__publicKey, axiom,
    ((![B : keymode, A : agent, C : keymode, A3 : agent]: (((publicKey @ B @ A) = (publicKey @ C @ A3)) => ((B = C) & (A = A3)))))). % injective_publicKey
thf(fact_172_not__symKeys__pubK, axiom,
    ((![B : keymode, A : agent]: (~ ((member_nat @ (publicKey @ B @ A) @ symKeys)))))). % not_symKeys_pubK
thf(fact_173_not__symKeys__priK, axiom,
    ((![B : keymode, A : agent]: (~ ((member_nat @ (invKey @ (publicKey @ B @ A)) @ symKeys)))))). % not_symKeys_priK
thf(fact_174_privateKey__notin__image__shrK, axiom,
    ((![B : keymode, X : agent, AA : set_agent]: (~ ((member_nat @ (invKey @ (publicKey @ B @ X)) @ (image_agent_nat @ shrK @ AA))))))). % privateKey_notin_image_shrK
thf(fact_175_shrK__notin__image__privateKey, axiom,
    ((![X : agent, B : keymode, AA : set_agent]: (~ ((member_nat @ (shrK @ X) @ (image_nat_nat @ invKey @ (image_agent_nat @ (publicKey @ B) @ AA)))))))). % shrK_notin_image_privateKey
thf(fact_176_MPair__used__D, axiom,
    ((![X5 : msg, Y5 : msg, H : list_event]: ((member_msg @ (mPair @ X5 @ Y5) @ (used @ H)) => ((member_msg @ X5 @ (used @ H)) & (member_msg @ Y5 @ (used @ H))))))). % MPair_used_D
thf(fact_177_MPair__used, axiom,
    ((![X5 : msg, Y5 : msg, H : list_event]: ((member_msg @ (mPair @ X5 @ Y5) @ (used @ H)) => (~ (((member_msg @ X5 @ (used @ H)) => (~ ((member_msg @ Y5 @ (used @ H))))))))))). % MPair_used
thf(fact_178_shrK__neq__pubK, axiom,
    ((![B : keymode, C2 : agent, A : agent]: (~ (((publicKey @ B @ C2) = (shrK @ A))))))). % shrK_neq_pubK
thf(fact_179_shrK__neq, axiom,
    ((![K3 : nat, Evs : list_event, B2 : agent]: ((~ ((member_msg @ (key @ K3) @ (used @ Evs)))) => (~ (((shrK @ B2) = K3))))))). % shrK_neq
thf(fact_180_neq__shrK, axiom,
    ((![S : nat, Evs : list_event, B2 : agent]: ((~ ((member_msg @ (key @ S) @ (used @ Evs)))) => (~ ((S = (shrK @ B2)))))))). % neq_shrK
thf(fact_181_shrK__notin__image__publicKey, axiom,
    ((![X : agent, B : keymode, AA : set_agent]: (~ ((member_nat @ (shrK @ X) @ (image_agent_nat @ (publicKey @ B) @ AA))))))). % shrK_notin_image_publicKey
thf(fact_182_publicKey__notin__image__shrK, axiom,
    ((![B : keymode, X : agent, AA : set_agent]: (~ ((member_nat @ (publicKey @ B @ X) @ (image_agent_nat @ shrK @ AA))))))). % publicKey_notin_image_shrK
thf(fact_183_analz_ODecrypt, axiom,
    ((![K3 : nat, X5 : msg, H : set_msg]: ((member_msg @ (crypt @ K3 @ X5) @ (analz @ H)) => ((member_msg @ (key @ (invKey @ K3)) @ (analz @ H)) => (member_msg @ X5 @ (analz @ H))))))). % analz.Decrypt
thf(fact_184_Crypt__notin__initState, axiom,
    ((![K3 : nat, X5 : msg, B2 : agent]: (~ ((member_msg @ (crypt @ K3 @ X5) @ (parts @ (initState @ B2)))))))). % Crypt_notin_initState
thf(fact_185_analz_Oinducts, axiom,
    ((![X : msg, H : set_msg, P : msg > $o]: ((member_msg @ X @ (analz @ H)) => ((![X2 : msg]: ((member_msg @ X2 @ H) => (P @ X2))) => ((![X2 : msg, Y : msg]: ((member_msg @ (mPair @ X2 @ Y) @ (analz @ H)) => ((P @ (mPair @ X2 @ Y)) => (P @ X2)))) => ((![X2 : msg, Y : msg]: ((member_msg @ (mPair @ X2 @ Y) @ (analz @ H)) => ((P @ (mPair @ X2 @ Y)) => (P @ Y)))) => ((![K : nat, X2 : msg]: ((member_msg @ (crypt @ K @ X2) @ (analz @ H)) => ((P @ (crypt @ K @ X2)) => ((member_msg @ (key @ (invKey @ K)) @ (analz @ H)) => ((P @ (key @ (invKey @ K))) => (P @ X2)))))) => (P @ X))))))))). % analz.inducts
thf(fact_186_analz_Osimps, axiom,
    ((![A2 : msg, H : set_msg]: ((member_msg @ A2 @ (analz @ H)) = (((?[X3 : msg]: (((A2 = X3)) & ((member_msg @ X3 @ H))))) | ((((?[X3 : msg]: (?[Y2 : msg]: (((A2 = X3)) & ((member_msg @ (mPair @ X3 @ Y2) @ (analz @ H))))))) | ((((?[X3 : msg]: (?[Y2 : msg]: (((A2 = Y2)) & ((member_msg @ (mPair @ X3 @ Y2) @ (analz @ H))))))) | ((?[K2 : nat]: (?[X3 : msg]: (((A2 = X3)) & ((((member_msg @ (crypt @ K2 @ X3) @ (analz @ H))) & ((member_msg @ (key @ (invKey @ K2)) @ (analz @ H)))))))))))))))))). % analz.simps
thf(fact_187_new__keys__not__used, axiom,
    ((![K3 : nat, Evs : list_event]: ((~ ((member_msg @ (key @ K3) @ (used @ Evs)))) => ((member_nat @ K3 @ symKeys) => ((member_list_event @ Evs @ nS_Sha1061662329shared) => (~ ((member_nat @ K3 @ (keysFor @ (parts @ (knows @ spy @ Evs)))))))))))). % new_keys_not_used
thf(fact_188_top__empty__eq, axiom,
    ((top_top_msg_o = (^[X6 : msg]: (member_msg @ X6 @ top_top_set_msg))))). % top_empty_eq
thf(fact_189_top__empty__eq, axiom,
    ((top_top_list_event_o = (^[X6 : list_event]: (member_list_event @ X6 @ top_to1178833912_event))))). % top_empty_eq
thf(fact_190_top__empty__eq, axiom,
    ((top_top_nat_o = (^[X6 : nat]: (member_nat @ X6 @ top_top_set_nat))))). % top_empty_eq
thf(fact_191_top__empty__eq, axiom,
    ((top_top_agent_o = (^[X6 : agent]: (member_agent @ X6 @ top_top_set_agent))))). % top_empty_eq
thf(fact_192_symKey__neq__priEK, axiom,
    ((![K3 : nat, A : agent]: ((member_nat @ K3 @ symKeys) => (~ ((K3 = (invKey @ (publicKey @ encryption @ A))))))))). % symKey_neq_priEK
thf(fact_193_priEK__noteq__shrK, axiom,
    ((![A : agent, B2 : agent]: (~ (((invKey @ (publicKey @ encryption @ A)) = (shrK @ B2))))))). % priEK_noteq_shrK
thf(fact_194_Crypt__imp__invKey__keysFor, axiom,
    ((![K3 : nat, X5 : msg, H : set_msg]: ((member_msg @ (crypt @ K3 @ X5) @ H) => (member_nat @ (invKey @ K3) @ (keysFor @ H)))))). % Crypt_imp_invKey_keysFor
thf(fact_195_Crypt__imp__keysFor, axiom,
    ((![K3 : nat, X5 : msg, H : set_msg]: ((member_msg @ (crypt @ K3 @ X5) @ H) => ((member_nat @ K3 @ symKeys) => (member_nat @ K3 @ (keysFor @ H))))))). % Crypt_imp_keysFor
thf(fact_196_initState__Spy, axiom,
    (((initState @ spy) = (sup_sup_set_msg @ (sup_sup_set_msg @ (sup_sup_set_msg @ (sup_sup_set_msg @ (image_nat_msg @ key @ (image_nat_nat @ invKey @ (image_agent_nat @ (publicKey @ encryption) @ bad))) @ (image_nat_msg @ key @ (image_nat_nat @ invKey @ (image_agent_nat @ (publicKey @ signature) @ bad)))) @ (image_nat_msg @ key @ (image_agent_nat @ shrK @ bad))) @ (image_nat_msg @ key @ (image_agent_nat @ (publicKey @ encryption) @ top_top_set_agent))) @ (image_nat_msg @ key @ (image_agent_nat @ (publicKey @ signature) @ top_top_set_agent)))))). % initState_Spy
thf(fact_197_analzp_Ocases, axiom,
    ((![H : msg > $o, A2 : msg]: ((analzp @ H @ A2) => ((~ ((H @ A2))) => ((![Y : msg]: (~ ((analzp @ H @ (mPair @ A2 @ Y))))) => ((![X2 : msg]: (~ ((analzp @ H @ (mPair @ X2 @ A2))))) => (~ ((![K : nat]: ((analzp @ H @ (crypt @ K @ A2)) => (~ ((analzp @ H @ (key @ (invKey @ K)))))))))))))))). % analzp.cases
thf(fact_198_Un__iff, axiom,
    ((![C : agent, A : set_agent, B2 : set_agent]: ((member_agent @ C @ (sup_sup_set_agent @ A @ B2)) = (((member_agent @ C @ A)) | ((member_agent @ C @ B2))))))). % Un_iff
thf(fact_199_Un__iff, axiom,
    ((![C : list_event, A : set_list_event, B2 : set_list_event]: ((member_list_event @ C @ (sup_su1529884788_event @ A @ B2)) = (((member_list_event @ C @ A)) | ((member_list_event @ C @ B2))))))). % Un_iff
thf(fact_200_Un__iff, axiom,
    ((![C : nat, A : set_nat, B2 : set_nat]: ((member_nat @ C @ (sup_sup_set_nat @ A @ B2)) = (((member_nat @ C @ A)) | ((member_nat @ C @ B2))))))). % Un_iff
thf(fact_201_Un__iff, axiom,
    ((![C : msg, A : set_msg, B2 : set_msg]: ((member_msg @ C @ (sup_sup_set_msg @ A @ B2)) = (((member_msg @ C @ A)) | ((member_msg @ C @ B2))))))). % Un_iff
thf(fact_202_UnCI, axiom,
    ((![C : agent, B2 : set_agent, A : set_agent]: (((~ ((member_agent @ C @ B2))) => (member_agent @ C @ A)) => (member_agent @ C @ (sup_sup_set_agent @ A @ B2)))))). % UnCI
thf(fact_203_UnCI, axiom,
    ((![C : list_event, B2 : set_list_event, A : set_list_event]: (((~ ((member_list_event @ C @ B2))) => (member_list_event @ C @ A)) => (member_list_event @ C @ (sup_su1529884788_event @ A @ B2)))))). % UnCI
thf(fact_204_UnCI, axiom,
    ((![C : nat, B2 : set_nat, A : set_nat]: (((~ ((member_nat @ C @ B2))) => (member_nat @ C @ A)) => (member_nat @ C @ (sup_sup_set_nat @ A @ B2)))))). % UnCI
thf(fact_205_UnCI, axiom,
    ((![C : msg, B2 : set_msg, A : set_msg]: (((~ ((member_msg @ C @ B2))) => (member_msg @ C @ A)) => (member_msg @ C @ (sup_sup_set_msg @ A @ B2)))))). % UnCI
thf(fact_206_analz__analz__Un, axiom,
    ((![G2 : set_msg, H : set_msg]: ((analz @ (sup_sup_set_msg @ (analz @ G2) @ H)) = (analz @ (sup_sup_set_msg @ G2 @ H)))))). % analz_analz_Un
thf(fact_207_parts__Un, axiom,
    ((![G2 : set_msg, H : set_msg]: ((parts @ (sup_sup_set_msg @ G2 @ H)) = (sup_sup_set_msg @ (parts @ G2) @ (parts @ H)))))). % parts_Un
thf(fact_208_image__Un, axiom,
    ((![F : agent > nat, A : set_agent, B2 : set_agent]: ((image_agent_nat @ F @ (sup_sup_set_agent @ A @ B2)) = (sup_sup_set_nat @ (image_agent_nat @ F @ A) @ (image_agent_nat @ F @ B2)))))). % image_Un
thf(fact_209_image__Un, axiom,
    ((![F : nat > nat, A : set_nat, B2 : set_nat]: ((image_nat_nat @ F @ (sup_sup_set_nat @ A @ B2)) = (sup_sup_set_nat @ (image_nat_nat @ F @ A) @ (image_nat_nat @ F @ B2)))))). % image_Un
thf(fact_210_image__Un, axiom,
    ((![F : nat > msg, A : set_nat, B2 : set_nat]: ((image_nat_msg @ F @ (sup_sup_set_nat @ A @ B2)) = (sup_sup_set_msg @ (image_nat_msg @ F @ A) @ (image_nat_msg @ F @ B2)))))). % image_Un
thf(fact_211_image__Un, axiom,
    ((![F : msg > msg, A : set_msg, B2 : set_msg]: ((image_msg_msg @ F @ (sup_sup_set_msg @ A @ B2)) = (sup_sup_set_msg @ (image_msg_msg @ F @ A) @ (image_msg_msg @ F @ B2)))))). % image_Un
thf(fact_212_analzp_OFst, axiom,
    ((![H : msg > $o, X5 : msg, Y5 : msg]: ((analzp @ H @ (mPair @ X5 @ Y5)) => (analzp @ H @ X5))))). % analzp.Fst
thf(fact_213_analzp_OSnd, axiom,
    ((![H : msg > $o, X5 : msg, Y5 : msg]: ((analzp @ H @ (mPair @ X5 @ Y5)) => (analzp @ H @ Y5))))). % analzp.Snd
thf(fact_214_Un__left__commute, axiom,
    ((![A : set_msg, B2 : set_msg, C2 : set_msg]: ((sup_sup_set_msg @ A @ (sup_sup_set_msg @ B2 @ C2)) = (sup_sup_set_msg @ B2 @ (sup_sup_set_msg @ A @ C2)))))). % Un_left_commute
thf(fact_215_Un__left__absorb, axiom,
    ((![A : set_msg, B2 : set_msg]: ((sup_sup_set_msg @ A @ (sup_sup_set_msg @ A @ B2)) = (sup_sup_set_msg @ A @ B2))))). % Un_left_absorb
thf(fact_216_Un__commute, axiom,
    ((sup_sup_set_msg = (^[A4 : set_msg]: (^[B3 : set_msg]: (sup_sup_set_msg @ B3 @ A4)))))). % Un_commute
thf(fact_217_Un__absorb, axiom,
    ((![A : set_msg]: ((sup_sup_set_msg @ A @ A) = A)))). % Un_absorb
thf(fact_218_Un__assoc, axiom,
    ((![A : set_msg, B2 : set_msg, C2 : set_msg]: ((sup_sup_set_msg @ (sup_sup_set_msg @ A @ B2) @ C2) = (sup_sup_set_msg @ A @ (sup_sup_set_msg @ B2 @ C2)))))). % Un_assoc
thf(fact_219_ball__Un, axiom,
    ((![A : set_msg, B2 : set_msg, P : msg > $o]: ((![X6 : msg]: (((member_msg @ X6 @ (sup_sup_set_msg @ A @ B2))) => ((P @ X6)))) = (((![X6 : msg]: (((member_msg @ X6 @ A)) => ((P @ X6))))) & ((![X6 : msg]: (((member_msg @ X6 @ B2)) => ((P @ X6)))))))))). % ball_Un
thf(fact_220_bex__Un, axiom,
    ((![A : set_msg, B2 : set_msg, P : msg > $o]: ((?[X6 : msg]: (((member_msg @ X6 @ (sup_sup_set_msg @ A @ B2))) & ((P @ X6)))) = (((?[X6 : msg]: (((member_msg @ X6 @ A)) & ((P @ X6))))) | ((?[X6 : msg]: (((member_msg @ X6 @ B2)) & ((P @ X6)))))))))). % bex_Un
thf(fact_221_UnI2, axiom,
    ((![C : agent, B2 : set_agent, A : set_agent]: ((member_agent @ C @ B2) => (member_agent @ C @ (sup_sup_set_agent @ A @ B2)))))). % UnI2
thf(fact_222_UnI2, axiom,
    ((![C : list_event, B2 : set_list_event, A : set_list_event]: ((member_list_event @ C @ B2) => (member_list_event @ C @ (sup_su1529884788_event @ A @ B2)))))). % UnI2
thf(fact_223_UnI2, axiom,
    ((![C : nat, B2 : set_nat, A : set_nat]: ((member_nat @ C @ B2) => (member_nat @ C @ (sup_sup_set_nat @ A @ B2)))))). % UnI2
thf(fact_224_UnI2, axiom,
    ((![C : msg, B2 : set_msg, A : set_msg]: ((member_msg @ C @ B2) => (member_msg @ C @ (sup_sup_set_msg @ A @ B2)))))). % UnI2
thf(fact_225_UnI1, axiom,
    ((![C : agent, A : set_agent, B2 : set_agent]: ((member_agent @ C @ A) => (member_agent @ C @ (sup_sup_set_agent @ A @ B2)))))). % UnI1
thf(fact_226_UnI1, axiom,
    ((![C : list_event, A : set_list_event, B2 : set_list_event]: ((member_list_event @ C @ A) => (member_list_event @ C @ (sup_su1529884788_event @ A @ B2)))))). % UnI1
thf(fact_227_UnI1, axiom,
    ((![C : nat, A : set_nat, B2 : set_nat]: ((member_nat @ C @ A) => (member_nat @ C @ (sup_sup_set_nat @ A @ B2)))))). % UnI1
thf(fact_228_UnI1, axiom,
    ((![C : msg, A : set_msg, B2 : set_msg]: ((member_msg @ C @ A) => (member_msg @ C @ (sup_sup_set_msg @ A @ B2)))))). % UnI1
thf(fact_229_UnE, axiom,
    ((![C : agent, A : set_agent, B2 : set_agent]: ((member_agent @ C @ (sup_sup_set_agent @ A @ B2)) => ((~ ((member_agent @ C @ A))) => (member_agent @ C @ B2)))))). % UnE
thf(fact_230_UnE, axiom,
    ((![C : list_event, A : set_list_event, B2 : set_list_event]: ((member_list_event @ C @ (sup_su1529884788_event @ A @ B2)) => ((~ ((member_list_event @ C @ A))) => (member_list_event @ C @ B2)))))). % UnE
thf(fact_231_UnE, axiom,
    ((![C : nat, A : set_nat, B2 : set_nat]: ((member_nat @ C @ (sup_sup_set_nat @ A @ B2)) => ((~ ((member_nat @ C @ A))) => (member_nat @ C @ B2)))))). % UnE
thf(fact_232_UnE, axiom,
    ((![C : msg, A : set_msg, B2 : set_msg]: ((member_msg @ C @ (sup_sup_set_msg @ A @ B2)) => ((~ ((member_msg @ C @ A))) => (member_msg @ C @ B2)))))). % UnE
thf(fact_233_analzp_OInj, axiom,
    ((![H : msg > $o, X5 : msg]: ((H @ X5) => (analzp @ H @ X5))))). % analzp.Inj
thf(fact_234_in__parts__UnE, axiom,
    ((![C : msg, G2 : set_msg, H : set_msg]: ((member_msg @ C @ (parts @ (sup_sup_set_msg @ G2 @ H))) => ((~ ((member_msg @ C @ (parts @ G2)))) => (member_msg @ C @ (parts @ H))))))). % in_parts_UnE
thf(fact_235_analz__image__freshK__simps_I63_J, axiom,
    ((![C : msg, G2 : set_msg, A : set_msg]: ((member_msg @ C @ (analz @ G2)) => (member_msg @ C @ (analz @ (sup_sup_set_msg @ A @ G2))))))). % analz_image_freshK_simps(63)
thf(fact_236_analz__cong, axiom,
    ((![G2 : set_msg, G3 : set_msg, H : set_msg, H2 : set_msg]: (((analz @ G2) = (analz @ G3)) => (((analz @ H) = (analz @ H2)) => ((analz @ (sup_sup_set_msg @ G2 @ H)) = (analz @ (sup_sup_set_msg @ G3 @ H2)))))))). % analz_cong
thf(fact_237_Un__UNIV__left, axiom,
    ((![B2 : set_msg]: ((sup_sup_set_msg @ top_top_set_msg @ B2) = top_top_set_msg)))). % Un_UNIV_left
thf(fact_238_Un__UNIV__left, axiom,
    ((![B2 : set_agent]: ((sup_sup_set_agent @ top_top_set_agent @ B2) = top_top_set_agent)))). % Un_UNIV_left
thf(fact_239_Un__UNIV__right, axiom,
    ((![A : set_msg]: ((sup_sup_set_msg @ A @ top_top_set_msg) = top_top_set_msg)))). % Un_UNIV_right
thf(fact_240_Un__UNIV__right, axiom,
    ((![A : set_agent]: ((sup_sup_set_agent @ A @ top_top_set_agent) = top_top_set_agent)))). % Un_UNIV_right
thf(fact_241_keymode_Oexhaust, axiom,
    ((![Y3 : keymode]: ((~ ((Y3 = signature))) => (Y3 = encryption))))). % keymode.exhaust
thf(fact_242_not__SignatureE, axiom,
    ((![B : keymode]: ((~ ((B = signature))) => (B = encryption))))). % not_SignatureE
thf(fact_243_keymode_Oinduct, axiom,
    ((![P : keymode > $o, Keymode : keymode]: ((P @ signature) => ((P @ encryption) => (P @ Keymode)))))). % keymode.induct

% Conjectures (4)
thf(conj_0, hypothesis,
    ((member_msg @ (crypt @ (shrK @ a) @ (mPair @ na @ (mPair @ (agent2 @ b) @ (mPair @ (key @ k) @ x)))) @ (parts @ (knows @ spy @ evs))))).
thf(conj_1, hypothesis,
    ((~ ((member_agent @ a @ bad))))).
thf(conj_2, hypothesis,
    ((member_list_event @ evs @ nS_Sha1061662329shared))).
thf(conj_3, conjecture,
    (((~ ((member_nat @ k @ (image_agent_nat @ shrK @ top_top_set_agent)))) & (x = (crypt @ (shrK @ b) @ (mPair @ (key @ k) @ (agent2 @ a))))))).
